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Ch.14 - Chemical Kinetics
All textbooksBrown 14th EditionCh.14 - Chemical KineticsProblem 38
Chapter 14, Problem 38

Consider the reaction of peroxydisulfate ion S2O8^2- with iodide ion I^- in aqueous solution: S2O8^2- (aq) + 3 I^- (aq) → 2 SO4^2- (aq) + I3^- (aq). At a particular temperature, the initial rate of disappearance of S2O8^2- varies with reactant concentrations in the following manner: Experiment S2O8^2- [M] I^- [M] Initial Rate [M/s] 1 0.018 0.036 2.6 * 10^-6 2 0.027 0.036 3.9 * 10^-6 3 0.036 0.054 7.8 * 10^-6 4 0.050 0.072 1.4 * 10^-5 (b) What is the average value of the rate constant for the disappearance of S2O8^2- based on the four sets of data? (c) How is the rate of disappearance of S2O8^2- related to the rate of disappearance of I^-? (d) What is the rate of disappearance of I^- when [S2O8^2-] = 0.025 M and [I^-] = 0.050 M?

Verified step by step guidance
1
Step 1: To find the average value of the rate constant for the disappearance of S2O8^2-, use the rate law expression: Rate = k[S2O8^2-]^m[I^-]^n. Determine the order of the reaction with respect to each reactant by comparing the initial rates from the experiments.
Step 2: Calculate the rate constant k for each experiment using the determined reaction orders and the given concentrations and initial rates. Use the formula: k = Rate / ([S2O8^2-]^m[I^-]^n).
Step 3: Average the calculated rate constants from all experiments to find the average value of the rate constant k.
Step 4: To relate the rate of disappearance of S2O8^2- to the rate of disappearance of I^-, use the stoichiometry of the balanced chemical equation. The rate of disappearance of I^- is three times the rate of disappearance of S2O8^2- because 3 moles of I^- react with 1 mole of S2O8^2-.
Step 5: To find the rate of disappearance of I^- when [S2O8^2-] = 0.025 M and [I^-] = 0.050 M, first calculate the rate of disappearance of S2O8^2- using the rate law and the average rate constant. Then multiply this rate by 3 to find the rate of disappearance of I^-.

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Rate of Reaction

The rate of a chemical reaction is a measure of how quickly reactants are converted into products. It is typically expressed in terms of the change in concentration of a reactant or product over time. In this context, the initial rate of disappearance of S2O8^2- is influenced by the concentrations of both S2O8^2- and I^-, which can be analyzed to determine the reaction order and rate constant.
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Rate Law

The rate law is an equation that relates the rate of a reaction to the concentration of its reactants, typically expressed as rate = k [A]^m [B]^n, where k is the rate constant, and m and n are the orders of the reaction with respect to reactants A and B. By analyzing the initial rates from the experiments, one can derive the rate law for the reaction between peroxydisulfate and iodide, which is essential for calculating the rate constant.
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Stoichiometry of Reaction

Stoichiometry refers to the quantitative relationship between reactants and products in a chemical reaction. In the given reaction, the stoichiometry indicates that one mole of S2O8^2- reacts with three moles of I^-. This relationship is crucial for determining how the rate of disappearance of S2O8^2- relates to the rate of disappearance of I^-, allowing for calculations of concentration changes over time based on the stoichiometric coefficients.
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Related Practice
Textbook Question

Consider the gas-phase reaction between nitric oxide and bromine at 273°C: 2 NO(g) + Br2(g) → 2 NOBr(g). The following data for the initial rate of appearance of NOBr were obtained:

Experiment [NO] (M) [Br2] (M) Initial Rate (M/s)

1 0.10 0.20 24

2 0.25 0.20 150

3 0.10 0.50 60

4 0.35 0.50 735 

(b) Calculate the average value of the rate constant for the appearance of NOBr from the four data sets.

Textbook Question

Consider the reaction of peroxydisulfate ion (S2O82-) with iodide ion (I-) in aqueous solution:

S2O82-(aq) + 3 I-(aq) → 2 SO42-(aq) + I3-(aq)

 At a particular temperature, the initial rate of disappearance of S2O82- varies with reactant concentrations in the following manner:

Experiment [S2O82-] (M) [I-] (M) Initial Rate (M/s)

1 0.018 0.036 2.6 × 10-6

2 0.027 0.036 3.9 × 10-6

3 0.036 0.054 7.8 × 10-6

4 0.050 0.072 1.4 × 10-5

(a) Determine the rate law for the reaction and state the units of the rate constant.

Textbook Question

(a) For the generic reaction A → B what quantity, when graphed versus time, will yield a straight line for a first-order reaction?

Textbook Question

(b) How can you calculate the rate constant for a first-order reaction from the graph you made in part (a)?