0.13 Crystal violet kinetics

1 = k’t+ 1 (second order)(5)

$[\text{CV}{]}_t$ $[\text{CV}{]}_o$

In Equations 3 - 5, $[\text{CV}{]}_o$ is the concentration of crystal violet in the reaction mixture at time zero before any reaction occurs; $[\text{CV}{]}_t$ is the concentration at any time during the course of the reaction. Equations 3, 4b, and 5 are each an equation of a straight line. If a plot of $[\text{CV}{]}_t$ versus time is linear, y = 0 and the reaction is zero order in CV. Similarly, a linear plot of ln $[\text{CV}{]}_t$ versus time indicates a first order reaction in CV, and a linear plot of 1 / $[\text{CV}{]}_t$ versus time indicates second order behavior. In every case, the slope of the resulting straight line would be the pseudo rate constant, k'. All three of these plots will be made to determine the actual value of y and the value of k'.

In order to do the graphing just described, we will need to have data showing how the concentration of CV changes with time. This data will be obtained using the MicroLAB colorimeter at the 590 nm wavelength and the Kinetics program. The light from the LED will pass through the solution containing CV and NaOH and then fall on the system photocell. The photocell circuit will then produce a current in microamps (I) which is proportional to the light intensity striking the photocell surface. This current is divided by the current obtained with the blank, and the result is termed Transmittance.

Solutions of crystal violet obey Beer's Law. Thus, the relationship between the observed current and the concentration of CV is given by

$A_t=-\text{log}(I_t/I_o)=\epsilon \text{bc}$ (6)

In Equation (6), $A_t$ is the reaction solution absorbance at any time t; $I_o$ is the photocell current observed for pure water (the blank value); It is the current observed for the CV reaction mixture at time t, $\epsilon$ is the molar absorptivity of crystal violet; b is the cell path length (2.54 cm for the MicroLAB colorimeter) vial; and c is the molar concentration of CV at time t, $[\text{CV}{]}_t$ . Since $\epsilon$ and b are constants at a given wavelength, it should be clear that the absorbance, $A_t$ , is directly proportional to the concentration of CV at any time during the reaction and can be used in place of $[\text{CV}{]}_t$ in preparing the graphs described above.

Experimental procedure

Part i.

Measurements

Open the MicroLAB program by selecting it, then click on the Kinetics Experiment Icon. Enter the experiment filename (CV then your name) when requested, then click OK. Data will come from the interface. Be sure the MicroLAB interface is connected to the computer and turned on. From that point follow the procedures listed below.

• Before beginning kinetic measurements, the current reading for pure $H_{2}O$ , $I_o$ , will be obtained. Fill a clean, rinsed colorimeter vial about ¾ full with distilled $H_{2}O$ , dry the outside of the cell thoroughly with a KimWipe being careful to remove any finger prints, insert the cell into the colorimeter and place the black cap over the cell. Note carefully and mark the positioning of the cell for future reference.
• Click on the Blank button. The program will now measure $I_o$ for each of the 10 wavelengths, divide each by itself and multiply by 100 to get the 100 % transmittance value.
• Empty the vial and dry it thoroughly inside and out.
• Set the Time Interval to 5 seconds, and the Number of Points to 300.
• Using the buret provided, dispense exactly 9.00 mL of $1\text{.}\text{50}\times {\text{10}}^{-5}$ M crystal violet solution into a clean, dry colorimeter vial
• Using the calibrated plastic dropper provided, add 1.0 mL of 0.050 M NaOH to the CV solution as rapidly as possible without splashing. Cap the vial, rotate it twice to mix the CV/NaOH, place the cell in the colorimeter in exactly the same manner as was used for the blank and cap the colorimeter. All of the operations in this step should be completed as quickly as possible so that the first measurement will be made as close to the beginning of the reaction as possible.
• As soon as the vial is in place and capped, press the Start button, the program will take readings at 5 second intervals for a period of 60 minutes and then automatically stop. If there is a need to stop data collection prior to the end of 60 minutes, click on the Stop button and the program will terminate. It 300 points is insufficient, increase the number of points.
• When the reaction is completed, save the file with the name CV.kin.XM.DH, where CV.kin defines the type of data, XM indicates the NaOH concentration (0.10 or 0.05, etc), and DH is the student’s initials.

Data analysis

• Retrieve your MicroLAB data file under the name you saved it.

Click on the Linear - Zero Order tab at the bottom of the graph. If the reaction you just did was zero order on the concentration of crystal violet, this will show a horizontal straight line. Print this screen as follows:

• Press Ctrl-Print Screen to capture the screen image.
• Open Wordpad by clicking Start>Programs>Accessories>Wordpad.
• Press Ctrl-V to paste the screen image into Wordpad.
• Press Ctrl-P to print the item.
• Repeat step (2), clicking on the Logarithmic - First Order tab. A linear graph in this instance would indicate first order dependence on the concentration of crystal violet. Print this screen also.
• Finally, click on the Inverse - Second Order tab to determine if the reaction is second order in crystal violet. Also print this screen
• With the linear plot you have identified the value of y, i.e., the order of the reaction with respect to CV. Record the value of y in your lab book. The slope of the straight line at the top of the linear regression plot is the best value of k'. Record this value with proper units and to the correct number of significant figures in your lab book. Attach your graphs to your lab book.

Part ii.

Measurements

Recall that the k' just obtained is a pseudo rate constant, whose value depends upon the concentration of ${\text{OH}}^{-}$ , i.e. $k\text{'}=k[{\text{OH}}^{-}{]}^x$ . In this part of the experiment, the value of x will be determined as well as the value of the true rate constant, k.

In Part I of the experiment, 9.00 mL of $1\text{.}\text{50}\times {\text{10}}^{-5}$ M crystal violet and 1.0 mL of 0.050 M NaOH were combined to form the reaction mixture. A second kinetic run will now be made in exactly the same way except that the concentration of NaOH will be doubled to 0.10 M.

• Repeat each of the six experimental steps 4 through 8 using 1.0 mL of 0.10 M NaOH in place of 0.050 M NaOH.

Data analysis

• Repeat data treatment steps 1 through 6 above, and again record the value of k' on your data sheet.
• From the ratio of the two k' values to one another, determine the order of reaction with respect to ${\text{OH}}^{-}$ (the value of x). Clearly indicate your reasoning in evaluating x.

Note: The value of x should be an integer. If your value is not an integer, it is probably due to experimental error (probably in measuring and adding the NaOH solutions). If necessary, round your value to the nearest integer.

• Calculate the value of the true rate constant k using each of the k' values. In the calculations, the concentrations of ${\text{OH}}^{-}$ will have to be adjusted to account for the dilutions which occurred when the NaOH and crystal violet solutions were mixed. Finally, average the two k values obtained. Again, be sure to watch significant figures and use proper units.
• Using the linear plot from your first kinetics experiment, calculate the value of the molar absorptivity, $\epsilon$ , for crystal violet under these experimental conditions. Include units in your answer. The colorimeter vial is 2.54 cm thick. (Hint: The intercept of your linear plot is important.).