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Ch.14 - Chemical Kinetics
Brown - Chemistry: The Central Science 15th Edition
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
All textbooksBrown 15th EditionCh.14 - Chemical KineticsProblem 38a
Chapter 14, Problem 38a

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.

Verified step by step guidance
1
Identify the changes in concentrations of S2O8^2- and I^- across the experiments to observe how the rate of reaction changes. This will help in determining the order of reaction with respect to each reactant.
Write the general form of the rate law for the reaction: Rate = k[S2O8^2-]^m[I^-]^n, where k is the rate constant, m is the order of the reaction with respect to S2O8^2-, and n is the order of the reaction with respect to I^-.
Use the data from the experiments to set up a system of equations based on the rate law. For each experiment, substitute the concentrations of S2O8^2- and I^- and the corresponding initial rate into the rate law equation.
Solve the system of equations to find the values of m and n. This can be done by comparing how the rate changes as the concentrations of each reactant change. If the rate changes proportionally to the concentration, the reaction is first order with respect to that reactant. If the rate changes quadratically, it is second order, and so on.
Once m and n are determined, use any of the experimental data sets to solve for k in the rate law equation. The units of k will depend on the overall order of the reaction (sum of m and n) and are generally expressed as M^(1-order) s^-1.

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Key Concepts

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

Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentration of its reactants. It is typically formulated as Rate = k[A]^m[B]^n, where k is the rate constant, [A] and [B] are the concentrations of the reactants, and m and n are the reaction orders with respect to each reactant. Determining the rate law involves analyzing experimental data to find the values of m and n, which indicate how the rate is affected by changes in concentration.
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Order of Reaction

The order of a reaction refers to the exponent to which the concentration of a reactant is raised in the rate law. It provides insight into the relationship between concentration and reaction rate. For example, a first-order reaction means that the rate is directly proportional to the concentration of that reactant, while a second-order reaction indicates that the rate is proportional to the square of the concentration. The overall order of the reaction is the sum of the individual orders.
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Units of the Rate Constant (k)

The units of the rate constant (k) depend on the overall order of the reaction. For a zero-order reaction, the units are mol/L·s; for a first-order reaction, they are s^-1; and for a second-order reaction, they are L/(mol·s). Understanding the units of k is crucial for ensuring that the rate law is dimensionally consistent and for converting between different units in chemical kinetics.
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Related Practice
Textbook Question

(a) The gas-phase decomposition of SO2Cl2, SO2Cl2(g) → SO2(g) + Cl2(g), is first order in SO2Cl2. At 600 K the half-life for this process is 2.3 × 105 s. What is the rate constant at this temperature?

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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

The following data were measured for the reaction BF3(g) + NH3(g) → F3BNH3(g):

Experiment [BF3] (M) [NH3] (M) Initial Rate (M/s)

1 0.250 0.250 0.2130

2 0.250 0.125 0.1065

3 0.200 0.100 0.0682

4 0.350 0.100 0.1193

5 0.175 0.100 0.0596

(d) What is the rate when [BF3] = 0.100 M and [NH3] = 0.500 M?

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

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