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

To understand the difference between first-order and second-order reactions, let's examine the properties of each:

First-Order Reactions:

• The rate law is given by \( v = k[A] \), where \( [A] \) is the concentration of the reactant.
• The rate of the reaction depends linearly on the concentration of one reactant.
• The half-life (\( t_{1/2} \)) of a first-order reaction is independent of the initial concentration, given by: \( t_{1/2} = \frac{0.693}{k} \).
• Examples include radioactive decay processes.

Second-Order Reactions:

• The rate law is given by either \( v = k[A]^2 \) or \( v = k[A][B] \), depending on whether it is with respect to one or two different reactants.
• The rate is dependent on the concentration of one reactant squared or the product of the concentrations of two different reactants.
• The half-life is dependent on the initial concentration for second-order reactions, given by: \( t_{1/2} = \frac{1}{k[A]_0} \).
• Second-order reactions are often found in reactions involving bimolecular collisions.

Correct Explanation:

The correct difference between first- and second-order reactions related to half-life is best captured by the statement:

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 \( [A]_0 \).

In conclusion, this means that the half-life of a first-order reaction remains constant regardless of how much reactant you start with, unlike in second-order reactions where the initial concentration directly influences the half-life.