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Experiment 6: Chemical Kinetics 1
Purpose: Determine the rate law for the reaction of the dye crystal violet with hydroxide. Reading: Olmstead and Williams, Chemistry , sections 13.3 and 13.4.
Introduction
The reaction of crystal violet with hydroxide is:
This reaction can be represented as:
CV+^ + OH-^ → CVOH purple colorless
The kinetics of this reaction can be monitored with a spectrophotometer by observing the decrease in absorbance of crystal violet with time. The rate law in general form is:
rate of disappearance of CV = rate of appearance of CVOH = k [CV]x^ [OH-]y^ (1)
Your task is to determine the form of the rate law, including x and y, and the rate constant for the decolorization of crystal violet.
Chemical Kinetics
Consider the hypothetical reaction: A + B → C + D
The rate of reaction is measured by observing the rate of disappearance of the reactants A or B, or the rate of appearance of the products C or D. The species observed is a matter of convenience. For example if A, B, and C are colorless and D is colored, the rate of appearance of D can be measured by observing an increase in the absorbance of the solution as a function of time. The rate of reaction is:
Rate of disappearance of A =
-Change in the concentration of A Change in time =
- ∆[A]
∆t
Rate of appearance of D =
Change in the concentration of D Change in time =^
∆[D]
∆t
(^1) Adapted from Chemistry The Central Science, Laboratory Experiments, 6th (^) Edition, by J.H.
Nelson and K.C. Kemp and Laboratory Inquiry in Chemistry, by R. C. Bauer, J. P. Birk, and D. J. Sawyer.
C+
N(CH 3 ) 2
N(CH 3 ) 2
N(CH 3 ) 2
N(CH 3 ) 2
N(CH 3 ) 2
N(CH 3 ) 2
OH
PURPLE (^) COLORLESS
In general, the rate of the reaction depends upon the concentration of one or more of the reactants. Thus, the rate of the reaction above is expressed as:
Rate = k[A]x^ [B]y
where [A] and [B] are the molar concentrations of A and B, x and y are the powers to which the respective concentrations must be raised, and k is the rate constant. The values of x and y must be determined experimentally. For example, if x = 2 and y = 1, then the rate law is:
Rate = k[A]^2 [B]
This reaction is first order in B, meaning that doubling the concentration of B while keeping A constant causes the reaction rate to double. Simultaneously, this reaction is second order in A, meaning that doubling the concentration of A while keeping B constant causes the rate to increase by a factor of four, since the rate of the reaction is proportional to the square of the concentration of A. The overall order of the reaction is the sum of the exponents: or third order in this case. The orders are determined experimentally by noting the effects of changing reagent concentrations on the rate of the reaction. The rate constant, k, is independent of the concentration. The rate constant is characteristic for a given reaction and varies only with temperature. Once the rate is known for a given set of concentrations, the value of k can be calculated. For our reaction of interest, the rate law will be determined by spectrophotometrically measuring the amount of reactant disappearing as a function of time. The values of x and y as well as the rate constant k will be determined for the rate law: rate = k[A]x^ [B]y. A cartoon of the instrument is provided below.
Sample Light Computer Spectrophotometer Cuvette Source
White light illuminates the sample and can be absorbed. The remaining transmitted light enters the spectrophotometer and the absorbance as a function of wavelength is determined and transferred to a computer. The amount of light absorbed by the sample can be determined by measuring the light with the sample in the optical path relative to a reference, or blank. Beer’s Law relates the measured absorbance, A, to concentration, C, of the chromophore as follows:
A = ε l c
where l is the path length, which is 1.00 cm in our case, and ε is the molar absorption coefficient. Determination of the absorbance allows calculation of the concentration if the molar absorption
coefficient ε is known for the chromophore at the chosen wavelength. Determination of
Experiment [A] (M) [B] (M) Rate (M/s) 1 0.1 00 0.1 00 0. 2 0.1 00 0.2 00 0. 3 0.1 00 0.4 00 0. 4 0.2 00 0.5 00 0. 5 0.3 00 0.5 00 0. 6 0.4 00 0.5 00 0.
Answer : 1. With Rate = k [A]x^ [B]y, to determine “x”, the data from experiments 4-6 are used, because [A] varies while [B] remains constant in these experiments. A plot of log(rate) vs. log [A] for experiments 4-6 gives a slope of about 2, Figure 1. The uncertainties in the concentrations and rates are around 2%. Therefore x = 2, within experimental uncertainty.
- The value of “y” can be determined by plotting log (rate) vs. log [B] for experiments 1-3. This yields a slope of about 1, Figure 2. Therefore y = 1, within experimental uncertainty.
3 Rate = k [A]^2 [B].
- The rate constant can be determined from any single experiment. For example, using the data in experiment 3: 0.0403 M/sec= k (0.100 M)^2 (0.400 M), or k = 10.1 M-2^ s-1.
y = 2.0456x + 0. R² = 0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
-0.
0
-0.8 -0.7 -0.6 -0.5 -0.4 -0.3 -0.
log (rate)
log [A]
Figure 1: log (rate) vs. log [A]
y = 0.9982x - 0. R² = 0.
-2.
-1.
-1.
-1.
-1.
-1.2 -1 -0.8 -0.6 -0.4 -0.2 0
log (rate)
log [B]
Figure 2: log (rate) vs. log [B]
Comparing the Time Course to the Integrated Rate Laws An initial rate study is an excellent method for determining the order with respect to hydroxide, since hydroxide is not a colored species. However, since crystal violet is the colored reactant, a time course study is a better method for determining the reaction order with respect to crystal violet. In a time-course study, the concentration of a reactant or product is followed as a function of time and compared to the integrated rate laws for different order reactions.
First-Order Rate Expression The rate law for a reaction that is first-order in the reactant is:
rate = –
d[A] dt = k [A]^ (6)
This rate law applies to the type of reaction with one reactant, for example A→ Products. How can we apply this rate law for our reaction, which is in the form of A + B→ products? In comparison with equation 2, the first order rate law in equation 6 would result x = 1 and y = 0 or
if [OH-]y is kept constant and included in k.
rate = (k[OH-]y) [CV]x^ = keff [CV] (7)
The effective rate constant is keff = (k[OH-]y). In other words, the first order rate law works fine, but we get an effective first order rate constant, keff, that includes the effect of the concentration of hydroxide. Keeping [OH-]y^ constant can be done experimentally by having hydroxide in great excess, in which case, the overall concentration change of hydroxide during the course of the reaction is negligible. The process is then said to be pseudo-first order in CV. The integrated rate expression is,
ln
[CV]
[CV]o = – keff^ t^ (8) or ln [CV] = – keff t + ln[CV]o (9)
where [CV]o is the initial concentration of CV at time zero and [CV] is the concentration at any time, t.
Second-Order Rate Expression If x = 2 and y = 0 or [OH-]y^ is held constant in equation 2:
rate = –
d[CV] dt = keff^ [CV]
the reaction is pseudo-second-order in CV and integration of equation 10 gives:
1 [CV] –^
[CV]o = keff^ t^ (11)
Determining the Reaction Order Since absorbance is directly proportional to concentration, according to Beer’s Law A=εlc, the
absorbance can be used for the curve fitting in place of the concentrations. For a first order reaction, the absorption coefficient cancels in the numerator and denominator of the ln term in Eq. 8, so either concentration or absorbance may be used to directly determine the rate constant.
For a second order reaction, since [CV] = A/εl,
- Set up an absorbance vs. time run on the SpectroVis Plus spectrophotometer at the
experimentally-determined λmax, and collect data every 4 seconds for 90 seconds. Again, the total volume of each trial should be 3.00 mL. Your first kinetics trial should contain a volume of crystal violet that will give an absorbance of about 1.2-1.5 (based on your findings from Part A ). Plan to add the same volume of 0.100 M NaOH as you have of crystal violet, but don’t add it yet! Add the crystal violet to your cuvette, then the appropriate volume of water that will make your final volume 3.00 mL (be sure to account for the NaOH that you’re about to add). Finally, add the NaOH, mix with the pipette tip, and immediately start collecting kinetic data with the spectrophotometer. You should see the absorbance drop as the crystal violet decolorizes in the presence of base. When data collection is complete, save the data using Save As… from the File menu as described in the SpectroVis Plus Instructions. Determine the initial rate as described in Part C. Data Analysis, below.
- Set up another 3.00 mL reaction, this time with less hydroxide than in the first trial (but make sure that you know this amount exactly). Again, add the same volume of crystal violet as last time (this amount will remain constant in this whole series of trials), water (make sure that you increase the volume of water to make up for the decrease in the amount of hydroxide). Add the 0.100 NaOH, and collect kinetics data again and save this data to disk. Don’t overlay the data; in other words, pull down the Data menu and choose Clear All Data before each run.
- Repeat until you have five kinetics trials, each with a total volume of 3.00 mL, a constant volume of crystal violet, and a known, varying amount of hydroxide.
C. Initial Rate Study Data Analysis
- Observe the data table in the Vernier software. The first column should be time in seconds; the second column, the absorbance.
- Using the following instructions, insert a new column for crystal violet concentration, using the absorbance data and your absorption coefficient calculated in Part A above to determine
these values (c = A/ε; path length is 1 cm). Choose New Calculated Column from the Data menu. Enter “[CV]” as the Name, “[CV]” as the Short Name, and set the unit to “M.” Enter the correct formula for the column into the Equation edit box: to do this, select “Absorbance” from the Variables list. Then type in “/” and your absorption coefficient. In the Equation edit box, you should now see displayed something like: “A”/1.234e4. Click. Click on the y-axis label in the plot window. Choose [CV] and uncheck any other boxes. The crystal violet concentration should now be plotted as a function of time.
- Autoscale the y-axis by clicking on. To do the linear curve fit, click the Linear Fit button, .The slope of the best-fit line can be used to determine the initial rate of the reaction for that experiment. We recommend that you use four significant figures in your determination of the slope.
- Repeat your initial rate determinations for each of the five kinetics trials that you perform in lab today. You now have a set of data that contains a rate for each initial hydroxide concentration.
- Plot log(rate) vs. log [OH-]initial in Excel. You can also use natural logarithms, ln. The slope of the best-fit line is the reaction order for OH-^ [“y” in the rate law equation (2) above].
D. Time-Course Kinetics Experiments
- Again, the total volume of each trial should be 3.00 mL. Your first kinetics trial should contain the volume of crystal violet that gives an absorbance of about 1.2-1.5. Choose the amount of sodium hydroxide from last week’s experiment that gives a half-time of about 1. mins; the half-time or half-life is the time it takes for the concentration to drop by a factor of two. Add the crystal violet to your cuvette, then the appropriate volume of water that will make your final volume 3.00 mL (be sure to account for the NaOH that you’re about to add). Finally, add the NaOH, mix with the pipette tip, and immediately start collecting kinetic data with the spectrophotometer. Collect data every 4 seconds for about 900 seconds. When the curve starts to look “flat,” stop collecting. Save the data as described in the SpectroVis Plus Instructions.
- Use the Data Analysis Instructions in the “SpectroVis Plus Spectrophotometers with Vernier Data Acquisition Software Instructions” Data Analysis Section. Determine the reaction order, and rate constant. This rate constant is the effective rate constant, see the Time-Course Data Analysis section below.
- You only need to complete one run successfully. If your curve fitting didn’t work out well, because the reaction ran either too fast or too slow, repeat the experiment with a different amount of hydroxide.
E. Time-Course Data Analysis
1. The rate constant from Part D is an effective rate constant, keff, since at the given concentration of the sodium hydroxide: rate = (k[OH-]y) [CV]x^ = keff [CV]x^ ; see equation 7. Therefore the rate constant that you determined in Part D is keff = (k[OH-]y). Determine the true rate constant, k, from the effective rate constant.
- Now that you have determined the values of both “x” and “y”, determine the value of the rate constant, k, for all five of the reactions in your initial rate study from Part B. Show your calculations in your lab notebook. Calculate the mean and the standard deviation of the rate constant values. Compare this average value with the rate constant from Part D. Consider the effect of random and systematic errors on the difference.
LABORATORY REPORT: Use the Report form for this experiment.
Use complete sentences, the proper number of significant figures, and include units. Equations, reactions, tables, and diagrams can be written by hand. The sections of your report are:
Introduction (2-sentence maximum): State the scientific purpose of the experiment. Describe the method you will use, in a general sense. Do not discuss the experimental procedure details or data analysis steps. Don’t include pedagogical goals (e.g to teach us how to use…..).
Procedure: Give one-sentence descriptions of the two methods that you used to determine the order of the reaction with respect to crystal violet and hydroxide. Reference the lab write-up on the CH145 On-line Laboratory Manual and list any changes. Give the cell material and path length and the manufacturer and model of the spectrophotometer.
Results: Give the temperature of the kinetics determinations. Give your results in tabular form for the concentrations and initial rates for the determination of the order with respect to hydroxide. Report the slope and intercept of the curve fit for the order determination. Attach the plot used for the initial rate study. Make sure the axes are labeled. Give the concentrations and
