Chemistry Lab - Kinetics of Crystal Violet

KINETICS: RATE LAW DETERMINATION OF THE CRYSTAL VIOLET/SODIUM HYDROXIDE REACTION INTRODUCTION: The field of chemistry that is concerned with studies of reaction rates is called chemical kinetics. It can be qualitative (e.g. a reaction can be described as being either "slow" or "fast") or it can be quantitative with such terms as obtaining a "specific reaction rate constant" for a reaction, or obtaining an "order" of a reaction. Quantitative studies lead to very important predictions not only about how fast a reaction proceeds and how much of a product will form after a certain time, but detailed studies can lead to understanding mechanisms of reactions. Consider the general reaction: A+B →C [1] The rate of this reaction can be measured by experimentally determining the amount of reactants A or B that is consumed as a function of time, or the amount of C that is formed as a function of time. Choosing which species to observe is usually a matter of convenience. Mathematically, the rate of reaction monitoring the concentration of A can be expressed as follows: Rate of disappearance of A = _ change in concentration of A = time required for change _ ∆[A] ∆t In most cases, the overall rate of the reaction will depend on the concentrations of the reactants. Rate = k[A] m[B]n [2] where [A] and [B] are the molar concentrations of species A and B, m and n are the powers to which the respective concentrations must be raised to describe the experimental rate, and k is the specific rate constant. A main goal in kinetic studies is to determine the numerical values of m and n from experimental data. Suppose that we found m = 2 and n = 1 for the hypothetical reaction shown in [1]. Then, the rate law would be expressed as: Rate = k[A] 2[B] [3] It should be apparent from equation [3] that if the concentration of B were doubled (keeping [A] the same) the reaction rate would double. On the other hand, if the concentration of A were to be doubled (keeping [B] the same) the rate would increase by a factor of four because the rate of the reaction is proportional to the square of the concentration of A. The powers to which the concentrations in the rate law are raised are called the order of the reaction. In this last example, the reaction is referred to being second order in A and first order in B. The overall order of the reaction is the sum of all the exponents: in the present example the overall reaction would be described as being third order. It is possible to experimentally determine the order of a reaction by noting the effects of changing reagent concentrations on the rate at which the reaction proceeds as explained above. It should be noted, however, that the order of a reaction is not necessarily dependent on the stoichiometry of the reaction. Thus a reaction of the general form: 2A + B → C [4] may have a rate law that is first order with respect to A and first order with respect to B. The k in the rate law is called the specific rate constant . It has a definite value that is independent of the concentration. It is characteristic for a given reaction and is temperature dependent. Once the rate of a reaction is known as a function of concentrations, the value of k can be calculated. Determining the rate law, rate constant and reaction order of a chemical reaction. There are several ways to determine the rate law, rate constant and reaction order of a chemical reaction. In this experiment, you will determine how the concentration of a reactant changes as function of time. By comparing how the experimental data follow concentration-time behavior for reactions with different rate laws, you can determine whether the reaction follows a zero, first, or second order kinetic law. As described in your text: if a reaction is zero order, a plot of concentration [C] vs time gives a straight line if a reaction is first order, a plot of ln [C] vs time gives a straight line and if the reaction is second order, a plot of 1/[C] vs time gives a straight line By analyzing the resulting plot, you can obtain the order of the reaction and evaluate the specific reaction rate constant. In this experiment, you will observe the reaction between crystal violet and sodium hydroxide. The relationship between concentration of crystal violet and the time elapsed during the reaction will be studied spectroscopically with the use of Spectronic 20 spectrophotometer. Under the assumption that absorbance is proportional to concentration of crystal violet (Beer's Law) the order of the reaction with respect to crystal violet will be determined by graphical analysis. The order with respect to sodium hydroxide will be determined next by keeping the concentration of crystal violet constant and changing the concentration of sodium hydroxide. Once the order with respect to crystal violet has been determined, you will also be finding the rate constant, k, and the half-life for this reaction. The Experiment: The equation for the reaction between crystal violet and sodium hydroxide is shown below: N(CH 3) 2 N(CH 3 ) 2 OH C+ N(CH 3 ) 2 + OH – N(CH 3 ) 2 C N(CH3 )2 N(CH 3) 2 A simplified version of the equation is:   CV+ CVOH + OH(crystal violet) (hydroxide) The rate law for this reaction is in the form: rate = k[CV +]m[OH-]n, 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 the hydroxide ion. By keeping the concentration of [OH -] very large compared to the concentration of [CV+], for all practical purposes the concentration of [OH-] remains constant and does not change (the system is swamped with [OH-]. In fact the technique is called “swamping”. The concentration of crystal violet will change dramatically though, allowing the order and rate constant with respect to crystal violet to be determined with only one reaction. The rate constant obtained in this manner is called the pseudo rate constant (k’), because it only applies to part of the reaction. The reaction is said to follow pseudo m th order kinetics. Under these conditions, the rate equation simplifies to: Rate = k’[CV+]m, where the pseudo rate constant k’ = k[OH -]n. Now, in order to evaluate n and k, two kinetic runs with different excess concentrations of [OH-], say [OH,1]and [OH -,2] are required. Each kinetic run will give different pseudo rate constants k1’ and k2’, where k1’ = k[OH-,1]n k2’ = k[OH-,2]n If the two [OH -] concentrations are known, a simultaneous solution of these two equations provides the values of the value of n and k. k1’/k2’ = (k[OH -,1]n/k[OH-,2]n) The above will allow you to calculate n, with a final substitution of m and n values to calculate k. As the reaction proceeds, a violet-colored reactant will be slowly changing to a colorless product. Using a Spectronic 20 set at a wavelength at 565 nm, 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). Absorbance will be used in place of concentration in plotting the following three graphs: • Absorbance vs. time: A linear plot indicates a zero order reaction (k = –slope). • ln Absorbance vs. time: A linear plot indicates a first order reaction (k = –slope). • 1/Absorbance vs. time: A linear plot indicates a second order reaction (k = slope). Analysis of the above graphs will provide the data needed for the completion of the lab report. MATERIALS 0.10 M NaOH 0.20 M NaOH 1.6 X 10-5 M crystal violet distilled water PROCEDURE 100-mL beaker stirring rod two 10-mL graduated cylinders one sample test tube 1. Use a 10-mL graduated cylinder to obtain 10.0 mL of 0.10 M NaOH solution. Use another 10-mL graduated cylinder to obtain 10.0 mL of 1.6 X 10-5 M crystal violet solution. 2. We are now ready to calibrate the spectronic 20 • The right top panel knob on the Spec 20 controls the wavelength adjustment. Turn the knob to 565 nm, the desired setting for this kinetic experiment. • The bottom left knob on the Spec 20 (same as the on /off knob above) should be turned until the meter reads 0.0% transmission. There must be no test tube in the instrument and the sample holder cover must be closed. • Next, by following the procedure below, we will set the Spec 20 to 100% transmittance. a. The sample tube should be clean and free of any scratches or cracks. b. Fill the test tube 3/4 full with the distilled water. c. Wipe the outside of the tube with a Kimwipe and place the tube in the sample holder. The tubes must be inserted with the same alignment every time. If there are no appropriate markings on your tube, draw a vertical line at the top of your tube with a grease pencil to allow you to do this. d. Close the cover. e. Using the bottom right knob adjust the meter until it reads 100% transmission. 3. We are now ready to collect data. To initiate the reaction, simultaneously pour the 10-mL portions of crystal violet and sodium hydroxide into a 100-mL beaker and stir the reaction mixture with a stirring rod. Empty the water from the sample test tube. Rinse the test tube with ~1 mL of the reaction mixture and then fill it 3/4 full(dry the tube after). Place the sample tube in the sample slot of the Spec 20 and close the lid. Monitor the absorbance reading on the Spec 20 for about 5 seconds (the absorbance reading should be gradually decreasing). Begin recording absorbance vs. time data in 10 second intervals. Continue this for at least 3 minutes of the reaction. 4. Repeat the above steps 1-3, this time using the same concentration of crystal violet and 0.20 M NaOH. CALCULATIONS/CONCLUSION: 1. Using your data from the 0.10 M NaOH, determine the order of the reaction with respect to crystal violet. Do this graphically using a program such as excel. Three plots should be made (you must make all three even if you find the linear one) with a data table included that shows the mathematical manipulations of the data. 2. Taking your linear plot, determine the equation of the line and show this on the graph. Using the slope of the line, determine the pseudo rate constant for the reaction (we call this a pseudo rate constant at this point because it is only with respect to crystal violet, not crystal violet and sodium hydroxide). 3. Using the half-life equation that goes with your reaction order, determine the halflife of this reaction. Explain exactly what this value you found tells you about the reaction. 4. At this point you should already know the order of the reaction with respect to crystal violet. Take the data from the 0.20 M NaOH trial and analyze as above, this time only doing the linear plot. Find the equation of the line and determine the rate constant. 5. Determine the order of the reaction with respect to NaOH. Use the theory discussed in the introduction. 6. Write the overall rate expression for the reaction studied in this lab, giving the value for k in your response.