Rate Law Determination of Crystal Violet Hydroxylation Revised 5/22/12 RATE LAW DETERMINATION OF CRYSTAL VIOLET HYDROXYLATION Adapted from "Chemistry with Computers" Vernier Software, Portland OR, 1997 INTRODUCTION In this experiment, you will investigate the kinetics of the reaction between crystal violet and sodium hydroxide. The equation for the reaction is shown below: A simplified (and less intimidating!) version of the equation is: (1) CV + + OH à CVOH crystal violet hydroxide ion Kinetics is the study of the speed or rate of a chemical reaction. The differential rate law for the hydroxylation of crystal violet is: (2) rate = -Δ[CV + ] = k [CV + ] m [OH ] n Δt where k is the rate constant for the reaction, m is the order with respect to crystal violet (CV + ), and n is the order with respect to hydroxide ion. To determine the orders of reaction (m and n ), the reaction will need to be done twice. 1
Even though the balanced chemical reaction has a 1:1 mole ratio between CV + and - OH, the actual ratios of reactants used in lab will be much different. The concentration of - OH will be approximately 1000 times that of concentration of CV + in trial 1; and 500 times in trial 2. In both trials, the hydroxide ion is in huge excess and can be assumed constant - neither will change appreciably during the reaction. Therefore, the hydroxide's concentration term and reaction order is grouped with the rate constant, k, to create the pseudo rate constants, k 1 and k 2. This allows for the simplification of the rate law: (3) rate 1 = -Δ[CV + ] = k 1 [CV + ] m where k 1 = k[oh ] 1 n ; [OH ] 1 is 0.020 M. Δt (4) rate 2 = -Δ[CV + ] = k 2 [CV + ] m where k 2 = k[oh ] 2 n ; [OH ] 2 is 0.010 M. Δt To find the reaction order of CV +, m, and the pseudo rate constants, k 1 and k 2, differential rate laws expressed in equations 3 & 4 must be integrated. (You should review integrated rate laws in your lecture text before continuing.) Integrated rate laws, when arranged in line equation form, result in a mathematical function of concentration for the y axis and time on the x axis. The mathematical function of concentration and the slope reveal the values of m, k 1, and k 2. As the reaction proceeds, a violet-colored reactant will be slowly changing to a colorless product. Using a Visible-Near InfraRed (Vis-NIR) spectrometer, the reduction of absorbance with time will be monitored. Because the solutions used in this experiment are dilute, Beer's Law can be invoked. Absorbance is proportional to the concentration of crystal violet (A = εl[cv + ]) and can be used instead of concentration when plotting data (A [CV + ]). A blank is needed to calibrate the spectrometer and correct for any impurities in the solvent (water) that may also be absorbing at λ max. Because, k, the actual rate constant, does not change (and is the same in both trials), the order of reaction with respect to OH (n) is found from the ratio of the pseudo rate constants and the ratio of the concentrations of hydroxide ion used in trials 1 and 2: (5) k = k 1 / [OH ] n 1 = k 2 / [OH n ] 2 (6) k 1 / k 2 = ([OH ] 1 / [OH ] 2 ) n To solve for n, apply the rule of logarithms: (7) n = log (k 1 /k 2 ) / log ([OH ] 1 / [OH ] 2 ) 2
SAFETY Wear safety goggles and lab aprons at all times in lab. Sodium hydroxide is caustic and can cause burns. Wash any affected areas immediately with cold water. Crystal violet leaves stains when spilled. Protect skin and clothing from contact and wash hands and glassware thoroughly when experiment is finished. PROCEDURE Part A: Calibrate & Blank the VIS-NIR Spectrometer Work in pairs. Wear safety goggles and lab aprons at all times. CAUTION: Sodium hydroxide solutions are caustic. Avoid spilling it on your skin or clothing. Crystal violet is a biological stain and it will stain skin, clothing and glassware. Avoid spills and wash hands thoroughly before leaving lab. 1. Obtain a VIS-NIR spectrometer from the stockroom. Use the USB cable to connect the VIS- NIR Spectrometer to the computer. (The cuvette holder/light source should be attached to the spectrometer.) Open Logger Pro. The spectrometer should automatically be recognized by the Logger Pro program. 2. Then calibrate the spectrometer by choosing Calibrate Spectrometer from the Experiment menu. The calibration dialog box will display the message: Waiting.seconds for lamp to warm up. (The minimum warm up time is one minute.) Note: For best results, allow the spectrometer to warm up for at least three minutes. Insert the blank cuvette (filled with deionized water) in the sample compartment. Click OK. 3. To create an absorption spectrum of crystal violet, fill a cuvette with ~2.0 x 10 5 M crystal violet solution and place in the spectrometer. Go to the experiment menu and choose Data Collection. Choose Full Spectrum for the Mode and Press Collect. Label any significant peaks with wavelengths. (The wavelength with the maximum absorbance should be labeled λ max. All absorbances should be recorded at this same wavelength.) Remove the "rainbow" background spectrum by right clicking on the spectrum, go to graph options, and uncheck "draw visible spectrum". Print copies of the spectrum for you are your partner. 3
Part B: Monitoring Change in Absorbance over Time, Trial 1 1. Prepare the computer to collect absorbance versus time data. Set λ max : Click on the Configure Spectrum button next to the icon for linear regression and curve fit. Click on the bubble for Absorbance vs. time. On the right side of the menu box, select the maximum wavelength (λ max ) found in Part B, #3 and then click OK. Go to the Experiment menu and choose Data Collection. Choose Time Based Entry for Mode and set the length to 24 minutes. Click Done. 2. The stockroom will follow these procedures to create aqueous solutions of NaOH and crystal violet: Place ~0.8 g NaOH in a 1L volumetric flask, dilute to volume with DI H 2 O. Place ~0.01 g crystal violet in a 2L volumetric flask, dilute to volume with DI H 2 O. Set up the calculation before coming to lab, but determine the exact solution concentrations with the more accurate masses provided on the labels of the reagent bottles. 3. Obtain 5.0-mL of both solutions in graduated cylinders. 4. To initiate the reaction, simultaneously pour the 5-mL portions of crystal violet and sodium hydroxide into a 100-mL beaker and stir the reaction mixture with a stirring rod. Click Collect. Important Note: Because initial data is sometimes sporadic, readings are not taken until 3 minutes have passed. Empty the water from the cuvette. Rinse the cuvette twice with ~1-mL amounts of the reaction mixture and then fill it 3/4 full. Do not put the cuvette in the spectrometer yet. To keep the solution from warming, remove the cuvette from the spectrometer between readings. You will need to be careful not to miss when the spectrometer is taking a reading it is automatic. 5. After about three minutes have passed since combining the 2 solutions, wipe the outside of the cuvette, place it in the cuvette slot of the spectrometer. Wait for the absorbance reading to be taken, then remove the cuvette from the spectrometer. After 1 minute have elapsed, again place the cuvette in the spectrometer, wait for the absorbance to be taken, then remove the cuvette again. Continue in this manner, collecting data about once every minute, until 24 minutes have elapsed. Data collection will end after 24 minutes. Place the solution in a 100 or 250 ml beaker for neutralization at the end of lab. 6. Print out the raw data and plot shown on the computer screen. Analyze the data graphically to decide if the reaction is zero, first, or second order with respect to crystal violet: 4
Zero Order: If the current graph of absorbance vs. time is linear, the reaction is zero order. First Order: To see if the reaction is first order, plot the natural logarithm (ln) of absorbance vs. time. If this plot is linear, the reaction is first order. See instructions in Step 6 to plot ln (A) vs. time. Second Order: To see if the reaction is second order, plot the reciprocal of absorbance vs. time. If this plot is linear, the reaction is second order. See instructions in Step 7 to plot (1/A) vs. time. 7. To create a plot ln Absorbance vs. time: Choose New Calculated Column from the Data menu. Enter the name and correct formula for the column into the appropriate boxes. Choose ln () from the Function list. Then select Absorbance from the Variables list. In the Equation edit box, you should now see displayed: ln( Absorbance ). Click OK. Choose Graph from the Insert menu to display the graph of ln absorbance vs. time. To see if the relationship is linear, click the Linear Regression button,. 8. Use the method described in Step 6 to create a plot a graph of 1/Absorbance vs. time. To enter the correct formula for the column into the Equation edit box, type "1" and "/", then select "Absorbance" from the Variables list. 9. Choose the linear plot from Steps 5-7 (Absorbance, ln Absorbance or 1/Absorbance vs. time), and print a copy. (Note: Save to a disk first in case of a crash.) Click the vertical-axis of the graph. Of "Absorbance", "ln Absorbance", or "1/Absorbance", check only the box of the choice that gave a linear plot. Click OK. Print a copy of the Graph window. Enter your name(s) and the number of copies to be printed. Note: Be sure the linear regression and the regression statistics box curve is displayed on the graph. (The slope of the line is needed to determine the pseudo rate constant, k 1.) Part C: Monitoring Change in Absorbance over Time, Trial 2 1. Prepare 10.00 ml of ~0.010 M NaOH by diluting the NaOH solution used in Trial 1. (Your procedure should clearly show your calculations, the exact NaOH concentration, and the glassware used to perform the dilution.) Repeat steps 2-9 in Part B using 5.00 ml of the ~0.010 M NaOH solution just made. 5
2. Combine Trial 2 s and Trial 1 s solution. Add small amounts of dilute HCl(aq) solution and check the solution with ph paper. Once ph 8, pour the neutralized solution down the drain. DISCUSSION & CALCULATIONS (1) What wavelength should be used to measure the absorbances for the kinetics trials? (2) Examine your plot. What is the order of reaction (m) with respect to crystal violet? (3) Calculate the pseudo rate constant, k 1, using the slope of the linear regression line. (Remember, k 1 or k 2 = slope for zero and first order reactions and k 1 or k 2 = + slope for second order reactions). (4) Write the correct rate law expression for the reaction, in terms of crystal violet only (omit OH ). (5) Calculate the half-life of the reaction (in minutes) using the pseudo rate constant, k 1, and the appropriate half-life equation. (6) Calculate the pseudo rate constant, k 2, using the slope of the linear regression line from the graph from Part C. (7) Find the order of reaction (n) with respect to hydroxide ion: n = log (k 1 / k 2 ) / log ([OH ] 1 / [OH ] 2 ) Do not round off value for n if it is a decimal or fraction. Report this value to 2 sig figs. (The concentration of OH was 0.020 M in Part A and 0.010 M in Part B.) (8) Now round off the value for n to an integer (0, 1, 2, etc.). Write the complete rate law expression using both CV + and OH in the expression with their appropriate orders. 6
QUALITATIVE ERROR ANALYSIS 1. What modifications could be made to the procedure to better account for random (indeterminate) errors? 2. List three potential systematic (instrumental, methodological, or personal) errors that could be made in this experiment. (Note: Be specific, systematic errors are in the details. For example, losing your solution because you knocked over the cuvette is not a systematic error it s a gross one.) 3. Did any gross errors occur? Did you mess up? Did the equipment or instrumentation fail? 7