Question

In: Chemistry

1. A student mixes 3.00 mL of 2.27 × 10−5 M crystal violet solution with 3.00...

1. A student mixes 3.00 mL of 2.27 × 10−5 M crystal violet solution with 3.00 mL 0.100 M sodium hydroxide both at 24.5 °C and collects the following data:

Time(Min) Absorbance
1.49 0.206
4.17 0.157
6.22 0.131
8.15 0.108
10.10 0.093
13.00 0.072
14.02 0.066
16.18 0.055
19.00 0.044

(a) Describe the graphical analysis steps the studentshould perform in order to determine the

(i) Order of the reaction with respect to crystal violet

(ii) Value of the rate constant, k (b) Use a graphing calculator or computer graphing software to determine the order of the reaction with respect to crystal violet. Justify your answer. (c) Write the law expression for this reaction. Justify your answer. (d) Determine the value of k including its units. Justify your answer. (e) Calculate the half –life of the reaction. Include units with your answer. (f) Determine the absorbance of crystal violet at 3.00 minutes.Justify your answer. (g) Determine the time at which the absorbance of crystal violet is equal to 0.060
.

Solutions

Expert Solution

(i) Order of the reaction with respect to crystal violet

The student should create a new data column for ln absorbance (abs) and a second new data column for absorbance−1 . Next, three graphs should be generated: abs vs. time, ln abs vs. time and abs−1 vs. time. The graph with the linear regression correlation coefficient, r closest to the absolute value of 1.0 has the best linear fit for the data and thus indicates the order of the reaction with respect to crystal violet. If the abs vs. time graph is the best linear fit, the order for CV is zero. If the ln abs vs. time graph is the best linear fit, the order for CV is 1st. If the abs−1 vs. time graph is the best linear fit, then the order for CV is 2nd.

(ii) Value of the rate constant, k

The value of k = slope of the line with the best linear fit

(b) Use a graphing calculator or computer graphing software to determine the order of the reaction with respect to crystal violet. Justify your answer.

The reaction is first order. This graphing calculator screen shot shows the three absorbance columns (abs given = L2, ln abs = L3 and abs-1​ = L4). The next step is to determine the r-value for each of these data columns vs. time

The best linear fit is indicated by the r-value closest to ±1 which is the graph of ln absorbance vs. time which means the reaction is first order. In this case, the determination could have been made by inspecting the graphs. It is clear that the first and third graphs are curves, but that is not always obvious. Students should be encouraged to calculate the r-values or “correlation” values as verification.

(c) Write the law expression for this reaction. Justify your answer.

rate = k[CV+ ] (students may elect to put an exponent of “1” if they wish) since the graph of ln absorbance vs. time yields the most linear fit.

(d) Determine the value of k including its units. Justify your answer.

k = slope for the ln absorbance vs. time graph shown center above ∴ k = 0.0877 min−1 or k = 8.87 × 10−2 min


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