Question

The correct difference between first- and second-order reactions is that

• A. the rate of a first-order reaction does not depend on reactant concentrations; the rate of a second-order reaction does depend on reactant concentrations
• B. a first-order reaction can be catalyzed; a second-order reaction cannot be catalyzed
• C. the half-life of a first-order reaction does not depend on [A]₀ ; the half-life of a second-order reaction does depend on [A]₀
• D. the rate of a first-order reaction does depend on reactant concentrations; the rate of a second-order reaction does not depend on reactant concentrations

Answer 1

The Correct Option is C

The question asks us to identify the correct difference between first-order and second-order reactions. Let's explore these concepts step-by-step:

Understanding Reaction Orders:

• First-order reactions: The rate of reaction depends linearly on the concentration of one reactant. The rate law for a first-order reaction is expressed as \( r = k[A] \), where \( k \) is the rate constant and \( [A] \) is the concentration of reactant A.
• Second-order reactions: The rate depends on either the concentration of two different reactants or the square of the concentration of a single reactant. The rate law for a second-order reaction can be written as \( r = k[A]^2 \) or \( r = k[A][B] \).

Half-life Comparison:

• First-order reactions: The half-life (\( t_{1/2} \)) of a first-order reaction is given by \( t_{1/2} = \frac{\ln 2}{k} \). Importantly, this indicates that the half-life is constant and does not depend on the initial concentration \( [A]_0 \).
• Second-order reactions: For a second-order reaction, the half-life is given by \( t_{1/2} = \frac{1}{k[A]_0} \). In this case, the half-life is inversely proportional to the initial concentration of the reactant, indicating dependence on \( [A]_0 \).

Evaluating the Given Options:

• The first option is incorrect because both first- and second-order reaction rates depend on reactant concentrations.
• The second option is incorrect because both first- and second-order reactions can be catalyzed.
• The third option is the correct answer, as it correctly states the difference in half-life dependencies between first- and second-order reactions: "the half-life of a first-order reaction does not depend on \( [A]_0 \); the half-life of a second-order reaction does depend on \( [A]_0 \)".
• The fourth option is incorrect because it contradicts the nature of first- and second-order reactions' dependencies on concentration.

Thus, the correct answer is: the half-life of a first-order reaction does not depend on [A]₀ ; the half-life of a second-order reaction does depend on [A]₀.