Consider the reversible, first-order interconversion of two molecules A and B: where k_f = 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 k_f and k_r have comparable values.
(c) What are the relative concentrations of B and A when the rates of the forward and reverse reactions become equal?

Verified step by step guidance

1. Identify that the system is at equilibrium when the rates of the forward and reverse reactions are equal.
2. Write the rate expressions for the forward and reverse reactions: Rate_forward = k_f[A] and Rate_reverse = k_r[B].
3. Set the rate expressions equal to each other to represent the equilibrium condition: k_f[A] = k_r[B].
4. Rearrange the equation to solve for the ratio of concentrations: [B]/[A] = k_f/k_r.
5. Substitute the given rate constants into the equation: [B]/[A] = (3.0 \(\times\) 10^{-3} \(\text{ s}\)^{-1}) / (1.0 \(\times\) 10^{-3} \(\text{ s}\)^{-1}).

Key Concepts

Equilibrium in Chemical Reactions

Equilibrium in a chemical reaction occurs when the rates of the forward and reverse reactions are equal, resulting in constant concentrations of reactants and products. At this point, the system is in a dynamic state where the conversion between reactants and products continues, but their concentrations remain unchanged over time.

Rate Constants (k_f and k_r)

Rate constants, denoted as k_f for the forward reaction and k_r for the reverse reaction, quantify the speed of each reaction. The values of these constants are crucial in determining the position of equilibrium; when k_f equals k_r, the system reaches equilibrium, and the concentrations of A and B can be calculated based on these constants.

Concentration Ratios at Equilibrium

At equilibrium, the ratio of the concentrations of products to reactants can be expressed using the rate constants. Specifically, the ratio of concentrations of B to A at equilibrium is given by the equation [B]/[A] = k_f/k_r. This relationship allows for the determination of relative concentrations when the rates of the forward and reverse reactions are equal.