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Ch.15 - Chemical Kinetics
All textbooksTro 6th EditionCh.15 - Chemical KineticsProblem 48
Chapter 15, Problem 48

Consider the tabulated data showing the initial rate of a reaction (A → products) at several different concentrations of A. What is the order of the reaction? Write a rate law for the reaction including the value of the rate constant, k.
[A] (M) Initial Rate (M/s)
0.050 0.100
0.075 0.225
0.090 0.324

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1
Step 1: Understand the rate law equation. The rate law for a reaction A → products is generally expressed as Rate = k[A]^n, where k is the rate constant, [A] is the concentration of reactant A, and n is the order of the reaction with respect to A.
Step 2: Determine the order of the reaction (n) by comparing the changes in concentration and the corresponding changes in the initial rate.
Step 3: Compare the first and second data points. Calculate the ratio of the rates and the ratio of the concentrations to find n. Use the formula (Rate2/Rate1) = ([A]2/[A]1)^n.
Step 4: Repeat the process for the second and third data points to confirm the order of the reaction.
Step 5: Once the order n is determined, use any of the data points to solve for the rate constant k using the rate law equation.

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Key Concepts

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

Reaction Order

The order of a reaction refers to the power to which the concentration of a reactant is raised in the rate law. It indicates how the rate of reaction is affected by the concentration of that reactant. For example, if the rate doubles when the concentration of A is doubled, the reaction is first order with respect to A. Understanding reaction order is crucial for determining the rate law.
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Rate Law

The rate law expresses the relationship between the rate of a chemical reaction and the concentrations of its reactants. It is typically written in the form Rate = k[A]^n, where k is the rate constant and n is the order of the reaction with respect to reactant A. The rate law can be derived from experimental data, allowing chemists to predict how changes in concentration will affect the reaction rate.
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Rate Constant (k)

The rate constant, k, is a proportionality factor in the rate law that is specific to a particular reaction at a given temperature. It reflects the speed of the reaction and is influenced by factors such as temperature and the presence of catalysts. The value of k can be determined experimentally and is essential for calculating the rate of reaction under varying conditions.
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Related Practice
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?

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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.

832
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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. 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? e. By what factor does the reaction rate change if [C] is doubled? f. By what factor does the reaction rate change if [C] is doubled (and the other reactant concentrations are held constant)?

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Textbook Question

The tabulated data were collected for this reaction: CH3Cl(g) + 3 Cl2(g) → CCl4( g) + 3 HCl(g)

Write an expression for the reaction rate law and calculate the value of the rate constant, k. What is the overall order of the reaction?

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Textbook Question

Indicate the order of reaction consistent with each observation.

a. The half-life of the reaction gets shorter as the initial concentration is increased.

b. A plot of the natural log of the concentration of the reactant versus time yields a straight line.

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Textbook Question

Indicate the order of reaction consistent with each observation c. The half-life of the reaction gets longer as the initial concentration is increased.

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