Experiment 7. Determining the Rate Law and Activation Energy for the Reaction of Crystal Violet with Hydroxide Ion
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1 Experiment 7. Determining the Rate Law and Activation Energy for the Reaction of Introduction In this experiment, you will observe the reaction between crystal violet and sodium hydroxide. Crystal violet is available as the chloride salt, which completely ionizes in water. The equation for the reaction of crystal violet cation with hydroxide ion is: + C OH + OH C A simplified version of the equation is: CV + + OH - CVOH crystal violet cation hydroxide ion violet colorless colorless The rate law for this reaction is of the form: rate = k[cv + ] x [OH - ] y, where k is the rate constant for the reaction, x is the order with respect to crystal violet (CV + ), and y is the order with respect to the hydroxide ion. In part A of this experiment, you will acquire data to find the order with respect to crystal violet (x), but not the order with respect to hydroxide (y). To simplify the data treatment, the hydroxide ion concentration is -4,000 times as large as the concentration of crystal violet. During the course of the reaction, the hydroxide-ion concentration remains essentially constant so the rate of reaction depends only on the crystal violet. As the reaction proceeds, a violet-colored reactant (crystal violet) reacts with hydroxide ion to form a colorless product. Using the 565 nm (green) light source of a colorimeter, you will monitor the absorbance of the crystal violet solution with time. We will assume that absorbance is proportional to the concentration of crystal violet (Beer s law). You will determine the molar absorptivity, ε, of crystal violet and calculate concentrations from the measured absorbances. The path length of the cell is 1.0 cm. With the concentration data the following three graphs can be plotted: Chem 14 Experiment 7 Page 1
2 Concentration vs. time: A linear plot indicates a zero order reaction (k = slope). ln Concentration vs. time: A linear plot indicates a first order reaction (k = slope). 1/Concentration vs. time: A linear plot indicates a second order reaction (k = slope). Once the order with respect to crystal violet has been determined, you will also finding the rate constant, k, for this experiment. This rate constant includes the effect of hydroxide ion so it is more properly termed a pseudo-rate constant. In part B of this experiment, you will determine the order in hydroxide ion in an experiment that will use the change in initial rate of reaction as a function of hydroxide ion concentration. Rather than measuring the initial rate, you will measure the observed rate constant for crystal violet because the observed rate constant includes the hydroxide ion and its order. In part C you will use data in which you measure the rate constant at different temperatures to determine the activation energy of the reaction. Apparatus and chemicals LabQuest with SpectroVis, plastic cuvettes, two 10-mL graduated cylinders, 50-mL beaker, stirring rod, alcohol thermometer, DI water, 0.10 M NaOH(aq), M crystal violet(aq). Safety Precautions: Crystal violet solutions may cause skin and eye irritation. Sodium hydroxide solutions are caustic and will cause skin burns and are extremely hazardous to your eyes. Any skin contact with either chemical should be immediately washed. Wash your hands with soap and water before leaving the lab. Procedure Prepare a data page in your notebook to accommodate the data. Prepare for lab as usual, with protective clothing, tied-back hair, nitrile gloves and safety goggles. Part A. Integrated Rate Laws: Determination of the order in Crystal Violet. 1. Turn on the LabQuest. The LabQuest app will launch automatically and the meter screen will be displayed.. Calibrate SpectroVis a. Fill a cuvette about ¾ full with distilled water and place it in the cuvette holder. Align the cuvette so a clear side of the cuvette is facing the light source. b. Choose Calibrate USB: Spectrometer from the Sensors menu. Allow the unit to warm up for at least 5 minutes before continuing. At the prompt, select Finish Calibration. After the message Calibration Completed. appears, select OK. 3. To determine the molar absorptivity, we need to measure the absorbance of a crystal violet solution. Mix 10.0 ml of M crystal violet with 10.0 ml of deionized water in the 50 ml beaker. Using a beral pipette, transfer some of the mixture into a cuvet Chem 14 Experiment 7 Page
3 to rinse it and then fill it ¾ full with the mixture. Place the sample in the cuvette slot of the SpectroVis. 4. Start the data collection. Tap the red Stop button to end the data collection. 5. The wavelength of maximum absorbance (λ max) is automatically selected, it should be around 581nm. 6. Record the absorbance in your lab notebook and remove the cuvette and dispose of the contents. Beer s law provides the relationship between absorbance and concentration: A = εbc Use Beer s Law to determine the molar absorptivity of crystal violet. ε = A/bc The path length, b, is 1.0 cm. Remember that you diluted the crystal violet when you mixed it with water so its concentration is NOT M. Record your data and calculations in your lab notebook. 7. On the Meter screen, tap Mode. Change the data-collection mode to Time Based. The rate should already say 0.5 samples/s and an interval of s/sample. Change the Duration to 440 seconds. It should then say you are collecting 1 samples. Select OK when you are ready to proceed. A message will appear warning you to either save or discard the full spectrum run. Save this run. 8. Use a 10-mL graduated cylinder to measure out 10.0 ml of 0.10 M NaOH solution. Caution: Sodium hydroxide solution is caustic. Avoid spilling it on your skin or clothing. 9. Use another 10-mL graduated cylinder to measure out 10.0 ml of M crystal violet solution. Caution: Crystal violet is a biological stain. Avoid spilling it on your skin or clothing. 10. You are now ready to begin monitoring data. To initiate the reaction, simultaneously pour the 10-mL portions of crystal violet and sodium hydroxide into a 50-mL beaker and stir the reaction mixture with a stirring rod. Rinse the cuvet with ~1-mL of the reaction mixture and then fill it ¾ full. Place the cuvet in the cuvet slot of the SpectroVis with the clear side facing the path of the light. Start the data collection. Place the alcohol thermometer in the remaining solution in the beaker and record the temperature (you will use this in part 3). During the ~7-minute data collection, observe the solution in the beaker as it continues to react. Data collection stops after ~7 minutes. Remove the cuvette from the SpectroVis compartment, and discard the contents in a labeled beaker for disposal. 11. Click on the X/Y table button on the top toolbar. The first column of the table should read Time (s) and the second column should read your max wavelength. Click on Table and New Calculated Column. Under name, change it to Concentration. Under Equation Type select X/A. Column for X should be the your Max Wavelength and A is your value of ε. We can leave out the path length since it is 1.00 cm. Click ok. This will pull up the graph. 1. We are going to add another column with the LN(Concentration). Click on Table and New Calculated Column. Under name, change it to LN(Concentration). Under Equation Type select Aln(x). Column of X is Concentration and A is 1. Click Ok. 13. We are going to add another column with the 1/Concentration. Click on Table and New Calculated Column. Under name, change it to 1/Concentration. Under Equation Type Chem 14 Experiment 7 Page 3
4 select A/X. Column of X is Concentration and A is 1. Click Ok. We now have data for zero, first and second order integrated rate laws. Zero Order: If the graph of concentration vs. time is linear, the reaction is zero order. First Order: If the graph of ln concentration versus time gives a straight line, then the reaction is first order. Second Order: If the graph of 1/concentration versus time gives a straight line, then the reaction is second order. 14. To better determine which order the reaction is with respect to crystal violet, we can calculate r values, which tell us the fraction of variability in the data that is explained by the linear relationship. A value close to 1 indicates a better straight line. We also need the slope and intercept values for the straight line graph. On the graph screen, go to Analyze, Curve Fit, and make sure the check box is selected for the graph you are analyzing. Under Fit Equation, choose Linear. Record the slope, intercept, and r value in your notebook. Take a photo of this screen for your lab report. Data Type Slope Intercept r Concentration ln (Concentration) 1/Concentration 15. Determine the order with respect to crystal violet by identifying the integrated rate law associated with the dataset that produced the best straight line. You will use the rate constant (determined from the slope of this graph) in the subsequent parts of this lab. Part B. Differential Rate Laws: Determining the order in hydroxide ion. Once you determine the order in crystal violet, you can determine the order in hydroxide ion. The data will be obtained in the same manner but at different concentrations of hydroxide ion. The concentration of hydroxide ion will still be in large excess, so it does not change in the course of the reaction, but if the concentration of hydroxide changes from 0.05 to 0.10 M and the relative rate of reaction changes from 1 to, you can deduce that the reaction is first order in hydroxide ion. If the relative rate changed from 1 to 4, it would be second order, and if it did not change the reaction would be zero order in hydroxide ion. Make M NaOH from 10.0 ml of 0.10 M NaOH and 10.0 ml of water. Label the beaker M NaOH. Make 0.05 M NaOH from 5.0 ml of M NaOH and 5.0 ml of water. Label the beaker 0.05 M NaOH. Set up the LabQuest as you did for the concentration-time experiment, except the Duration should be changed to 10 seconds. Collect the absorbance as a function of time for the following two solutions (all at room temperature). Chem 14 Experiment 7 Page 4
5 ml of 0.05 M NaOH solution ml of M crystal violet. (Initial concentration of NaOH = 0.05 M.) ml of 0.05 M NaOH solution ml of M crystal violet. (Initial concentration of NaOH = M.) You already have data for 10.0 ml of 0.10 M NaOH ml of M crystal violet (0.050 NaOH) from the results of the experiment in Part A. The data you need will be the rate constant (which is calculated from the slope) as a function of initial NaOH concentration. Prepare a table in your lab notebook like the one shown below. Rate constant [NaOH]initial Use the relative ratio method to determine the order with respect to hydroxide ion. Part C. Arrhenius Equation: Determining the activation energy. Repeat the minute experiment with 0.10 M sodium hydroxide and crystal violet for two other temperatures (heated and cooled). Use the procedure in Part A, including measuring temperature of the mixed solutions, except changing the duration to 10 seconds. At the end of the lab, you will have the rate constant at three different temperatures. Prepare a table of rate constants and temperatures in your lab notebook (see below). From the dependence of the rate constant on temperature you can determine the activation energy of the reaction. Rate constant Temperature Lab Report Grading Rubric (10) Pre-lab Exercise () Title (3) Name of investigator(s) and date (15) Abstract (10) Experimental (procedures and apparatus used in the experiment) (30) Results. Include the calibration graph(s) and calibration statistics from Excel. (30) Discussion and Conclusions. Discuss the main points and results of the lab. Explain what each spectrum shows. Show sample calculations and use statistics if possible. Include the answers to the questions enumerated individually so they are easier to grade. Chem 14 Experiment 7 Page 5
6 This experiment is done in pairs with each partner working together in the lab but submitting a completely individual lab report. Questions. 1. Write the correct rate law expression for the reaction in Part A in terms of the crystal violet concentration (omit the hydroxide ion concentration).. The rate constant, k, is sometimes referred to as the pseudo rate constant, because it does not take into account the effect of the other reactant, OH -. Explain the difference between the pseudo rate constant that you reported and the actual rate constant. 3. Use the change in rate constant with hydroxide concentration to determine the order in hydroxide ion concentration. 4. Use all your data and write the overall reaction rate law including both crystal violet and hydroxide concentrations and the value for the rate constant including correct units. You know the orders for each reactant, but in order to find the rate constant for the overall reaction, we need to calculate a rate. To find rate, use the straight line equation from Part A to solve for concentrations at time = 0 and some other time (say 1 sec). Calculate rate as Δconcentration/Δtime. With the rate of reaction (in M s -1 ), the initial concentration of crystal violet with Part A, the initial concentration of hydroxide in Part A, and the orders, the overall rate constant and law can be determined. 5. Is the rate law the same at all temperatures? Explain. 6. Use the temperature dependence of the activation energy to determine the activation energy for the reaction. Estimate the uncertainty in the activation energy. References This experiment is adapted from: tion/ Chem 14 Experiment 7 Page 6
7 Experiment 7 Pre-Lab Exercise Name: Section: In the reaction of A + B C only A absorbs light. The absorbance decreases in the course of the reaction as shown below. The two graphs of absorbance v. time are at different concentrations of B. 1. Calculate the orders in [A] and [B].. Design an experiment to determine the rate constant in terms of molarity and seconds. 3. Look at the MSDS for crystal violet solution and crystal violet solid. Identify the most serious hazards of both forms and the protective measures that can minimize risk. Chem 14 Experiment 7 Page 7
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