Suppose that the gas-phase reactions A → B and B → A are both elementary reactions with rate constants of 4.7×10⁻³ s⁻¹ and 5.8×10⁻¹ s⁻¹, respectively. (a) What is the value of the equilibrium constant for the equilibrium A(g) ⇌ B(g)? (b) Which is greater at equilibrium, the partial pressure of A or the partial pressure of B?

Verified step by step guidance

1. Identify the rate constants for the forward reaction (A → B) and the reverse reaction (B → A). The rate constant for A → B is 4.7×10⁻³ s⁻¹ and for B → A is 5.8×10⁻¹ s⁻¹.
2. Understand that at equilibrium, the rate of the forward reaction (A → B) equals the rate of the reverse reaction (B → A). This can be expressed as k_f[A] = k_r[B], where k_f and k_r are the rate constants for the forward and reverse reactions, respectively, and [A] and [B] are the concentrations of A and B.
3. Rearrange the equilibrium expression to find the ratio of the concentrations of B to A at equilibrium: [B]/[A] = k_f/k_r.
4. Substitute the given rate constants into the expression to find the ratio: [B]/[A] = (4.7×10⁻³ s⁻¹) / (5.8×10⁻¹ s⁻¹).
5. Compare the ratio [B]/[A] to determine which is greater at equilibrium. If [B]/[A] > 1, then [B] is greater; if [B]/[A] < 1, then [A] is greater.

Key Concepts

Equilibrium Constant

The equilibrium constant (K) for a reaction at equilibrium is defined as the ratio of the concentrations (or partial pressures) of the products to the reactants, each raised to the power of their stoichiometric coefficients. For the reactions A ⇌ B, K can be calculated using the rate constants of the forward (k₁) and reverse (k₂) reactions: K = k₁/k₂. This constant helps determine the relative amounts of A and B at equilibrium.

Rate Constants

Rate constants (k) are specific to each reaction and indicate the speed at which a reaction proceeds. In this case, the rate constant for the forward reaction (A → B) is 4.7×10⁻³ s⁻¹, while for the reverse reaction (B → A) it is 5.8×10⁻¹ s⁻¹. The magnitude of these constants influences the equilibrium position, with larger constants favoring the formation of products or reactants.

Le Chatelier's Principle

Le Chatelier's Principle states that if a system at equilibrium is disturbed, the system will adjust to counteract the disturbance and restore a new equilibrium. In the context of the given reactions, knowing the rate constants allows us to predict which species will be favored at equilibrium, as the system will shift towards the side with the lower energy or higher stability based on the rate constants.