Consider the reversible, first-order interconversion of two...

Consider the reversible, first-order interconversion of two molecules A and B: where $k_{\mathrm{f}}=3.0 \times 10^{-3} \mathrm{s}^{-1} \mathrm{s}^{-1}$ is the rate constant for the forward reaction and $k_{\mathrm{r}}=1.0 \times 10^{-3} \mathrm{s}^{-1}$ is the rate constant for the reverse reaction. We'll see in Chapter 13 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 $k_{f}$ and $k_{\mathrm{r}}$ have comparable values. (a) What are the rate laws for the forward and reverse reactions? (b) Draw a qualitative graph that shows how the rates of the forward and reverse reactions vary with time. (c) What are the relative concentrations of B and A when the rates of the forward and reverse reactions become equal?

Consider the reversible, first-order interconversion of two molecules A and B:
where $k_{\mathrm{f}}=3.0 \times 10^{-3} \mathrm{s}^{-1} \mathrm{s}^{-1}$ is the rate constant for the forward reaction and $k_{\mathrm{r}}=1.0 \times 10^{-3} \mathrm{s}^{-1}$ is the rate constant for the reverse reaction. We'll see in Chapter 13 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 $k_{f}$ and $k_{\mathrm{r}}$ have comparable values.
(a) What are the rate laws for the forward and reverse reactions?
(b) Draw a qualitative graph that shows how the rates of the forward and reverse reactions vary with time.
(c) What are the relative concentrations of B and A when the rates of the forward and reverse reactions become equal?

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Key Concepts

Graphical Representation of Reaction Rates

Graphical analysis in kinetics involves plotting the reaction rates as functions of time to visualize the dynamics of the system. Such graphs typically show an initial phase where the forward and reverse rates differ, followed by a leveling off at equilibrium where both rates become equal.

Chemical Equilibrium

Chemical equilibrium occurs in a reversible reaction when the forward and reverse reaction rates become equal, resulting in constant concentrations of reactants and products. The equilibrium position can be characterized by an equilibrium constant, which for first-order reactions is related to the ratio of the forward and reverse rate constants.

First-Order Reaction Kinetics

First-order reaction kinetics describe reactions in which the rate is directly proportional to the concentration of a single reactant. This simplification allows the determination of rate constants and the prediction of how quickly a reaction will progress toward equilibrium.

Rate Laws

Rate laws are mathematical expressions that relate the reaction rate to the concentration of reactants. In the context of reversible, first-order reactions, the forward and reverse reactions each have their own rate expression that is directly proportional to the concentration of the reactant being consumed in that step.

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