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Ch.14 - Chemical Kinetics
All textbooksTro 4th EditionCh.14 - Chemical KineticsProblem 39a
Chapter 14, Problem 39a

A reaction in which A, B, and C react to form products is first order in A, second order in B, and zero order in C.
a. Write a rate law for the reaction.

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Identify the order of reaction with respect to each reactant: first order in A, second order in B, and zero order in C.
Recall that the rate law for a reaction is expressed as: \( \text{Rate} = k[A]^m[B]^n[C]^p \), where \( k \) is the rate constant, and \( m, n, \) and \( p \) are the orders of the reaction with respect to A, B, and C, respectively.
Substitute the given orders into the rate law expression: \( m = 1 \), \( n = 2 \), and \( p = 0 \).
Write the rate law using the substituted values: \( \text{Rate} = k[A]^1[B]^2[C]^0 \).
Simplify the rate law expression, noting that any term raised to the power of zero is equal to one: \( \text{Rate} = k[A][B]^2 \).

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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 of a chemical reaction expresses the relationship between the rate of the reaction and the concentration of its reactants. It is typically formulated as rate = k[A]^m[B]^n[C]^p, where k is the rate constant, and m, n, and p are the orders of the reaction with respect to each reactant. The orders indicate how the rate is affected by changes in concentration.
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Rate Law Fundamentals

Order of Reaction

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. It can be determined experimentally and indicates how the rate of reaction changes with varying concentrations. For example, a first-order reaction in A means that doubling the concentration of A will double the reaction rate, while a second-order reaction in B means that doubling B will quadruple the rate.
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Average Bond Order

Zero-Order Reactions

In a zero-order reaction, the rate of reaction is constant and does not depend on the concentration of the reactant. This means that changes in the concentration of the zero-order reactant (in this case, C) have no effect on the reaction rate. Zero-order behavior often occurs when a reactant is saturated or when the reaction is limited by a factor other than concentration.
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Related Practice
Textbook Question

What are the units of k for each type of reaction?

a. first-order reaction

b. second-order reaction

c. zero-order reaction

Textbook Question

This reaction is first order in N2O5: N2O5(g) → NO3(g) + NO2(g) The rate constant for the reaction at a certain temperature is 0.053/s. a. Calculate the rate of the reaction when [N2O5] = 0.055 M

Textbook Question

This reaction is first order in N2O5: N2O5(g) → NO3(g) + NO2(g) The rate constant for the reaction at a certain temperature is 0.053/s. b. What would the rate of the reaction be at the concentration indicated in part a if the reaction were second order? Zero order? (Assume the same numerical value for the rate constant with the appropriate units.)

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Textbook Question

A reaction in which A, B, and C react to form products is first order in A, second order in B, and zero order in C. b. What is the overall order of the reaction?

Textbook Question

A reaction in which A, B, and C react to form products is first order in A, second order in B, and zero order in C c. By what factor does the reaction rate change if [A] is doubled (and the other reactant concentrations are held constant)? d. By what factor does the reaction rate change if [B] is doubled (and the other reactant concentrations are held constant)? e. By what factor does the reaction rate change if [C] is doubled? f. By what factor does the reaction rate change if the concentrations of all three reactants are doubled?

Textbook Question

A reaction in which A, B, and C react to form products is zero order in A, one-half order in B, and second order in C. a. Write a rate law for the reaction.