Determination of Reaction Rate Law from the Reaction of Crystal Violet with Sodium Hydroxide ______________________________________________ Abstract: This experiment helps determine the rate of reaction of crystal violet while it reacts with sodium hydroxide with respect to crystal violet. The amount of sodium hydroxide is varied in this experiment while crystal violet is kept at a constant. The transmittance of crystal violet is observed and recorded using a colorimeter and the data obtained is used to plot graphs which are manipulated using LoggerPro software to produce the desired outcome; rate of reaction of crystal violet.

Upon completion of the experiment it was seen that the rate of reaction of crystal violet turned out to be 1 which meant the reaction was first order with respect to crystal violet. This was deduced upon plotting the graph of ln Absorbance versus time of crystal violet and by drawing the line of best fit, which showed that the slope graph was 1 which is the rate of reaction. This whole experiment was based upon the equation: Rate= k [CV+] [OH-], where k stands for the rate constant.

Introduction: Kinetics, which is the study of how fast a reaction takes place or in other words the rate of a reaction, is the main ideology in this experiment. Reaction rates can be measured in a number of ways: by monitoring the amount of product formed, by measuring the loss in mass of reactants, for reactions involving gaseous products measuring the volume of gas produced, by electrolytic conductivity, pH measurement or for colored reactants or products measuring the transmittance by the use of a colorimeter.

In this experiment the last method of measurement is used which is colorimetry. Colorimetry is a method of determining the kinetics of a reaction using a spectrometer which observes the amount of light that is absorbed or transmitted through a colored solution. As a reaction proceeds, the reactants either fades away or the product forms the color. By monitoring these changes the amount of product formed or reactant used up with respect to time can be monitored. The amount of light that is absorbed by a colored substance can be measured by calculating percentage absorbance or transmittance.

A very helpful device known as colorimeter which is present in almost all equipped labs makes this quite simple to deduce. The machine displays the amount of light that passes through or absorbed by the substance. This instrument is based on the optics law or more commonly known as Beer-Lambert law, which is used in measuring the concentration of a solute in contrast to its absorbance. The colorimeter measures the wavelengths of different solutions as they vary. Distilled water is used as a reference in this experiment as it contains no colored elements and has a value of zero when inserted into the colorimeter.

Crystal violet, a purple dye commonly used in inks or printers is reacted with sodium hydroxide, commonly known as caustic soda which is a powerful base. Sodium hydroxide is a colorless solution which when reacted with crystal violet causes it to lose its purple color and form a colorless product. The purpose of this experiment is to determine the order of the reaction with respect to crystal violet by using colorimetry. The amount of crystal violet is kept at a constant during the whole experiment while various amounts of sodium hydroxide, each of varying concentration are used.

This method of determining rates is called the isolation method. Amount of reactant used with respect to time or the rate of reaction can be determined by plotting a graph of concentration versus time for the reactant if the reaction is first order. The slope is a measure of how much reactant is used per unit of time. As the concentration of reactant reduces in a chemical reaction, the slope is a negative value, hence by considering the absolute value of the slope, the rate of reaction of that reactant can be found for the reaction.

If the reaction was to be of second order, a graph of ln of concentration versus time would produce the rate of reaction by determining the slope like before. It must be noted that only the absolute value of the slope matters in this situation. Third order reactions have somewhat a similar story except they require a plot of 1/concentration versus time to determine rate of reaction. When all three graphs are plotted, the graph with the line of best fit, or the one in which all point seem to be on a straight line is the correct one for the reaction. This is easily drawn using the LoggerPro software.

When all three graphs are drawn, the graph with the best fit line and lowest root mean square error, or the lowest deviation from the best fit line, is the graph to be used to determine reaction kinematics. This knowledge is acquired from the equations of the integrated rate laws which are explained in the textbook. The solutions are mixed in small amounts in cuvettes and inserted into the colorimeter, which reads the percentage transmittance during the time period. The colorimeter has an enclosed space for the cuvette to be inserted making sure light from other sources does not interfere with the reaction, hence providing accurate results.

The rate of the reaction is determined by using the equation: Rate= k [CV+] [OH-], where k is the rate constant for the reaction. Materials: Solutions of crystal violet and sodium hydroxide were available in the laboratory which were previously prepared of concentrations 2. 00 E-5 and 2. 00 E-2 respectively. Deionized water was used in calibration while cuvettes were used to transfer substances into the colorimeter. Magnetic stirrers along with stir bars were used in mixing the reagents together which were transferred to the beaker via pipettes to ensure accurate results were produced.

Methods: Three solutions were made to be put into the cuvttes. The first of them contained 20ml of crystal violet and 20ml of sodium hydroxide. The second had 20ml crystal violet along with 10ml of distilled water and 10ml of sodium hydroxide. The third solution contained 20ml crystal violet with 15ml distilled water and 5ml sodium hydroxide. The reagents were mixed well in beakers, each containing the different solutions and were stirred sufficiently on a magnetic stir plate. The colorimeter was calibrated with distilled water which set a reference value of zero making sure that all succeeding readings would be accurate.

A small sample of the first solution was placed in a cuvette which was inserted into the colorimeter. Data collection started immediately and was recorded for 15 min, the whole duration of the cuvette in the colorimeter. The different values of transmittance were recorded and the data was plotted into a graph with the help of LoggerPro software. The same procedure was repeated for the second and third solution and thereby obtaining three different Absorbance versus time graphs for each. Care was taken at every step of this experiment to ensure that errors were minimized to the fullest.

The colorimeter was calibrated every time before placing a new cuvette into it to make sure results were accurate. The dye was handled with care as it leaves stain marks on any surface it is spilled on. Goggles were worn throughout the experiment to keep the eyes from risk of exposure. Safety gloves were worn to handle all reagents as one of them, sodium hydroxide, is a strong base and has significant corrosive properties. The graphs obtained from the three solutions were then manipulated using the LoggerPro software which enables he application of various calculus functions to produce different graphs, all of which lead to determination of the order of the reaction. A line of best fit was applied to all three graphs and the slopes (m), absorbance value at 7min (a) and the root mean square error (RMSE) were recorded. The first graph was reopened and a new column of ln Absorbance was made, using this data, another plot of ln Absorbance versus time was created using LoggerPro. This was done again for the second and third solutions.

The graph of Absorbance versus time for the first solution was opened again to produce a graph of 1/Absorbance versus time which was saved. All of these were made possible using LoggerPro. All of the graphs produced had a line of best fit through them which made it easy to determine slope and RMSE values for each of them along with absorbance values at 7 minutes, which is the half life of the reaction period or half the time for the data to be collected. All of the data collected from the graphs were tabulated and values were used in determining the reaction rate of the reaction.

Results: Figure 1: Graph slowing relationship of Absorbance versus time for first solution Figure 2: Relationship of ln Absorbance versus time for first solution Figure 3: Plot of 1/Absorbance versus time for first solution Figure 4: ln Absorbance versus time plot for solution 2 Solution| Order(p)| ? RMSE? | 1| 0| 0. 01641| 1| 1| 0. 01129| 1| 2| 0. 3810| Table 1: RMSE values for the three graphs for solution 1 Solution| Order (p)| [OH-]0/M| Kps= -Slope(m)*| 1| 1| 10. E-3| 0. 09287| 2| 1| 5. 0E-3| 0. 1238| 3| 1| 2. 5E-3| 0. 01038| *(m= slope from plot of ln Absorbance versus time)

Table 2: Slopes of the different ln Absorbance versus time for three graphs Figure 5: Plot of kps (slope) versus [OH-]0 Figure 6: Graph of ln kps versus ln [OH-]0 Solution| Order(p)| Slope (m)| Value at 7 min (a)| RMSE| ? RMSE/a? | 1| 0| -0. 02360| 0. 271| 0. 01641| 0. 0605| 1| 1| -0. 09287| 0. 271| 0. 01129| 0. 0416| 1| 2| 0. 40210| 0. 271| 0. 3810| 1. 405| 1| 1| -0. 09287| 0. 271| 0. 01129| 0. 0416| 2| 1| -0. 12380| 0. 134| 0. 01566| 0. 1169| 3| 1| -0. 010380| 0. 492| 0. 00693| 0. 0141| Table 3: Data obtained from all the graphs plotted

It was observed during the reaction that the color changed from purple to colorless at the end when taken out of the cuvette. Discussion: Table 1 shows the absolute (RMSE /a) values for the first solution. The RMSE values are obtained from the graphs produced from solution 1(graphs 1, 2 and 3). The graph with the least absolute RMSE/a value is the one with the best fit line with the greatest accuracy; hence the graph 2 or the plot of ln Absorbance versus time for solution 1 is the most accurate one as it has an absolute RMSE/a value of 0. 129. Thus it can be deduced from the table that the reaction is first order with respect to crystal violet. Since it is now known that the reaction is first order with respect to crystal violet, the functional relationship for p=1 is: ln Absorbance= [ln Absorbance]0- kpst; This equation is familiar since it is one of the integrated rate law equations as seen previously. First order reactions are determined if the plot of ln Absorbance versus time have a line of best fit which is accurate.

Thus the equation above shows that the best fit line from the plot would equal to –kps. Therefore the kps values would be equal to negative of the slopes of ln Absorbance versus time graphs for all three solutions which is depicted in Table 2. To determine the order of reaction with respect to [OH-] some more calculations are required and more graphs are required to be plotted. The kps values obtained from Table 2 along with the [OH-]0 values aid in the plotting of another kps versus [OH-]0 graph. The graph that is obtained is shown in Figure 5.

To double check the accuracy of the graph, a second graph of ln kps versus ln [OH-]0 is plotted which would be the graph if the reaction was to be of order 1 with respect to [OH-] which is depicted in Figure 6. When the two graphs are compared to each other and their slopes and RMSE values compared from the data collected in Table 3, it is seen that the reaction is actually in fact order 1. 5 which when rounded off to the nearest integer would be equal to 1. q= slope of plot of ln kps versus ln [OH-]0= 1. 581 as seen from Figure 6.

The RMSE value is also a very low value which means that this value would be very accurate and hence the reaction would be first order with respect to sodium hydroxide. The discrepancy in the final value of q can be accounted for by transfer losses, when the reagents were being transferred from the pipette to the beaker; some of it remains in the pipette and causes the concentration to be a little lower than actually reported. It should also be noted that the same cuvette was not used throughout the experiment.

Different cuvettes are made from different plastics from varying compositions which mean they have different permeability which doesn’t allow the same wavelengths of light to pass through all of them, thus the colorimeter reads differently which causes errors. The reaction starts off with a purple color as crystal violet is a purple solution and sodium hydroxide is colorless. As time elapses, the violet color starts to fade away and the solution becomes colorless as their product is a colorless aqueous solution.

Conclusion: Thus the above experiment concludes that the reaction was first order with respect to crystal violet and also first order with respect to sodium hydroxide. The overall reaction order was 2 with respect to crystal violet and sodium hydroxide. The overall of the rate law for the reaction would be: Rate: k [CV+] [OH-]. To ensure results are more accurate in the future, a single cuvette should be used when carrying out the whole experiment and all of the reagents must be transferred efficiently without loses to and from the beaker to ensure 100% efficiency along with using proper safety equipment while handling chemicals.

References: 1. Atkins, P. W. (1978). Physical chemistry. San Francisco: W. H. Freeman. 2. Allen, J. P. (2008). Biophysical chemistry. Malden, MA: Blackwell Pub. 3. Lindon, J. C. , Tranter, G. E. , & Holmes, J. L. (2000). Encyclopedia of spectroscopy and spectrometry. San Diego: Academic Press. Appendix: Solution 1: Order 0, ? RMSE/a? = 0. 01641/0. 271= 0. 0605 Order 1, ? RMSE/a? = 0. 01129/0. 271= 0. 0416 Order 2, ? RMSE/a? =0. 3810/0. 217= 1. 4050 Solution 2, Order 1, ? RMSE/a? =0. 01566/0. 134= 0. 1169 Solution 3, Order 1, ? RMSE/a? = 0. 00693/0. 492= 0. 0141

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