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Ch.14 - Chemical Kinetics
All textbooksMcMurry 8th EditionCh.14 - Chemical KineticsProblem 127a
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Chapter 14, Problem 127a

Consider the reversible, first-order interconversion of two molecules A and B: where kf = 3.0⨉10-3 s-1 is the rate constant for the forward reaction and kr = 1.0⨉10-3 s-1 is the rate constant for the reverse reaction. We'll see in Chapter 15 that a reaction does not go to completion but instead reaches a state of equilibrium with comparable concentrations of reactants and products if the rate constants kf and kr have comparable values.
(a) What are the rate laws for the forward and reverse reactions?

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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. For a first-order reaction, the rate is directly proportional to the concentration of one reactant. In this case, the rate laws for the forward and reverse reactions can be expressed as rate = k[A] for the forward reaction and rate = k[B] for the reverse reaction, where k represents the rate constants.
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Equilibrium Constant

The equilibrium constant (K) is a value that expresses the ratio of the concentrations of products to reactants at equilibrium for a reversible reaction. It is calculated using the rate constants of the forward and reverse reactions: K = kf/kr. When kf and kr are comparable, the system reaches a state of dynamic equilibrium, where the concentrations of A and B remain constant over time.
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First-Order Reactions

First-order reactions are characterized by a rate that depends linearly on the concentration of one reactant. This means that if the concentration of the reactant is doubled, the rate of the reaction also doubles. In the context of the given question, both the forward and reverse reactions are first-order, which influences how we derive their respective rate laws and understand their kinetics.
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Related Practice
Textbook Question

Consider the following concentration–time data for the reaction of iodide ion and hypochlorite ion (OCl-). The products are chloride ion and hypoiodite ion (OI-).

(a) Write a balanced equation for the reaction.

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Textbook Question

Consider the following concentration–time data for the reaction of iodide ion and hypochlorite ion (OCl-). The products are chloride ion and hypoiodite ion (OI-).

(b) Determine the rate law, and calculate the value of the rate constant.

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views
Textbook Question

Consider the following concentration–time data for the reaction of iodide ion and hypochlorite ion (OCl-). The products are chloride ion and hypoiodite ion (OI-).

(d) Propose a mechanism that is consistent with the rate law, and express the rate constant in terms of the rate constants for the elementary steps in your mechanism. (Hint: Transfer of an H+ ion between H2O and OCl- is a rapid reversible reaction.)

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Textbook Question

Consider the reversible, first-order interconversion of two molecules A and B: where kf = 3.0⨉10-3 s-1 is the rate constant for the forward reaction and kr = 1.0⨉10-3 s-1 is the rate constant for the reverse reaction. We'll see in Chapter 15 that a reaction does not go to completion but instead reaches a state of equilibrium with comparable concentrations of reactants and products if the rate constants kf and kr have comparable values.

(b) Draw a qualitative graph that shows how the rates of the forward and reverse reactions vary with time.

362
views
Textbook Question

Consider the reversible, first-order interconversion of two molecules A and B: where kf = 3.0⨉10-3 s-1 is the rate constant for the forward reaction and kr = 1.0⨉10-3 s-1 is the rate constant for the reverse reaction. We'll see in Chapter 15 that a reaction does not go to completion but instead reaches a state of equilibrium with comparable concentrations of reactants and products if the rate constants kf and kr have comparable values.

(c) What are the relative concentrations of B and A when the rates of the forward and reverse reactions become equal?

333
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Textbook Question
Assume that you are studying the first-order conversion of a reactant X to products in a reaction vessel with a constant volume of 1.000 L. At 1 p.m., you start the reaction at 25 °C with 1.000 mol of X. At 2 p.m., you find that 0.600 mol of X remains, and you immediately increase the temperature of the reaction mixture to 35 °C. At 3 p.m., you discover that 0.200 mol of X is still present. You want to finish the reaction by 4 p.m. but need to continue it until only 0.010 mol of X remains, so you decide to increase the temperature once again. What is the minimum temperature required to convert all but 0.010 mol of X to products by 4 p.m.?
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