# Experiment 2 Kinetics II Concentration-Time Relationships and Activation Energy

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1 2-1 Experiment 2 Kinetics II Concentration-Time Relationships and Activation Energy Introduction: The kinetics of a decomposition reaction involving hydroxide ion and crystal violet, an organic dye used as a biological stain, will be studied in this experiment. The exact formula and structure of crystal violet (C 25 H 30 ClN 3 ), as well as the products formed in the reaction, are not important for this lab. A representation of the chemical reaction is given below. C 25 H 30 ClN 3 (aq) + OH (aq) products (1) Crystal violet (abbreviated CV) absorbs visible light (hence the violet color) with a maximum absorbance at a wavelength of about 510 nm. The OH (aq) and the products of the decomposition do not absorb visible light. Therefore, as the CV decomposes and the violet color disappears, the concentration of the CV can be monitored by measuring the absorbance of the reaction mixture with a device known as a colorimeter. The absorbance is a measure of the amount of light absorbed by the dye in the reaction mixture. You will examine two aspects of the kinetics of this reaction. First, by determining how the CV concentration varies with time, you will determine the order of the reaction with respect to CV and thus obtain the rate law and rate constant. Second, you will determine the effect of temperature on the rate constant and thus calculate the Arrhenius activation energy for the reaction. Determination of a Calibration Curve: According to Beer s Law, the absorbance of a sample is proportional to the concentration of the absorbing species according to: A = a b C where A is absorbance, a is the molar absorptivity (a constant for a given compound at a given wavelength), b is the path length of the light through the sample (also a constant), and C is the varying concentration of the compound that absorbs. Since a and b are both constants, equation (2) has the form of a straight line, y = mx + b, with an intercept, b, of zero. A plot of absorbance vs. concentration will therefore be linear with a slope of ab. (2) Absorbance (A) slope = ab Concentration (C)

2 2-2 By measuring the absorbance of solutions of CV with known concentration, a calibration curve can be prepared. Using the equation of the line for the calibration curve, any concentration of CV can be determined from the measured absorbance of the solution. The colorimeter actually measures how much light is transmitted through the sample. The transmittance is defined as the fraction of the incident light that passes through the sample and reaches the detector. In this experiment, the Vernier colorimeter will automatically convert the transmittance to absorbance (a dimensionless quantity). Determination of the Order of the Reactant CV: The rate expression for reaction (1) is: Rate = k[cv] m [OH - ] (3) where k is the rate constant of the reaction and m is the order of the reaction with respect to CV. It is known that the order of the reaction with respect to the OH ion is 1. Analysis of the kinetics can be greatly simplified by keeping the hydroxide concentration much larger than the concentration of the crystal violet, [OH ] >> [CV]. When this is done, so little OH is consumed compared to the initial high concentration of hydroxide, that [OH ] remains virtually constant throughout the course of the reaction. This allows for a modified expression for the rate law: - m Rate = k[oh ][CV] = k [CV] m with k = k[oh ] (4) The constant k is called a pseudo rate constant because it is a constant that relates the m reaction rate to [CV], but only provided that [OH ] remains constant. Note that k would have a different value for a different [OH ]. In order to determine the value of m, you will measure the absorbance of the reaction mixture as a function of time. Once the absorbance (and hence [CV]) has been measured as a function of time, it is possible to determine the reaction order from the relationship between [CV] and time. For zero, first and second order reactions, there are different concentration-time relationships derived using calculus. The resulting equations are discussed in your textbook and class notes and are summarized in Table 1 (page 2-3). Therefore to determine the order, m, of the reactant CV from your [CV] vs. time data, you will create three plots, [CV] vs. time, ln[cv] vs. time, and 1/[CV] vs. time. The plot that gives a straight line for your data determines the reaction order as indicated in Table 1. Furthermore, the absolute value of the slope of the linear plot equals the pseudo rate constant, k, which always has a positive value. (Note that measured slope is either positive or negative, and that the units of the slope differ, as indicated in Table 1). Also since the known order for [OH ] is n=1, from equation (4), we get k' k = (5) [OH ]

3 2-3 which allows calculation of the rate constant, k, from the pseudo rate constant, k, obtained as the slope and the known value of [OH ] for the reaction mixture. Order with respect to R Rate Expression and Concentration- Time Relationship Graph Slope k units Zero, n = 0 [R] t = k t + [R] 0 [R] vs. t k M s -1 First, n = 1 ln[r] t = k t + ln[r] 0 ln[r] vs. t k s -1 Second, n = 2 1/[R] t = k t + 1/[R] 0 1/[R] vs. t k M -1 s -1 Table 1. A summary of concentration-time relationships for pseudo- zero, first and second order rate laws. [R] represents the concentration of the reactant, CV, in the rate law. Note that although the slope may be negative, k is always positive. Determination of the Energy of Activation for the Reaction: The value of the rate constant, k, is constant only for a single temperature. The values of k at different temperatures are related by the Arrhenius equation, k = A e -Ea / RT where T is temperature in Kelvin; R is the universal gas constant, J mol 1 K 1 ; E a is the activation energy of the reaction in J mol 1 ; and A is a proportionality constant called the Arrhenius pre-factor (don t confuse this with absorbance!). Taking the natural logarithm of both sides of equation (6) results in the following expressions: Ea ln k = ln A +, which can be written as: RT Ea 1 ln k = + ln A (7) R T Since (E a /R) and ln A are constant, this has the form of a straight line. Thus a plot of lnk vs. 1/T will yield a slope equal to (E a /R), allowing calculation of E a. However if data is collected at only two temperatures, T 1 and T 2, the activation energy can be found algebraically by writing equation (7) twice, substituting once with k 1 and T 1 and again with k 2 and T 2. Since the term, ln A, is constant, subtracting the two equations results in: k ln k 1 Ea 1 = R T2 T (6) (8)

4 2-4 Note that the two different reaction temperatures (which must be expressed in degrees Kelvin, K) will each have a different value of k. In this experiment the reaction will be done at room temperature and at ~1 o C to find two different values of k. Then equation (5) will be used to evaluate k at each temperature. Equation (8) will then be used to determine the activation energy of the reaction. Pre-Lab Notebook: Provide a title, purpose, reaction(s), summary of the procedure, and a table of reagents like the one below. Table of Physical Properties of Chemicals Used: Compound Formula Mass, FM (g/mol) Hazards Crystal violet Sodium hydroxide Create a Standard Solutions Table similar to the one in step 7 of Part A and fill in the values of CV concentration for every flask prior to the start of lab. Use the molarity, 2.5x10 5 M, and volumes of the CV stock solution in flasks B-F given in the Standard Solutions Table to calculate concentrations in the flasks after dilution to 50.0 ml with DI water. Note that the molarities of the standard solutions, B-F, will be given by [CV] = (2.5x10 5 M)(volume in L of CV stock solution)/0.0500l since each standard solution will have a total volume of 50.0mL. Equipment: 150 ml Beakers (2) 50 ml Volumetric flasks (5) 100 ml Beakers (3) Ice-Water Bath 600 ml Beaker for waste Stopwatch 400 ml Beaker for CV stock solution Vernier LabPro Buret Vernier Colorimeter and cuvettes 100 ml Graduated cylinder Vernier Temperature Probe 10 ml Graduated pipet TI-84 Calculator Disposable pipets Stock Solutions: M Crystal Violet (0.020 g in 2.0 L) 0.40 M NaOH Experimental Procedure: Work in pairs. Before beginning, do Step C-2. Also note that due to possible discoloration of the cuvettes by the CV dye, the cuvette you use should be rinsed with 3M HCl and then DI water at the start of each of the following parts. Part A: Determination of the Calibration Curve: 1. Following the first section of the Vernier tutorial, set up the Vernier system in DATAMATE with the colorimeter connected to channel 1. Allow the colorimeter to warm up for at least 5 minutes while the standard solutions are prepared.

8 2-8 Lab Report Outline for Kinetics II Graded Sections of Report Percent of Grade Pre-Lab 10 In-Lab 10 Post-Lab Report (You will save considerable time and effort by using Excel to carry out your calculations and plotting. But in your report s post-lab section, show required calculations as indicated below, being sure to number each step.) Part A: Calibration Curve: 1. Show a sample calculation of [CV] for standard solution C Attach an Excel spreadsheet giving the Step A-7 table of data and a clearly labeled Beers Law plot showing the equation of the line and a trend line. 10 Part B: Kinetic run room temperature: 1. Show a sample calculation of [CV] from the first high absorbance value recorded in your Excel file using the trendline equation from the calibration curve In Excel, using the equation of the line from the calibration curve, convert each of the absorbance values into [CV]. (Hint: with Excel, you only need to apply a formula to the first cell and copy it to the remaining rows). Attach an Excel table with values of [CV], ln[cv], and 1/[CV] with times for 300 seconds of the run (starting with the highest Absorbance) Find the reaction order, m, by plotting the following (use only the 300 seconds of data): 1: Concentration vs. time (If linear, reaction is zero order, m = 0) 2: ln(concentration) vs. time (If linear, reaction is first order, m = 1) 3: 1/(concentration) vs. time (If linear, reaction is second order, m = 2) Attach the plots to the report (with a trend line through the linear plot only) and state in the post-lab section: The plot that is linear corresponds to m = State From the slope of the linear plot, k = at o C 5 5. Show the calculation of [OH ] in the reaction mixture (= mol OH /L reaction mixture). The moles of OH in the reaction mixture equals (M V) of the NaOH stock solution added. Volume in L of reaction mixture is the sum of the CV and OH stock solution volumes Using Eqn (5), calculate k from k and [OH ] and state its value. (correct units)_ 5 Part C: Energy of Activation: 1. Use the same equation that gave a linear plot in Step B-3, plot the data from the run at ~1 o C. Attach this chart (with trendline and equation) to your report State From the slope of the linear plot, k = (correct units) at o C As in step B-5, show the calculation of [OH ] used for this run Using equation (5), calculate k at ~1 o C from k and [OH ]. State its value. (units) From the 2 sets of k and T values, calculate E a using Eqn (8). (Use T in degrees K!) 10

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