A student performed an initial rate study to determine the rate law for the reaction:S 2 O 82- (aq) + 3I -(aq) ® 2 SO 42- (aq) + I 3-(aq)The results of the study are given in the table below:Experiment [S 2 O 82- (aq)] o(mol L-1 )[I- (aq)] o(mol L-1 )Initial rate(mol L-1 s -1 )1 0.200 0.100 8.35 x 10-32 0.100 0.050 1.05 x 10-33 0.200 0.050 4.25 x 10-34 0.300 0.150 ?i. (1 mark)Determine the order with respect to S 2 O 82-. Justify your answer.ii. (1 mark)Determine the order with respect to I- . Justify your answer.iii. (1 mark)Write the rate law for the overall reaction.iv. (1 mark)What is the overall order of the reaction?v. (1 mark)Calculate the value for the rate constant k of the reaction from the data given forexperiment 1.vi. (2 marks)Given your value for k and your determined rate law, calculate the initial rate forreaction number 4.k1k-1k3vk2v
Question
A student performed an initial rate study to determine the rate law for the reaction:S 2 O 82- (aq) + 3I -(aq) ® 2 SO 42- (aq) + I 3-(aq)The results of the study are given in the table below:Experiment [S 2 O 82- (aq)] o(mol L-1 )[I- (aq)] o(mol L-1 )Initial rate(mol L-1 s -1 )1 0.200 0.100 8.35 x 10-32 0.100 0.050 1.05 x 10-33 0.200 0.050 4.25 x 10-34 0.300 0.150 ?i. (1 mark)Determine the order with respect to S 2 O 82-. Justify your answer.ii. (1 mark)Determine the order with respect to I- . Justify your answer.iii. (1 mark)Write the rate law for the overall reaction.iv. (1 mark)What is the overall order of the reaction?v. (1 mark)Calculate the value for the rate constant k of the reaction from the data given forexperiment 1.vi. (2 marks)Given your value for k and your determined rate law, calculate the initial rate forreaction number 4.k1k-1k3vk2v
Solution
i. The order with respect to S2O82- is 1. This is determined by comparing experiments 1 and 3 where the concentration of I- is constant. Doubling the concentration of S2O82- results in the rate doubling as well, indicating a first order reaction.
ii. The order with respect to I- is also 1. This is determined by comparing experiments 1 and 2 where the concentration of S2O82- is constant. Halving the concentration of I- results in the rate decreasing by a factor of 8, indicating a first order reaction.
iii. The rate law for the overall reaction is: Rate = k[S2O82-][I-]
iv. The overall order of the reaction is 2 (1 from S2O82- and 1 from I-).
v. The rate constant k can be calculated from the data given in experiment 1 using the rate law. Rearranging the rate law gives k = Rate / ([S2O82-][I-]) = (8.35 x 10^-3 mol L^-1 s^-1) / ((0.200 mol L^-1)(0.100 mol L^-1)) = 0.417 L mol^-1 s^-1.
vi. Using the determined rate law and value for k, the initial rate for reaction number 4 can be calculated as: Rate = k[S2O82-][I-] = (0.417 L mol^-1 s^-1)(0.300 mol L^-1)(0.150 mol L^-1) = 0.0188 mol L^-1 s^-1.
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