The equilibrium constant for the dissociation of molecular iodine, I₂(𝑔) ⇌ 2 I(𝑔), at 800 K is 𝐾_𝑐 = 3.1×10⁻⁵. (b) Assuming both forward and reverse reactions are elementary reactions, which reaction has the larger rate constant, the forward or the reverse reaction?

Verified step by step guidance

1. Identify the reaction and its reverse: The given reaction is I₂(g) ⇌ 2 I(g). The forward reaction is the dissociation of I₂ into 2 I atoms, and the reverse reaction is the recombination of 2 I atoms to form I₂.
2. Understand the equilibrium constant (K_c): K_c is defined as the ratio of the rate constant of the forward reaction (k_f) to the rate constant of the reverse reaction (k_r). The formula is K_c = k_f / k_r.
3. Analyze the value of K_c: Given that K_c = 3.1×10⁻⁵, which is a small number, it indicates that the equilibrium heavily favors the reactants over the products at 800 K.
4. Determine the larger rate constant: Since K_c is small and represents the ratio of k_f to k_r, this implies that k_r (rate constant for the reverse reaction) is much larger than k_f (rate constant for the forward reaction).
5. Conclude which reaction has the larger rate constant: The reverse reaction, which is the recombination of I atoms to form I₂, has the larger rate constant compared to the forward reaction of dissociation of I₂ into I atoms.

Key Concepts

Equilibrium Constant (Kc)

The equilibrium constant, Kc, quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction at a specific temperature. For the dissociation of I2, Kc = [I]^2 / [I2]. A small Kc value, like 3.1×10^−5, indicates that at equilibrium, the concentration of reactants (I2) is much greater than that of products (I), suggesting the reaction favors the reactants.

Rate Constants and Reaction Rates

Rate constants (k) are specific to each reaction and temperature, determining the speed of the reaction. The forward reaction rate constant (k_forward) relates to the formation of products, while the reverse reaction rate constant (k_reverse) relates to the formation of reactants. The relationship between Kc and the rate constants is given by Kc = k_forward / k_reverse, which helps in comparing their magnitudes.

Elementary Reactions

Elementary reactions are single-step processes where reactants convert directly to products without intermediates. Each elementary reaction has a specific rate law that reflects its molecularity. In this case, both the forward and reverse reactions are assumed to be elementary, allowing for a straightforward comparison of their rate constants based on the equilibrium constant.