Category: Experiment

Abstract

The objective of this experiment was to determine the concentrations of unknown samples using UV/VIS Spectroscopy. As such, two experimental setups were performed using 0.04 M. potassium dichromate. The first was to determine the unknown concentrations of samples A and B using linear dilution while the other employed the serial decimal dilution method.

From the results, it was established that the concentrations for samples A, B, 2A and 2B were approximately equal to 0.018M and 0.0026 M, 0.002M and 0.012M respectively. Also, the results trends of the graphs were consistent with Beer’s law.

The concentration rates are approximations thanks to the systemic and random errors experienced e.g., stray radiations which may be minimized but not eliminated completely

Introduction

Many molecules are sensitive to UV light such that they absorb this light at a specific wavelength different from another element. The degree of absorbance is proportional to the intensity of the beam (Skoog, West & Holler, 1992).UV-VIS Absorption Spectroscopy is an analytical technique that derives its operation principles from Beer’s law which states that: “Absorbance is directly proportional to the path length, b, and the concentration, c, of the absorbing species” (Sigurds, 1986). This can be represented mathematically as A= εbc, where ε represents the constant of proportionality, known as absorbtivity. With this principle of operation, and absorbed spectrum portrays a band pattern corresponding to the constituent structural groups making up the molecule (Skoog et al., 2004).

Objective

The aim of performing this experiment was to determine the concentrations of unknown samples using UV/VIS Spectroscopy.

Procedure

In this experiment, two setups were arranged. While the first one was to achieve the objective courtesy of linear dilution, the latter employed the use of serial dilution. As such, for the first one, 0.04M potassium dichromate solution was diluted linearly to obtain data of concentrations and its corresponding absorbencies using a UV/VIS spectrometer. A graph of absorbance versus concentrations was plotted to generate a standard curve vital in determining unknown samples A and B. For the other setup though using the same concentration of potassium dichromate, a serial dilution was done to develop a standard curve vital in the determination of samples 2A and 2B.

Results

With regards to the experiment, the data below were obtained.

Table 1: Showing linear dilution.

Table 2: of experiment’s serial dilution.

Discussion and Analysis

As exhibited by graph 1 above, for samples illuminated at an absorbance of 350 nm, the concentrations for samples A and B are approximately equal to 0.018M and 0.0026 M respectively. On the other hand, for the samples illuminated by absorbance of 500 nm, as portrayed by graph 2, the concentrations for samples 2A and 2B are approximately equal to 0.002M and 0.012M respectively.

To achieve consistent results for this experiment the solution should have been maintained at a concentration not exceeding 0.01M. Otherwise, there would be a deviation from Beer’s law thanks to the interaction between neighbouring molecules (Hawthorne & Thorngate, 1979). This error, a random type, can be eliminated by maintaining the prescribed concentration below 0.01M (Szalay, 2008). Moreover, a systemic error such as stray radiations can lead to uncertainty concerning Beer’s law thanks to instrumental artifacts. However, this can be decimalized by the use of absorbance of a range between 0.3 and 1 since they are less vulnerable to stray light noise problems notwithstanding (Steiner, Termonia, & Deltour, 1972).

HPLC is one area where UV/VIS Spectrophotometric-standard curve technique is applicable. As such, a UV/VIS spectrophotometer acts as a detector responsible for the peaks, which corresponds to concentrations of the analyte. Just like calibration curves, there ought to be a standard sample for reference (Vandenbelt & Henrich, 1953).

The calculation that follows reveals the amount in grams of K2CrO7 that would be required to prepare a 0.2M standard solution in a 100ml standard flask. Then the number of moles of K₂CrO₇ required is given as below:

From equation, mole=Molarity*Volume;

mole= 0.2*100 =0.002 moles

Therefore, mass of K₂CrO₇ required =0.002*Formula mass=0.002*242.2 =0.4844 grams.

The calculation that follows will reveal the amount in volume of 0.05M working standard solution of dichromate required to obtain a final concentration of 0.005M in a 5ml volume test tube. We need to obtain 5 ml of 0.005M sample from 0.05M. Therefore, a volume of 5*0.005/0.05 ml which is equivalent to 0.5ml of the dichromate is required to prepare the sample.

Serial dilution is a consecutive dilution of a solute in a solution. As such, the concentration assumes a geometric progression sequence with a constant dilution factor just like in table 2 above (Szalay, 2008). This method is useful in creating exceedingly high diluted solutions as well as decreasing the concentration of minute organisms or unicellular cells present in a sample.

Conclusion

In synopsis, it can be concluded that the objective of the experiment was met since it was possible to determine the concentrations of samples A, B, 2A and 2B as 0.018M and 0.0026 M, 0.002M and 0.012M respectively. Also, the results trends of the graphs were consistent with Beer’s law.

References

Albert, A., & Serjeant, E.P. (1971). The Determination of Ionization Constants: A Laboratory Manual. Kansas City: Chapman & Hall.

Atkins, P.W., & Jones, L. (2008). Chemical Principles: The Quest for Insight (4th Ed.). Vatican CityState: W.H. Freeman.

Department of Chemistry. (2008). Redox Reactions. Web.

Hawthorne, A., & Thorngate, J. (1979). Application of Spectroscopy. Birmingham City, UK: University of Alabama.

Hulanicki, A. (1987). Reactions of acids and bases in analytical chemistry. New York City: McGraw-Hill Companies Inc.

Kenkel, J. (1994). Analytical Chemistry for Technicians. Boca Raton, US: Lewis Publishers.

Perrin, D.D., Dempsey, B., & Serjeant, E.P. (1981). pKa Prediction for Organic Acids and Bases. Kansas City: Chapman & Hall.

Reichardt, C. (2003). Solvents and Solvent Effects in Organic Chemistry: Solvent Effects on the Position of Homogeneous Chemical Equilibria. New York City: John Wiley & Sons, Inc.

Scorpio, R. (2000). Fundamentals of Acids, Bases, Buffers & Their Application to Biochemical Systems. Birmingham City, UK: University of Alabama.

Sigurds, S. (1986). Applications Of UV-Visible Number UV-31 Derivative Spectrophotometry. Steinhauserstrasse, Switzerland: Peter Lang Publishing Group.

Skoog, D., West, D., & Holler, F. (1992). Fudamentals of Analytical Chemistry. Fort Worth, US: Saunders College Publishing.

Skoog, D.A.; West, D.M.; Holler, J.F.; Crouch, S.R. (2004). Fundamentals of Analytical Chemistry (8th ed.). Salt Lake City: Thomson Brooks/Cole Publishers.

Steiner, J., Termonia, Y., & Deltour, J. (1972); Analitical Chemistry. Geneva: ILO Publications.

Szalay, L. (2008). Atomic Absorption Spectrophotometry (AAS). Budapest, Hungary: Petrik Lajos Publications.

Vandenbelt, J., & Henrich, C. (1953). Application Spectroscopy. Geneva: ILO Publications.

Introduction

The experiment aims at establishing KHT molar solubility in MgSO₄, Glucose, HCL, and H₂0. The test will also ascertain existing variations in the effects as related to other ions. Equilibrium expression is a vital instrument that can be used to illustrate the solubility of a variety of electrolytes. This experiment will attempt to establish the exact solubility of Potassium Bitartrate, which is connoted by [K⁺] [HT^–] dissolution as presented in equation 1 below.

Equation 1; KHT (s) ⇄K⁺(aq) + HT^– (aq)

As summarized in equation 1, equilibrium expectorate is the reciprocal of products over reactants with the exclusion of solids and liquids as a constant value (K). As discussed in the Le Chatelier’s Principle, the liquids and solids, connoted by K, are not considered. Based on this principle, the final equation for equilibrium expression for Potassium Bitartrate in this experiment is KHT = [K⁺] [HT^–]. The KHT is excluded for the reason that it is solid in the physical state. Therefore, if the results of the experiment established that the constant K is greater than 1 (K>1), it is an indication that the mixture is made up mostly of solubility products. On the other hand, if the constant K is less than 1 (K<1), it will indicate that the mixture is made up mostly of reactants. The experiment will also involve the calculation of the solubility product constants denoted by Ksp of KHT. Ksp is the product of dissolved ions saturation as a fraction of their coefficients. Thus, the calculated molarity of NaOH is used to compute the molar solubility of KHT, which is the quantity of KHT moles that are liquefied in every liter before saturation level.

As illustrated in Le Chatlier’s Principle, the addition of reactants results in a reaction that favors the product side. On the other hand, the addition of products would lead to a reaction that favors the reactant’s side. In contrast, a subtraction on either side, that is, products and reactants would give a different result. This is summarized in equation 2 below.

Equation 2; KHT (s) ⇄ K⁺(aq) + HT^– (aq)

From the above equation, it is apparent that any addition of KHT would not result in changes in the product’s side because of its physical solid nature. It is also insoluble at the point of solution saturation.

In the course of the experiment, titration will be used to determine the unknown solution concentration (acid) from a known solution (base). The right quantity of the unknown solution will be measured using a burette frequently to the point of complete reaction. Phenolphthalein indicator will be used to confirm completion of the reaction at the point where the solutions change color to light pink. After collecting all the values when the reaction is completed, the next step is to calculate solubility products constant and molarity solubility of KHT. Since the NaOH concentration is known, it is measured in milliliters (MLS) in terms of the quantity required to completely neutralize the unknown solution. The MLS was then converted to liters (l) and multiplied by the known concentration to compute the added moles. The next step is converting the NaOH moles into KHT moles since they have a similar ratio of 1:1. Equation three below highlights the similarity in the ratio of NaOH and KHT moles.

Equation 3; HT^–+ HO^–⇄H2O + T^-2

The KHT moles were then divided by 25ml of the solution containing dissolved KHT to establish its molar solubility as summarized in equation 4.

Equation 4

Computing Ksp was done by getting the product of KHT average Molar Solubility for each trial and itself since the Ksp constant of KHT is equal to its concentration at ratio 1:1 as explained in equation five below.

Equation 5; KHT (s) ⇄ K⁺(aq) + HT^– (aq)

Ksp = [K⁺] [HT^–] = [KHT]²

A strong base (NaOH) was used to titrate the solutions since anion (HT^–) is a relatively weak acid. This step is followed by dissolving KHT with 0.05M of MgSO4, water, and 0.025M of MgSO4. As captured in table 1, the findings were recorded for each trial.

Procedure

The first step involved filling three Erlenmeyer flasks. The first flask was filled with 200ml of 0.05 MgSO₄ and 100ml of water to halve the concentration to 0.025 M. The second flask was filled with 200ml of water and the last was filled with 200ml 0.05 M MgSO₄. This was followed by adding a gram of KHT in each flask and stirring for about 20 minutes using the magnetic stirrer. The third step involved pipetting 25.00ml of each solution in the three flasks into three beakers. The fourth step was adding three drop Phenolphthalein in each of the three beakers. The last step was a titration of each beaker with a NaOH-filled burette and volumes required to change the color of solutions in each beaker to light pink noted. The steps were repeated for two trials for each solution.

Results

The results of the two trials for each of the three solutions are summarized in table 1 below.

Table 1. Experiment results.

Discussion

The experiment aimed at establishing the variances in KHT molar solubility in Glucose, MgSO₄, and water. The results indicate that the highest milliliters of NaOH are required to turn the MgSO₄ solution to light pink as compared to other solutions. This reveals that there are no common ions between MgSO₄ and KHT. In the KCI solution, it takes half the MLS of NaOH that is taken up in the water solution to change the color to light pink. A reasonable explanation could be that there are many common ions between KHT and KCI, thus the little MLS of NaOH was taken up. There was negligible variation in the NaOH quantity used for water and glucose solutions. Another interesting finding was that increased KCI concentration resulted in increased usage of NaOH due to a rise in common ions. The same scenario occurred when the concentration of MgSO₄ was increased.

The findings confirmed the literature review which indicated that adding Kor HT or would give a different result for each solution because of its aqueous nature and being on the product side. As observed, it shifted the chemical reaction to the reactant’s side. In the case of substance subtraction, that is, removing KHT from the solutions, there would be no shifts in the reactants side. However, subtraction of Kor HT on the side of products resulted in a shifting reaction on the right side to adjust the equilibrium. The highest quantity of base (NaOH) was used in the solution with MgSO₄ simply because of the existence of negligible common ions. To provide accurate readings, air bubbles from the burette were removed to minimize error in the measurement of NaOH usage is recorded. Another source of error is contamination in the equipment in the preceding trials. This was avoided through the proper rinsing of the experiment instruments.

Experimental objectives

• Is to forecast the bending moment diagram, collapse load, the number, and the position at which plastic hinges for the portal are formed
• To compare the predicted values with the experimental values found from the experiment and do analysis
• To determine dislocation, failure mode, and not directly member forces in a portal subject to mounting perpendicular and tangential loading

Theoretical Background

Modern engineering plan is founded on the “Elastic Theory of Bending” and the technique is to compute the utmost stresses, which crop up and maintain them in the limit of operational stresses in both tension and compression. These functional stresses are computed from a “factor of safety” and ultimate/yield stress. However, according to Sivakumar(2008), this way of computing is a bit impractical because “Mild Steel Structures do not fail when thew edge Stress of any cross-section reaches the Yield point and will continue to withstand the load as long as the central core of the section remains within the Elastic State”(p. 3).

As the weight on a certain beam is steadily augmented, the maximum stresses will happen at the intense fibers of the most feeble part of the beam. At this state, the exterior fibres are in the plastic state and every raise in weight will lead to substantial enlargement in strain level and consequently deflection at that particular point of the beam. Additionally, rearrangement of stress occurs. At this point, it is presumed stress is invariable in the plastic section. Once the structure achieves a plastic state across the entire cross-section, any additional loading will lead to extreme stress i.e. “enlargement in the curvature at that part and a plastic hinge will be developed” (Romero et al, n.d, p. 3). A single or extra similar hinges are necessary for the total collapse of the structure. The actual number is determined by the kind of structure and if it is, for instance, a supported beam, stiff beam, or a fitted beam. The value or amount of load/weight needed to generate this state is what is known as “The Collapse Load and the ratio of the Collapse Load to the Working Load are called the Load Factor” (Roylance 2000, p. 4). In plastic structure, this feature (factor) is employed as an alternative to the ordinary Factor of Safety.

Assumptions are made in order to be able to compute the bending moment required to generate a “plastic hinge in a specific cross-section and sharing of bending moment alongside the beam at the collapse”(Roylance 2000,p. 5). Some of the assumptions made include: 1) the matter observes Hooke’s Law, 2) the objects are isotropic and uniform in the plastic and elastic states. 3) no ensuing axial force acting on the material, 4) The “cross-section of the beam is symmetrical about an axis through its centroid parallel to plane of bending among others” (Romero et al, n.d, p. 7).

Once force has been applied on a given beam and it is in a ‘partially plastic’ state, any further increase in the load will lead to further enlargement of zones deepness, and, it is presumed that plastic elastic can take place at yield stress leading to two stress wedges i.e. compression and tension regions. The plastic region takes up the entire cross-section area and is explained as having achieved a ‘fully plastic’ state. Once in a fully plastic state, any further increase at the moment leads to “member to act as if hinged at the neutral axis and this is called a plastic hinge and the bending moment that leads to the generation of a ‘plastic hinge’ is called the ‘full plastic moment’ and is represented by ‘Mp’” (Roylance 2000, p. 8).

Plastic pivots or hinges are formed because of bending or twisting in a configuration member at which an infinite rotary motion can occur at a stable Plastic Moment at that given section. So long as there are a number of positions of “local” utmost bending/twisting moment alongside the portal frame or beam there are a number of points of “local” greatest Bending Moment along the beam, the first Plastic Hinge will be generated at the numerical greatest point provided working load stipulations are still under operation(Gere & Timoshenko 1990, p. 328). If additional Plastic Hinges are needed for cave-in or collapse of the frame, then it will take place at the subsequent lesser value selected from the remaining neighboring maxima. As soon as adequate plastic hinges have been generated to switch the structure/arrangement into a mechanism then the collapse of the entire structure will take place. The actual number of Plastic hinges required for breakdown does not change for a specific structure depending on the set loading circumstance, even though a section of the beam may collapse separately by the generation of a slight number of hinges. The structure acts like a hinged mechanism leading to rotation of neighboring hinges in contradictory directions structure. In short, the collapse or ultimate weight/load is achieved when a mechanism is produced. The actual number of plastic pivots generated due to weight applied on the frame or any beam should be just enough to create a mechanism (Gere & Timoshenko 1990, p. 340).

Results

The experiment was performed and results were recorded in the excel sheet as below:

Discussion

Calculations

• From the data obtained during the experiment, we can determine the ultimate load according to the following procedure: since this is a simply supported beam, a single point of highest Bending Moment and the collapse state will be achieved when a Plastic Hinge is generated at this specific point.
  Maximum Bending Moment is given by=Wab/I under the load

Since we have a single plastic hinge, the Bending Moment at hinge W_C=MpXI/ab

Using the equation My/Mw = Fy/Fw and Mp=S (Fy/Fw) Mw and making simpler the equation we see that Maximum Bending Moment=S ( (Fy/Fw)W). We can now determine the ultimate load as plastic moment= 8Nm and yield stress= 246Mpa while cross-section areas= 12.7mm by 3.2mm

Ultimate load,Wy/2X 5= (3.2 X 12.7²/6) 246

Ultimate load, Wy= 8.464 and the loading ratio=H/V=105/210=0.5

• Collapse mechanism, number, and position of hinges: To comprehend how the collapse mechanism occurs, a clear understanding of plastic hinges is necessary. A plastic hinge is formed as a result of bending or twisting in a structural/configuration member at which an unlimited rotary motion can occur at a steady Plastic Moment at that given region. Provided there are several positions of “local” utmost bending/twisting moment alongside the beam there are a number of points of “local” greatest Bending Moment along the beam, the first Plastic Hinge will be generated at the numerical greatest point provided working load stipulations are still under operation. If additional Plastic Hinges are needed to cave in, then they will take place at the subsequent lesser value selected from the remaining neighboring maxima. As soon as adequate plastic hinges have been generated to switch the structure/arrangement into a mechanism then the collapse of the entire structure will take place. The actual number of Plastic hinges required for breakdown does not change for a specific structure depending on the set loading circumstance, even though a section of the beam may collapse separately by the generation of the slight number of hinges. The structure acts like a hinged mechanism leading to rotation of neighboring hinges in contradictory directions structure. The collapse or ultimate weight/load is achieved when a mechanism is produced. The actual number of plastic pivots generated due to weight applied on the frame or any beam should be just enough to create a mechanism, which in this case mechanism occurs after three hinges are formed at different positions.
• Static check: in a portal, a frame as shown in the diagram below, has stiff joints therefore, when the load is varied, locations of greatest Bending Moment will take place at the joints. In a cave-in, a few or every joint will be converted into Plastic Hinges. The figures below are the bending moment that illustrates the possible mechanism of collapse under loading conditions. Theoretically, the structure has a span of 1 and has an elevation of H. A weight of V is applied at the center (vertical load) and horizontal weight of H. Under these circumstances, Plastic Hinges may be generated in any arrangement at locations A B C D, and E.
  

A breakdown state will occur when adequate hinges are generated to form a “mechanism.” The possible three ways of collapse mechanism include:

1. The portal frame cave in with hinges at positions B, C, and D
2. swing disintegration with hinges at positions A, B, D, and E
3. joint fall down with turning points at locations A,C, D, and E

• Plotting of bending moment diagram: from the results obtained as indicated in the excel sheet, the following bending moment diagram is generated. First, we must compute the bending moment at different locations on the beam. This is given by the formula, Bending Moment, M=” Force x distance between the location of application of force and the location at which we want to compute bending moment” (Turchetto 2009, p. 4). Taking horizontal displacement and force, we calculate bending moments as below. The degree of consecutive shear ordinates augmented and therefore the gradient of the bending moment graph is positive since the graph is approaching the vertical axis. Unexpected alterations in the shear figure produced unexpected alterations in the gradient of the bending moment curve. Intense moments create perpendicular lines in the bending moment arc.

• For this portal frame, after the first hinge was formed, two more hinges were formed. From the structure in section C, when a weight of V is applied at the center (vertical load) and horizontal weight of H. Under these circumstances, Plastic Hinges may be generated in any arrangement at locations A B C D, and E. A horizontal weight applied on the frame will lead to sway cave in with rotations angle θ taking place at points D and B. while for vertical load, the rotary motion of angle θ occurs at points D and B. Finally, the third hinge is due to a combined weight where there is no rotary motion location B, and cave in will lead to the generation of plastic hinges at positions C and D.
• From the results, we see that theoretical and experimental are related with small deviations. These deviations are a result of assumptions made for example that the beam will behave ideally and obey Hooke’s Law. This is not practically true. Those assumptions are the basis of deviation. Hypothetically, the plastic pivots are presupposed to shape at positions at which plastic rotary motions take place. Consequently, the measurement lengthwise of a plastic hinge is deemed as zero. Practical, the ultimate load was found out to be 8.464Nm while the theoretical one as 8Nm. We have a difference of 0.464, which can be attributed to both experimental error and assumptions made while experimenting. Percentage error is given by the following calculations: percentage error=0.464X100/8=5.8%. This is well within the acceptable deviation range. Sources of error could have mainly resulted due to inaccurate measurements and also wrong positioning of the load on the portal frame. Finally, an error will occur if the meter is not properly zeroed.

Conclusion

The experiment was carried and from the results obtained, the bending moment diagram, collapse load, the number, and the position at which plastic hinges for the portal are formed were determined. The number of plastic hinges formed that led to the collapse of the portal frame was found to be three. The collapse load was achieved when a mechanism was produced as a result of varying the load both vertical and horizontally. The actual number of plastic pivots generated due to weight applied on the frame or any beam should be just enough to create a mechanism, which in this case mechanism occurred after three hinges are formed at different positions. This agrees with the theoretically predicted number of plastic hinges.

Further, we see the objectives of the experiment being achieved where the experimental value and practical values were compared. In theory, the plastic moment was 8Nm but practical, it was found out to be 8.464Nm. The percentage error was found to be 5.8 percent. This is well within the acceptable deviation range. Sources of error could have mainly resulted due to inaccurate measurements and wrong positioning of the load on the portal frame. From the experiment, the dislocation, collapse mode, and not directly member forces in a portal subject to mounting perpendicular and tangential loading were examined and the diagram plotted. Therefore the objectives of the experiment were met.

List of References

Codecogs Engineering 2010, Plastic theory of bending, Prentice Hall, New York.

Gere, J & Timoshenko, S 1990, Mechanics of materials, Wakefield Pres, Kent Town.

Romero, J, Mappa, P, Herskovits, J & Mota-Soares, C 2003, Optimal truss design including plastic collapse constraints, Institute Superior Techno Journal, vol. 3, no.1, pp.1-8.

Sivakumar, MS 2008, Strengths of materials, Indian Institute of Technology Madras Journal, vol. 12, no. 2, pp.1-20.

Roylance, D 2000, Statics of Bending: Shear and Bending Moment Diagrams, Massachusetts Institute of Technology Physics Journal, vol. 230, no 30, pp. 1-12.

Introduction

Hormones are regarded as the necessary signal molecules for different organisms. Hormones and ferments in fruits are mainly used for ripening. Additionally, plant tissues use hormones for communication, and signalization of the required state: ripening, metabolism, germination, and so on. Ethylene is one of the key hormone groups that are used by plants for several functions. Since ethylene is a gas, it diffuses faster than liquids. The experiment, which is described in this paper, is aimed at defining the functions of ethylene associated with avocado ripening. Therefore, various concentrations of ethylene will be used. As is stated by Biale (139), ethylene presence is the main reason for auxin redistribution, hence, the growth and ripening of the fruit will be epinastic. The independent variable of the experiment is the number of avocados, while the dependent variable is the rate of softening and ripening.

Hypothesis

The tissues of avocado will soften due to the effect that ethylene produces on the tissues and cells of the fruit. It is emphasized by Erickson and Tadaaki (93), that avocados do not ripen while attached to the branches, and ethylene increases the speed of ripening. This will be tested by placing avocados under the test bell jars and adding ethylene under some of the jars.

Methods and Materials

• Materials:
  • Avocados
  • Peller
  • Bell jars
  • Scales
  • Ruler
  • Probe knife
• Method:
  • Previously to the experiment beginning, half of the avocados that are taken for the test should be peeled. One test avocado will stay unpeeled, and the other will be peeled also (test avocados will not be subjected to ethylene reaction). Test measurements will involve scaling of the force needed to take equal amounts of a probe. Additionally, all avocados will be weighed and measured.
• Step 1:
  • Define the test part of the fruits tested (external flesh, and internal flesh – from the side of a pit).
• Step 2:
  • Measure force needed to take probe (ripening level of each fruit)
• Step 3:
  • Place each fruit under a bell jar for making the conditions of the experiment equal (sunlight, temperature, pressure).
• Step 4:
  • Leave jars for 2 days. This period will be enough for ethylene production, and for the ripening of the fruits.
• Step 5:
  • Measure the force required for taking the probe

Expected Results

It is expected that avocados placed under the jars with a certain amount of ethylene will become softer in comparison with the fruits that were not subjected to ethylene reaction. Internal and external probes will require comparatively equal efforts, while peeled avocados will be softer in comparison with unpeeled fruits. This is explained by the fact that skin will be a natural barrier to ethylene.

Analysis

The ruler will be used for defining the measures of each fruit, as if softening is caused by drying, the measures will decrease. Scales are required for defining the possible dehydration rate, as well as for weighting the test probes. The larger probe taken with the same effort will mean better ripening of fruit. Hence, the experimental fruit results will be compared with the results of the test avocados.

Conclusion

The results should support the hypothesis. If it is not confirmed, the test and experiment avocados will show the same results while taking the probe. (Claypool, 180) These results may be the reason for the improper experimental environment, hence, the test should be repeated.

Works Cited

Biale, James. The Climacteric Rise in Respiration Rate of Avocado Fruit. Journal of Agricultural Research. 1999 39:137-142.

Claypool, Leiton. A Colorimetric Method for CO Determination ¡n Respiration Studies. Journal of scientific Farming. 2004 40:177-186.

Erickson, Louis, Tadaaki Yamashita. Effect of Temperature on the Ripening of Mass Avocados. Journal of Agricultural Research 2001. 48:92-94.

Abstract

Identification of three unknown bacterial strains was performed using simple agar plate pouring and differential staining analyses. The growth of the bacterial cultures was evaluated using colony counting methods. In addition, the morphology of the bacterial colonies was evaluated, as well as their reactions to lactose utilization assays. Bacterial plating methods involved streaking the unknown bacterial samples onto TSA and MacConkey agar plate for differentiation based on a growth in selective culture media. Further differentiation of the bacterial unknowns was performed through additional colorimetric tests, resulting in the validation of the identity of each bacterial species. The techniques employed in this experiment have resulted in the determination of the 3 bacterial species, namely Escherichia coli, Streptococcus pyogene and Yersinia enterocolitica.

Introduction

Identification of the precise species of bacteria is important because this information will provide information on the correct diagnosis of disease. More importantly, the identification of a bacterial pathogen will provide hints on the proper treatment that should be given to a patient. Currently, there are a number of laboratory tests that can be employed to identify the specific type of bacteria that is being tested.

There are currently several microbiological assays that can help in the identification of bacterial species. The principle behind these assays is that each species has a unique physiological feature that can be tested in the laboratory using in vitro conditions. For example, there are particular bacterial species that have the capacity of degrade red blood cells. This process of hemolysis is caused by exotoxins that are produced by a specific type of bacteria. Upon the destruction of a red blood cell, the contents are thus released to the red blood cell’s immediate environment. One of the major proteins that appear after such process is hemoglobin, which is a transport protein that carries oxygen to the rest of the body. In this experiment, three bacterial strains of unknown identities will be tested in order to determine the exact microbiological species that is present in the test tubes.

Materials and methods

The experiment involved the identification of three unknown bacterial strains which were provided as broth cultures. Bacterial agar cultures were initiated by plate streaking onto TSA plates which are considered as basic non-differential growth media. In addition, another culture was initiated by streaking the broth onto a MacConkey agar plate which selectively allows the growth of Gram-negative bacteria and selects for lactose fermentation through the decrease in the pH level of the culture medium. The MacConkey media also contains pH indicators which generate dark purple bacterial colonies. After 24 hrs incubation at 37^oC atmosphere, the colonies that emerged on each plate were counted. In addition, the morphology of the bacterial colonies were analyzed.

In the first series of the analysis, Gram staining was conducted in order to classify each of the three unknown bacterial strains are either Gram-positive or Gram-negative. The three unknown bacterial samples were also inoculated on microbiological differential culture media following the aseptic transfer technique. In order to determine the Gram staining profile of the bacterial unknowns, the catalase test was performed. In this test, hydrogen peroxide was added to the bacterial sample and the reaction of the bacterial sample to the presence of hydrogen peroxide, in the form of bubbles, was taken note of.

Another assay that was conducted in our experiment involved the mannitol salt agar (MSA) plate, wherein the test sample was inoculated onto an agar plate that was supplemented with blood. It has been established that the MSA plate can only allow the survival of a specific bacterial strain which is Staphylococcus. After allowing the bacterial unknown to growth for 24 hours, the color of the agar culture media was checked. The initial color of the agar plate was red, due to the presence of the pH indicator, phenol red.

For those bacterial samples that tested negative in Gram staining, these were inoculated in citrate, triple sugar iron (TSI) and eosin methylene blue (EMB).

Results

The bacterial unknowns were cultured onto TSA and MacConkey plates and tested after 24 hours of incubation at 37^oC atmosphere. The TSA plate was visually observed to carry two bacterial species because they could be distinguished according to the morphology of the colonies. One type of colony was composed of pin-shaped Gram positive bacteria, while the other type of colony was composed on pin-shaped Gram negative bacteria. Further culturing of the colonies in MacConkey agar showed that one of the two colony resulted in a color reaction, showing a purple colony on the plate. On the other hand, the other type of colony remained colorless on the MacConkey agar plate.

The other bacterial unknown that was grown in blood agar plate did not show any change in color. Furthermore, addition of hydrogen peroxide to the blood agar plate resulted in the generation of bubbles. The MSA plate containing another bacterial unknown did not show any change in the color of the media. Another bacterial unknown that was inoculated into EMB plates resulted in dark purple colonies. The bacterial unknown that was inoculated in the citrate culture slant resulted in a blue culture medium. The TSI culture tube with another bacterial unknown was found to generate bubble in the culture medium yet there was no precipitate that was observed. The other bacterial unknown that was grown in the EMB plate showed colorless bacterial colonies. The citrate slant was also found to be of blue color as well as the absence of bubble or precipitate. The techniques employed in this experiment have resulted in the determination of the 3 bacterial species, namely Escherichia coli, Streptococcus pyogene and Yersinia enterocolitica.

Discussion

In order to perform bacterial identification, one needs to collect a sample material that is suspected to carry the bacteria of interest. Upon collection of the biological sample that carries the bacteria, these microorganisms may be cultured in the laboratory for further analysis and possibly, manipulation. The growth of bacteria pertains to a process wherein a single bacterial cell generates two identical daughter cells. This simple doubling of bacteria is observed in cultures that are classically conducted in microbiological laboratories. The quantification of bacterial growth is generally performed through the use of either direct or indirect cell counting methods. Colony counting is an example of a direct counting technique while the measurement of turbidity is an illustration of an indirect counting procedure.

The progress of a bacterial curve is generally described through the use of a growth curve (Novick, 1955). Four different phases comprise a bacterial growth curve. The lag phase involves the adaptation of inoculated bacteria to the conditions of the culture medium. This phase denotes that time that the bacteria are undergoing maturation. The logarithmic or exponential phase involves the doubling of bacteria in culture. The rate of division is observed to logarithmically increase through time. The growth conditions and the chances of survival of the resulting daughter cells influence bacterial growth rate. The logarithmic growth of the bacterial culture is dependent on the availability of nutrients in the culture medium. The stationary phase pertains to the decrease in growth rate due to the exhaustion of nutrients in the culture medium and in turn, wastes have accumulated in the culture medium. During the death phase, the cultured bacteria lose nutrient resources and die.

In the first series of the analysis, Gram staining was conducted in order to classify each of the three unknown bacterial strains are either Gram-positive or Gram-negative. In this test, the addition of hydrogen peroxide determines that a bacterial species is Gram positive. On the other hand, when no bubbles are observed in the reaction of hydrogen peroxide to the bacterial sample, the test sample contains Gram negative bacteria.

Another assay that was conducted in our experiment involved the mannitol salt agar (MSA) plate, wherein the test sample was inoculated onto an agar plate that was supplemented with blood. It has been established that the MSA plate can only allow the survival of a specific bacterial strain which is Staphylococcus. The growth of this particular bacterial species is due to the presence of 7.5% NaCl which is also present in the MSA agar culture media. Another feature that allows the MSA agar plate to selectively allow growth of Staphylococcus in the presence of mannitol is the change in the pH level of the culture media. The fermentation of mannitol results in the lowering of the pH level and this can be monitored by incorporating a pH indicator in the culture media. In our case, phenol red was the pH indicator that was employed for determining any changes in the pH of the culture media. When the pH of the media decreases, the color of phenol red changes to yellow and indicates that the pH had changed to a lower level.

For those bacterial samples that tested negative in Gram staining, these were inoculated in citrate, triple sugar iron (TSI) and eosin methylene blue (EMB). The citrate culture media also contained a pH indicator of bromthymol blue which indicates when the bacteria utilize citrate for nourishment. When this occurs, carbon dioxide is produced as a by-product of the reaction, which in turn increases the pH of the culture media and changes the color from green to blue. The change in the culture media is due to the reaction of carbon dioxide with the sodium ions and the alkaline products that are present in the culture media.

The observations in the TSI culture media are mainly based on the bacteria’s capacity to use lactose and sucrose for nourishment. Phenol red is also present in the TSI media and thus indicates any changes in the pH that are associated with lactose and sucrose utilization. Alkaline production is determined when the red color of phenol red changes to yellow. When a bacterial species ferments the sugars present in the culture media, the media will then turn acidic and thus the bacteria will consequently not be able to ferment any sugar formats any further. In case that the bacteria produce sulfur gas while being cultured in the media, a black precipitate will result on the culture plate. In addition, when a bacterial species generates carbon dioxide or possibly hydrogen gas, one will observed bubbles that will appear in the media.

The EMB plate can differentiate bacterial strains through the principle of fermentation. When a bacterial strain can ferment lactose, acid will be produced and this will accumulate in the culture media, which in turn reacts with the dye that was incorporated in the EMB plate. This reaction can be observed through visual inspection of the plates after 24 hours. Should the bacterial sample be incapable of fermentation of lactose, the colonies will be of pink color and this is simply due to the media uptake.

Bacterial cells should be grown to its exponential growth stage in order to have a sufficient amount of DNA. Once the appropriate amount of bacterial cells is present, the bacterial cells can now be called competent cells because these are ready for DNA manipulation. Plasmid DNA from bacterial cells will be extracted with minipreparation techniques that involve lysing the bacterial cells and centrifuging the cellular solution in order to remove other organelles of the bacterial cell. The bacterial plasmid will then be exposed to the same restriction enzyme that was used in the human cytokine DNA segment, also generating sticky ends that are ready to reassociate with other sticky DNA ends (Zhu 3089). The cleaved human cytokine DNA fragments can then be introduced into the bacterial plasmid because both DNA molecules are sticky. The principle of reassociating foreign and host DNA molecules is to employ the same restriction enzyme so that the sticky ends have the same recognition sequences that are complementary to each other. Once the human cytokine DNA fragment is inserted into the plasmid, it is now possible to let the plasmid make more copies of itself inside the bacterial cell.

Bacterial cells multiply very fast and also, the transcription and translation rates of these cells are very short as compared to human cells (Duarte 107). Molecular biology techniques allow the manipulation of DNA segments of interest. After incubation of the bacterial cultures that contain plasmids that carry the human cytokine genes, it is then possible to allow the bacterial cells to perform the process of translation, which is the production of protein products based on the transcription results. Translation of the specific human cytokine genes in the plasmid allows that production of human cytokine which can then be collected using isolation techniques (Grunstein 3961). The human cytokine is then further purified using mass chromatographic techniques in order to remove any other unnecessary proteins and other smaller cellular material. The human cytokine protein is then resuspended in a stable buffer such as sterile double distilled water or a buffer such as phosphate buffer in saline solution so that the human cytokine protein remains in its native state. The bottled human cytokine products that are now sold in pharmacies are thus produced through the abovementioned techniques.

References

1. Duarte SP, Fortes AG, Prazeres DM and Marcos JC. “Preparation Of Plasmid DNA Polyplexes From Alkaline Lysates By A Two-step Aqueous Two-phase Extraction Process.” Journal of Chromatography A. 1164(2007),105-12.
2. Grunstein M and Hogness DS. “Colony Hybridization: A Method For The Isolation Of Cloned DNAs That Contain A Specific Gene.” Proceedings of the Natiional Academy of Sciences U.S.A. 72(1975);3961-3965.
3. Novick A. “Growth Of Bacteria.” Annual Review of Microbiology 9(1955),97-110.
4. Zhu K, Jin H, He Z, Zhu Q, Wang B (2006): A Continuous Method For The Large-scale Extraction Of Plasmid DNA By Modified Boiling Lysis.” Nature Protocols. 1(2006):3088-93.

Summary

This guide describes how to set up and perform experiments related to the deflections and reactions of a rectangular portal. The equipment clearly demonstrates the principles involved and gives practical support to your studies.

Description

Figure 1 shows the Frame Deflections and Reactions experiment. It consists of two supports (or springing) and either a uniform or non-uniform section aluminum alloy portal frame. The left-hand side of the portal is pinned to its support and is restrained from turning by a moment arm. The moment arm contacts a load cell, so, measuring the restraining moment. The right-hand side of the portal fixes to a mechanism which prevents rotation but allows movement in the horizontal direction against a second load cell. The load cell reacts and so measures the horizontal reaction produced by the portal. A digital indicator positioned at the top corner of the portal measures the sway (horizontal movement). Vertical loads are applied to the portal using a knife-edge hanger and masses.

In the experiments, we will use measured and calculated values of moments, reactions and sway to study the linear elastic behavior of the portal, the sway of the frame due to the asymmetry of the frame or the loading position.

How to Set Up the Equipment

The Frame Deflections and Reactions experiment fits into a Test Frame. Figure 2 shows the Frame Deflections and Reactions experiment in the Structures Test Frame. Before setting up and using the equipment, always:

• Visually inspect all parts (including electrical leads) for damage or wear. Replace as necessary.
• Check electrical connections are correct and secure. A competent person must only carry out electrical maintenance.
• Check all components are secured correctly and fastenings are sufficiently tight.
• Position the Test Frame safely. Make sure it is on a solid, level surface, is steady, and easily accessible.

(Never apply excessive loads to any part of the equipment.)

The following instructions may have already been completed for you. If so, go straight to Section 2.

1. Place an assembled Test Frame (refer to the separate instructions supplied with the Test Frame if necessary) on a workbench. Make sure the ‘window’ of the Test Frame is easily accessible.
2. There are four securing nuts in the top groove of the bottom member of the frame. Slide them to approximately the positions shown in Figure 2.
3. Fit the left-hand support to the frame using two thumbscrews (on the front only) into the frame securing nuts.
4. Fit the right-hand support in roughly the correct position and fasten as per the left-hand support.
5. Adjust the position of the right-hand support until the distance between the pivots is 500 mm.
6. Fit the uniform portal frame to the pivots using two shims on each side. Ensure the frame is secure by tightening the grub screw at each end.
7. Referring to Figure 2, mount the digital indicator onto the back of the Test Frame. Ensure that there is at least 3 mm of travel in each direction. If there is not fine adjust the positions of the two supports, maintaining the 500 mm between centers.
8. Check the frame is square and true on the supports; adjust the supports if required.
9. Make sure the Digital Force Display is ‘on’. Connect the mini DIN lead from ‘Force Input 2’ on the Digital Force Display to the socket marked ‘Force Output (Thrust)’ on the right-hand side of the support. Connect a second mini DIN lead from ‘Force Input I’ to ‘Force Output (Moment) on the left-hand support.
10. Undo the knob securing the dial indicator and swing it away so that the contactor no longer touches the portal frame. Carefully zero the force meter using the dial on each support of the experiment for both inputs (use the selector switch to view the appropriate input). Gently apply a small load with a finger to the center of the frame cross member and release. Zero the meter again if necessary. Repeat to ensure the meter returns to zero.

Note: If the meter is only ±0.l. N, lightly tap the Test Frame (there may be a little ‘stiction’ and this should overcome it).

Experiment 1: Analysis of a No-Sway Portal Frame

In this experiment, we will apply increasing vertical load to the centre of the uniform portal frame and investigate how this affects the horizontal reactions and fixing moments. You may find the following table useful in converting the masses used in the experiments to loads.

Table 1: Grams to Newtons conversion table

Undo the screw on the reverse of the digital indicator and swing it 90° clockwise so the contactor no longer touches the frame (it is not required for this experiment). Position a knife-edge hanger in the center of the frame cross-member. A line indicates the center. Ensure that the force meter reading is zero, and then put a mass (on a hanger) of 100 g on the knife-edge. Record the resulting force meter readings for the ‘moment’ and ‘thrust’. Increase the mass in 100 g increments. Record the force meter readings for each increment in Table 2. Using the Vernier provided, accurately measure the section of the frame and calculate the second moment of area of the section. Make a note of this value.

Table 2: Results for Experiment 1

Analysis and Calculations

Calculate the moments from the moment force by multiplying it by the length of the moment arm (0.05 m) complete Table 2.

Plot graphs of the moment and horizontal reaction against the applied load (convert the mass to a load in Newtons).

The relationship between the horizontal reaction and the load as shown in the graph is a linear positive relationship. Notably, as the horizontal force increases, the load also increases by a linear- positive factor of force. However, the relationship between the moment of force and the load is a non-linear negative relationship. In this case, a positive moment of force corresponds to a non-linear negative factor of load. At a load of 4.9N from the graph, the horizontal and moment forces are 0.98N and -0.18N respectively.

State the nature of the relationship between the moment and horizontal reaction and the load. Read off values for a load of exactly 4.9 N.

Sketch the detected shape of the frame below:

Use static equilibrium and the symmetry of the frame to calculate values for the vertical reactions, V_A and V_E.

• Vertical reactions, VE for 100g

Moment about A
V_Ex (0.025m+0.025m)-0.49Nx0.025m-0.98NX0.025m=0
VE=0.735N
Therefore, Vertical reaction, VA:
VA=0.98N-VE
VA=0.245N

• For 200g

Moment at A
VEX0.05-0.98NX0.025m-1.96NX0.025m=0
VE=1.47N
Therefore, VA
VA=1.96N-VE
VA=0.49N

• For 300g

Moment at A
V_EX0.05-1.47X0.025-2.94NX0.025=0
V_E=2.205N
Therefore, VA
V_A=2.94N-VE
V_A=0.735N

• For 400g

Moment at A
VEX0.05-1.96X0.025-3.92X0.025=0
VE=2.94N
Therefore, VA
VA=3.92N-VE
VA=0.98N

• For 500g

Moment at A
VEX0.05-2.45X0.025-4.9NX0.025=0
VE=3.675N
Therefore, VA
VA=4.9N-VE
VA=1.225N

Using Static equilibrium, calculate the horizontal reaction and moment reaction at points A and E.

Reactions for both horizontal and moments at 100g

Sum of Moment at E=0 (Hibbeler, 2020)

0.735×0.025-0.98xEx=0

H_E=0.01875N

However,

+ sum of Fx=0

-Mf-0.01875+0.025×0.49=0

Mf=0.0065N

At 200g

H_E=0.01875N

However,

+sum of Fx =0

-Mf-0.01875+0.025×0.98=0

Mf=-0.00575N

At 300g

H_E=0.01875N

However,

+sum of Fx=0

-Mf-0.01875+0.025×1.47=0

Ax=-0.018N

At 400g

H_E remains constant= 0.01875N

However,

SUM of Fx=0

-Mf-0.01875+0.025×1.96=0

Mf=-0.03025N

At 500g

H_E remains constant= 0.01875N

However,

Sum of Fx=0

-Mf-0.01875+0.025×2.45=0

Mf=-0.0425N

Do your results correspond favourably with theoretical answers? Comment on any discrepancies.

The experimental values of the results above do not correspond to the theoretical values. The difference in values may be due to the disparities of the diffusion voltage or the non-zero electric fields at the borders of the deflection machine. The diversity in the values could also results from errors in the deflection computation of flexural members of the frame deflection machine. Temperature affects the expansion of metals. In this regard, the room temperature could results in errors as they often lead to abnormal expansion of the aluminium alloy, which is used as the frame beam. Lastly, errors due to calibration of the frame deflection machine might results in experimental errors, hence differences in both the theoretical and experimental data.

Reference List

Hibbeler, R.C. (2020) Mechanics of materials. 8th edn. New York, NY: McGraw-Hill.

Random Variable

A random variable is one whose values are determined by the results of a randomly occurring phenomenon. In other words, its value is not constant, but it may assume any potential values of that occurrence (experiment) (Lambert, 2018). Y is a discrete random variable if its values or representative area can be counted. On the contrary, it is considered a continuous random variable if it’s quantities or representative array of values are not quantifiable and it accepts any numbers on the reference axis or its interval.

Explanation

Y is a discrete random variable if its values or sample space can be counted. For instance, the number of people who arrived at the office between 7:00 A.M and 8:00 AM on a Monday. Conversely, Y is considered a continuous random variable if the quantities or representative array of values are not quantifiable. For example, the lifespan of a car battery. Here, Y may have any value between 0 and ∞, making it a continuous random variable.

Binominal Experiment

A binomial experiment has four properties and may be utilized in a binomial distribution if the four conditions listed below are met:

• The representative sample (n) is constant;

n = 15 in this case; hence this hypothesis is true.

• There are only two possibilities that may occur when a function is replicated: success or failure;

In this case, the laptop can either match the standards or fall short; this premise is true.

• The likelihood of success is the same and fixed for each duplication;

In this case, the percentage of laptops manufactured that meet standards are set at 0.95; therefore, this hypothesis is fulfilled.

• The simulations (or trials) are self-contained.

Given all assumptions are met, a binomial distribution may be employed to depict this operation.

1. If more than one laptop does not match the criteria, the whole batch must be examined, which is unnecessary. The needed probability is P(X > 1), which may be calculated using the excel function “1-BINOMDIST(1,15,0.05, TRUE)”. The probability obtained is 0.170953.
2. Accepting the lot would be wrong if the number of defects is less than or equal to 1, provided the faulty rate is 0.25. The needed probability is P(X = 1), which may be calculated using the function “BINOMDIST(1,15,0.25, TRUE)” in Excel. The probability obtained is 0.08018.

References

Lambert, B. (2018). A student’s guide to Bayesian statistics. Sage.

Introduction

This experiment was necessary to study the reaction of food coloring with bleach. However, the principles on which the experiment was based can be applied to any other reactions. The main purpose of this test was to determine the reaction rate of two substances. The rate of a chemical reaction is the quantity of chemical that is reacted or generated for a given time interval (“Rate and Order Reactions”). The rate law demonstrates how the rate correlates with the concentrations of the components of the reaction. It is possible to note that “the power of the concentration in the rate law expression is called the order with respect to the reactant or catalyst” (“Rate and Order Reactions”). There are zero-order, first-order, and second-order reactions.

There are several aspects of chemical reaction rates that are necessary for the understanding of the results of the experiment. The first important characteristic is absorbance. It demonstrates the amount of light absorbed by a given sample. It is also called optical density, extinction, or decadic absorbance (Helmenstine). This characteristic can be measured by means of a spectrophotometer.

This device allows collecting necessary data in order to conduct quantitative analysis. A spectrophotometer calculates absorbance by measuring the quantity of light that goes through a given sample. The absorbance will be zero if all light passes through (Helmenstine). However, if the light does not pass through a sample at all, the absorbance is absolute. In order to calculate it, the Beer-Lambert law is applied.

Another important aspect is the correlation between concentration and time. However, as absorbance is directly proportional to concentration, it was used to determine this correlation. Also, the collected data allowed determining the order of the reaction with respect to a given substance. The results of the calculations and graphs helped to demonstrate that it was the first-order reaction. The hypothesis of this work is that the reaction between the given substances is a first-order reaction.

Procedure

The stock solution that was prepared for this experiment contained six drops of the blue dye and distilled water. A 400ml beaker was used to mix the substances. The next step was to measure the absorbance of the stock solution. In order to do it, the stock solution was poured into the test tube. Then, it was put in the spectrophotometer. The wavelength was set from 700nm to 400nm, reducing 20nm each time. After the data was collected, the maximum wavelength at which the absorbance was the highest was determined.

The next part of the experiment was to determine the right proportion of Clorox and blue dye solution to do the rate study. 1 mL of Clorox was mixed with different amounts of the blue stock solution using a graduated cylinder. The first proportion was 1 mL of Clorox and 10 mL of the blue dye solution. After mixing two substances, the discoloration time was measured. This pattern was repeated several times with different amounts of the blue dye. This experiment was completed when the discoloration time was about fifteen minutes.

The final part was to make absorbance versus time measurements. The Spectronic 20 was blanked with water. Then, the blue dye and Clorox were mixed together and transferred into the cuvette to record the absorbance every minute.

Results

The results are presented in the two graphs attached to this report. Figure 1 demonstrates the correlation between the absorbance and wavelength. The highest absorbance was 2.05. The wavelength at the highest absorbance was 620. Figure 2 demonstrates the correlation between time and absorbance. The best proportion was 1 mL of Clorox and 30 mL of the blue dye solution, and the discoloration time was 14.26 minutes. Figure 3 demonstrates the correlation between concentration and time. Figure 4 demonstrates the correlation between time and 1 divided by concentration.

Discussion

The main goals of this experiment were to determine the maximum wavelength at which the absorbance was the highest, the best proportion of Clorox and the blue dye solution, the discoloration time, and the correlation between absorbance and time. The experiment revealed that the maximum wavelength was 620, and the discoloration time was 14.26 minutes. The best proportion was 1 mL of Clorox and 30 mL of the blue dye solution. The correlation is presented in figures 2, 3, and 4.

In order to determine the absorbance, the Beer-lambert law was applied, A= Ebc. A is the amount of light absorbed by the solution for a given wavelength; E is the molar absorptivity; b is the distance that the light travels through the solution; c is the analyte concentration (“How to Calculate Molar Absorptivity”). The spectrophotometer that was used in this experiment calculated the amount of light that was absorbed by the sample applying this law. The results were shown on the display of the spectrometer.

In order to determine the best proportion and discoloration time, the same pattern was repeated several times until the discoloration time was approximately 15 minutes. The result was 14.26 minutes. This proportion was necessary to conduct the third part of the experiment in which the correlation between absorbance and time was determined.

The final part of the experiment allowed measuring the absorbance of the obtained proportion of Clorox and the blue dye at the maximum wavelength. The results confirm the initial hypothesis. The reaction was first order as its rate was directly proportional to the concentration of one of the reactants. Therefore, if the concentration doubles, the reaction rate will double as well. It might be seen in figure 2. The absorbance was used in this experiment instead of concentration because they are directly proportional. The data presented in figure 3 also prove that the reaction is first-order because the plot resulted in a straight line. Finally, if it was a second-order reaction, figure 4 would present a straight line. However, it demonstrates a different correlation.

There were some random errors that occurred during the experiment. The first error occurred in the second part. As the measurements were made visually, they could not be accurate enough. For this reason, the measurements were repeated several times. It helped to minimize the inaccuracy in collecting data.

Another error occurred in the third part. As recording the absorbance depended on the speed of transferring the resulting substance into the cuvette, it might have also caused inaccuracy in the measurements. Therefore, it affected the results. However, such errors could not significantly change the outcomes of the experiment. That is why they can be neglected.

Conclusion

The experiment helped to determine the reaction rate of Clorox and blue food dye. Clorox is a bleach that is used to remove color or make it lighter. Food dye is a substance that is used to color food or drinks. The mix of food dye and bleach was colorless. In order to determine the absorbance for this reaction, it was necessary to measure the quantity of the light that went through the resulting solution. Other important data included discoloration time and the right proportion of the two substances. Analysis of the collected data revealed that this was a first-order reaction.

Works Cited

Helmenstine, Anne. “Absorbance Definition.” ThoughtCo. 2017. Web.

“How to Calculate Molar Absorptivity.” WikiHow. Web.

“Rate and Order Reactions.” Science. Web.

Introduction

The cooling curves of the pure compounds and various mixtures were used to construct a solid-liquid phase diagram of the biphenyl and naphthalene systems. A phase diagram shows melting, freezing, vaporization, and sublimation. These graphs represent the temperature, pressure, and composition relationships. One of the easiest ways is to use cooling curves to create phase diagrams and determine phase transition temperatures. The melting point of a substance may be determined by measuring the rate at which it cools from a liquid to a solid at a constant atmospheric pressure. Assuming the composition of the samples is known, the rate at which each combination cools may be used to establish the eutectic temperature. Eutectic systems are those in which the melting or solidifying point is lower than the melting point of any one component. The binary phase diagram illustrates the combined cooling curves of the two components to show how each affects the total cooling of the solution.

Each component of the mixture contributes to the solution’s solidification as it cools. At a given time, one of the components will begin to solidify, which may be referred to as compound Y. This slows the cooling process, as seen by the graph’s decreasing slope. Since compound Y is in the solid state, the liquid becomes enriched in compound X, which rises until the eutectic point. A eutectic point will be reached at this moment when both chemicals X and Y have solidified, and the temperature will no longer change. The cooling of the mixture will continue after the solidification of the mixture has occurred at a pace defined by the heat capacities of the two solids and the composition of the provided mixture. The binary system’s phase diagram may then be mapped using the pure and depressed melting points. From this, the limiting tangent slopes may be used to determine the enthalpy of fusion for each component.

The chemical potential of solid X in a mixture is stated to be the same as pure solid Y at the same temperature and pressure. The following equation (1) can be used to describe the liquid and solid phases of a component’s potential chemical relationship at pressure P and temperature T.

The chemical potential relationship of pure solid A and solid A in the mixture can thus be determined using equation (2)

Using Raoult’s law, one may determine the chemical potential of a liquid at equilibrium based on its activity. In this experiment, naphthalene and biphenyl mixtures are observed. N-N and B-B interactions (N representing naphthalene and B representing biphenyl) in the liquid phase are assumed analogous to the N-B interactions in the solid phase.

where n – number of moles, m – a mass of the chemical compound, M – molar mass.

where X_N(B)i – a molar fraction of naphthalene (N) or biphenyl (B) in the composition

Reagents

1. Pure Biphenyl
2. Pure Naphthalene

Procedure

Preparation of the sample

• Weigh 2g of naphthalene on filter paper, then transfer it into a small test tube with caution.
• Insert a rubber stopper in the sample tube, then put the sample into a beaker filled with boiling water.
• Once the sample has dissolved, remove it, and place it in ice water to let it cool.
• Insert the probe by removing the stopper while ensuring the PTFE spacer keeps the probe centered.
• The tip of the probe should be in the lower third of the melted sample, so not all the way down where it would touch the stirring bar because if it does it would affect the graphing of the sample.
• Record the temperature readings up to 10^oC to obtain the cooling curve.
• Place the sample tube in boiling water until it melts, and then remove the probe.
• Let the molten sample cool and add 0.2g of biphenyl.
• Melt the mixture and swirl to homogenize the liquid.
• Once the sample has dissolved, remove it, and place it in ice water to let it cool.
• Remove the sample from the ice water bathe, heat the solid, remove the probe and add another 0.4g, 1g, and 2g of biphenyl to the sample mixture simultaneously to obtain the cooling curve for each.
• Follow the same procedure but start with 2g of biphenyl to obtain the cooling curve.
• Add 0.2g naphthalene to this sample to obtain the cooling curve.
• Repeat the above step for 0.4g and another 0.4g of naphthalene to the biphenyl sample to obtain the cooling curve for each. The total for the cooling curves would be 9 at the end.

Computer-Assisted Data

• Initiate the data acquisition software to record the data for the cooling curve of each sample.
• Save the data file and record the file name.

Results

First, the cooling curves for all the nine mixtures were determined, and the results can be found in Figures 1 and 2 for 2 grams of naphthalene + 0.2/0.4(1)/0.4(2)/1 grams of biphenyl and 2 grams of biphenyl + 0.2/0.4(1)/0.4(2) grams of naphthalene accordingly. Based on these graphs, the final solidification temperatures (freezing points) were identified and documented in Table 1.

Table 1. Determining Freezing Points for Various Mixtures.

Next, to determine the mole fraction for both biphenyl and naphthalene solutions, it is necessary first to calculate the number of moles of each component in different samples using equation #3. Therefore, the sample estimation for the first sample (pure naphthalene) is as follows:

The results for other samples can be seen in Table 2. Note that the molar mass for naphthalene and biphenyl was estimated using formula #4. Thus, as the former reagent consists of 10 carbons and 8 hydrogens, the molar mass equals 128.1705. On the other hand, the latter reagent consists of 12 carbons and 10 hydrogens, and therefore, its molecular weight is 154.2078. Now, it is possible to determine the mole fraction of naphthalene and biphenyl using equation #5. The mole fraction of the former organic compound for sample #2 is calculated as:

Similarly, the mole fractions of both components were calculated, and the results can be found in Table 2.

Table 2. Sample Molar Composition and Mole Fraction.

Based on the received mole fraction rate and temperature values, it is possible to construct a phase diagram and identify the measured eutectic point in which solid and liquid phases are in thermodynamic equilibrium. The latter indicates the lowest melting point among all the studied mixtures and equals 312.26 against x_N = 0.42 which can be observed in Figure 1.

Corresponding regression equations for the two substances:

Naphthalene:

Biphenyl:

Hence,

The next step was plotting the mole fraction of naphthalene and biphenyl against the depressed freezing point. Figure 2 shows the corresponding dependence plot for the mole fraction of naphthalene and Figure 3 for biphenyl. It is noteworthy that in both cases only three points are used: the pure substance and the first two additions of the corresponding reagent.

As can be seen, a linear regression was used for both data sets, and it is interesting that the linear trend was more significant for the mole fraction of naphthalene. It follows that as naphthalene or biphenyl was mixed with the appropriate reagent, there was a consistent decrease in the freezing point. In addition, the use of linear regression equation coefficients for each of the plots allows us to estimate the value of

. For naphthalene, the following calculations are correct:

Thus, the values of

were determined for the two substances. It can be seen that for pure naphthalene this value is higher by about 1.7 times than for biphenyl.

Discussion

This experiment determined how the melting point of the naphthalene-biphenyl system changed according to the composition of the solution. As expected, the freezing point of pure naphthalene and biphenyl gradually reduced when mixed with the second compound. For instance, the melting point of pure naphthalene was 352.2 K, but when the 0.6 grams of biphenyl were added, the final solidification temperature was equal to 344.2 K. Yet, such temperature reduction persisted only until a certain threshold – eutectic point – was reached, which is the lowest melting point for the naphthalene-biphenyl binary system. The thermodynamic equilibrium point between the solid and liquid phases was determined by plotting the graphs of both functions on a single coordinate system and determining their intersection point. Thus, it was found that eutectic temperature is equal to 312.26 K while eutectic composition includes 0.42 of naphthalene and 0.58 of biphenyl.

Next, it is necessary to compare the values received during this experiment with those generally accepted in the literature. According to previous research conducted by the National Institute of Standard and Technology (2021a, 2021b), the melting points of pure biphenyl and naphthalene are 342.15 K and 353.15 K. Additionally, Hua et al. (2010) determined that the eutectic temperature is 314.15 K while the composition of naphthalene to biphenyl is 40% against 60%, respectively. Contrary, in the current study, the ideal solubility curves with a eutectic temperature equal to 312.26 K and 42% of naphthalene percent in the composition. Therefore, it can be concluded that the findings of this study are very close to those of previous research, but differ from the ideal eutectic point, although not greatly.

Finally, the heat of fusion was calculated for both compounds, where the

, and

. Nevertheless, these results were different from the ones obtained by previous studies. In this regard, previous findings suggest that

has varying values from

to

, average, 17.85. (National Institute of Standard and Technology, 2021b). On the other hand,

equals the number in the range from

to

, average, 19.14 (National Institute of Standard and Technology, 2021a). Therefore, it can be concluded that there is a significant difference between the results obtained during this study and the ones found in the previous literature.

Conclusion

In summary, the current research presented the cooling curves of two pure chemical components, namely biphenyl and naphthalene, and their mixtures. Moreover, it intended to identify the melting points of each studied sample and based on this information, determine the eutectic composition and temperature. It was found that the melting points for pure naphthalene and biphenyl are equal to 352.2 K and 340.2 K, respectively, which is almost in line with the generally accepted values. As for the eutectic point, both the eutectic temperature and composition were close to the numbers received in a previous study. Yet, as for the values received by plotting the ideal solubility curves, both the eutectic composition and temperature were significantly different but still relatively close to the values claimed by this study and previous research.

References

Hua, D., Hong, J., Hu, X., Hong, Y., & Li, J. (2010). Solid–liquid–gas equilibrium of the naphthalene–biphenyl–CO2 system: Measurement and modeling. Fluid Phase Equilibria, 299(1), 109-115.

National Institute of Standard and Technology. (2021a). Biphenyl. Web.

(n.d.). Solid-Liquid Equilibrium in a Binary System. Unknown

Abstract

This study of rat behavior seeks to show the role of sucrose presented in different forms: liquid, pellets as the reinforcer of rat behavior in laboratory conditions.

The research is based on empirical methods and theoretical studies and similar experiments in the literature. The hypothesis of the experiment is proved by careful analysis of statistical and quantitative data using necessary statistical tools. The results of the research may be helpful for the practitioners and researchers interested in applying the findings of behavioral science in medicine, psychology, and biology.

Introduction

Research on rat behavior is an essential part of behavioral studies which are very fruitful for the development of neurophysiology, innovative medicine approaches, animal behavior disciplines, and biology in general. Rats were traditionally used as the dominant object for research experimentations as their biological and behavioral reactions are the most appropriate for hypothesizing and laboratory research. A Skinner box with necessary inventory is usually used as a tool for conducting experiments.

There is no denying the importance of the fact that the secure normal passing of experiments and well-grounded scientific results, one should formulate and use a sound methodological base of research and elaborate genuine hypothesis. If this is done, we are likely to obtain significant results.

As it was noted, experimentation on rates is widely used and its theoretical and practical results are significantly covered in the literature.

For instance Kawai, N., & Nakajima, S. Provide the outline of rat experiments on so-called ‘comfort’ responses which were conducted to investigate the role of the passive maternal stimulus on the immobility of 9-and and the 16-day rat pups (1997). As the experiment shows that there was a significant increase in dorsal immobility which may essentially reduce struggling between pups in the presence of their mother and hence help rat mothers to transport the infants back into their nest.

As Campbell’s analysis of locomotion shows during the second week of a rat’s life it increases as the struggle for survival becomes dominant.

Some other experiments were aimed at investigating the consequences of home separation on rats’ fear responses. Their research found that in the case of passive home stimulus availability the heart rate is increased and the general level of anxiety grows.

Another branch of research investigates behavioral responses to food and flavors. Ward et al. found out that rats acquire preferences of separate flavor as a conditioned stimulus and mixed flavors with some additional substances as unconditional. This happens because if all that rats learned was only the association between a given flavor and a certain reaction being evoked by nutrient – in this case, satiation treatment would not affect the preference of flavor.

Some other experiments were conducted to analyze the impact of stress and alcohol reactions on fetal development in male rats. Kawai, N., & Nakajima, S. (1997) show that exposure to stress is a significant factor in lowering rats’ ratio of copulation but not significantly affecting ejaculation. Alcohol exposure is not reported as a factor in lowering sexual activities. However, when alcohol is combined with stress effects it is likely to substantially affect low sexual activity in rats (Carlson, 2007).

Another important experiment was conducted in the 70s and is known as Rat Park. It was designed to prove the hypothesis that the drugs do not result in addiction and that evident rat addiction to morphine can be attributed to living conditions but not drugs themselves. As the experiment showed, rats that were given morphine when they were consequently provided with a choice of water with or without morphine, chose plain water.

Information for the method

As some previous studies show, the rat’s response to low-concentration sucrose reinforces, will see an increase in terms of the food-pellet rather than liquid-sucrose.

The current experiment examines whether the upcoming sucrose-pellets reinforcement can produce an effect similar to the abovementioned. We chose the sucrose pellet for several reasons. First of all, it significantly differs from the previously used food pellets in a number of ways such as taste, color, nutritional values. Hence, it was possible to compare every produced induction (Bouton, 2007).

Method

Subjects. The subjects are eight experimental male Dawley rats. These subjects were kept individually, had their free access to water (only), and were deprived of food for the period of 2 weeks. They also experienced 14/10 hours dark/light schedule. Besides this, the subjects were kept at approximately 85 % of the free-feeding weight due to the use of special feeding methods.

Apparatus. The apparatus is the experimental Skinner box for rats. It was located a 5cm responding lever near the left edge of the front panel and above 8cm from the grid floor.

This lever was extended to 2 cm within the chamber. It was required a 0,25N force to depress this lever. A similar lever was located on the right side of the panel. However, it should be noted that it was not utilized in this given experiment. We also used stimulus lights – 3cm in diameter which were located above each lever.

Besides this, we used a liquid-drop dispenser and the pellet dispenser which were put at the front panel. Both dispensers could give reinforcers into the 3cm diameter cup located in the box. We centered the houselight at the back wall of the chamber and it was approximately 2cm below the room’s ceiling. The technical equipment was also used for lowering the noise level and the experimental events programmed and data gathered using IBM computer which ran special software.

Procedures: Rat subjects were trained in order to press the left lever using the method of shaping by successive approximations. When each rat pressed the lever more than one hundred times, it could participate in the experimental procedures.

Subject rats had to respond in the sessions, approximately 50 minutes in length. The left lever had to be pressed on the random interval throughout the given session. The reinforcers used were programmed at the probability of 0,0167 every one second as a certain reinforcer was not yet scheduled for the delivery.

There is no denying the importance of the fact, that the pattern supposed that the scheduled reinforcer should have been used before the next interval began. During the session, the above light and the houselight were illuminated.

During the experiment, three types of experimental conditions were used. In the first type of condition (Suc-such), 0,2ml of the liquid sucrose played the role of reinforcer during all the sessions. In another type (Suc-FoodPel), the liquid-sucrose reinforcers were given during the first half of the full session and Noyes 45-mg sucrose-pellet was utilized as the reinforcer during the second half of the session. Each type of experimental condition was used during a total of 20 sessions which were conducted daily, from five to seven days per week.

Experiment subjects were divided into 2 separate groups. The first group of experimental rats was responding for 1% sucrose (mixed with the tap water) and the second group was responding for the 5% liquid sucroses. The following order of conditions was given to one pair of the subjects from each group: Sucrose-SucrosePellet, Sucrose-FoodPellet, and Sucrose-Sucrose. Another pair of experimental subjects were receiving a reverse order of experimental conditions.

The sucrose concentration was changed for each group if they managed to complete all three conditions. Each pair of rats then had to respond to the same conditions but in reverse order, as they experienced them during the previous session.

Results and Discussion

The table shows the subject’s response to experimentation conditions in the fixed and variable intervals which correspond to Sucrose-Sucrose, Sucrose-FoodPellet, and Sucrose – SucrosePellet situations. The empirical results represent standard error for responding in 2 minutes intervals.

As the results represented in the table show, during the first half of the session, the induction was essentially present. For both levels of sucrose concentration, the response was higher during the first half session, than when food and sucrose pellets were utilized as the reinforcer during the second half of the session.

There is no denying the importance of the fact that the availability of induction did not significantly vary among different pellet types. And thirdly, all pellets provided higher levels of response during the second half of the session than liquid-sucrose concentrations.

Statistical analysis also confirms these hypotheses. Rats respond higher for 5% sucrose than for 1% sucrose and the rate of response significantly varied depending on the half of the session and the type of reinforcer used. However, it should be taken into consideration that the substantial effect of chemical reinforcers during the second halves of the session does not mean that the effect of liquid sucrose and sucrose pellets was equally strong during the second half of a session.

It was also found out that the pellet type of reinforcer does not significantly change experimental results. However, the effect of 5 minutes intervals was significant and it indicated that the rates of response varied during the first halves of the session when the pellets were given during the second halves of the session.

Other effects did not reach the mark of statistical significance. Hence, the abovementioned results support the point of view that the induction could be observed when rats were responding to either 1 or 5% sucrose, and both types of experimental pellets produced the same induction effects.

Responses to the second halves of the sessions showed that different reinforcers maintain varying response levels and rates and these rates significantly change during the second half of the session, accordingly. The interactions between the level of sucrose concentration and the second-half reinforcers were found as significant.

The statistical analysis has proven that a 5-minutes interval is the most significant in defining response levels during the second half of the session and less significant during the first half.

The total results of this experiment show that the induction which was produced by the upcoming reinforcers can not be limited to the utilization of food pellets. Similar induction results were produced by using the solid sucrose pellets as a reinforcer. These results may be the source of certain generalizations. It seems that the abovementioned results run contrary to the idea that the difference in taste between different reinforcers plays its role in the process of induction. However this experiment does not provide empirical grounds for such kind of conclusion, it shows that the opposite point of view is not relevant.

To sum it up, the experiment was conducted and the hypothesis set was proved by the empirical data collected.

References

Bouton, M.E. (2007). Learning and Behavior: A Contemporary Synthesis.

Carlson, N.R. (2007). Physiology of Behavior. 9^th edition. Needham Heights, Mass: Allyn and Bacon.

Kawai, N., & Nakajima, S. (1997). US Postexposure Effect on Conditioned Flavor Preference in the Rat. The Psychological Record, 47(3), 499.

Schwartz, B. and Robbins, S.J (1998). The psychology of learning and behavior. (4^th Ed.). Norton.

Ward, O. B., Ward, I. L., Denning, J. H., Hendricks, S. E., & French, J. A. (2002). Hormonal Mechanisms Underlying Aberrant Sexual Differentiation in Male Rats Prenatally Exposed to Alcohol, Stress or Both. Archives of Sexual Behavior, 31(1), 9.

Wilson, C., & Kaspar, A. (1994). Changes in Immobility Responses in Rat Pups with Maternal Stimuli. Journal of General Psychology, 121(2), 111-120.