One difference between first- and second-order reactions is that ________.

Question

A. the rate of both first-order and second-order reactions do not depend on reactant concentrations

B. 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

_C. a first-order reaction can be catalyzed; a second-order reaction cannot be catalyzed

D. the rate of a first-order reaction depends on reactant concentrations; the rate of a second-order reaction does not depend on reactant concentrations

E. None of the above are true.

Answer 1

Hi Elva!

The correct answer is B. Let's go through all of the answer choices to see why:

A. the rate of both first-order and second-order reactions do not depend on reactant concentrations

The rate law for a first-order reaction is Rate = k[A] and the rate law for a second-order reaction is

Rate = k[A]², where [A] is the concentration of reactant A. As we can see, the concentration of A is in both rate laws. This means that the rates of both types of reactions DO depend on reactant concentrations. The rate of zero-order reactions, in contrast, does not depend on reactant concentrations.

Please note, a rate law for a second-order reaction that depends on the concentration of two reactants is

Rate = k[A][B], where [A] is the concentration of reactant A and [B] is the concentration for reactant B. As you can see, the rate for this type of second-order reaction is also dependent on the concentration of the reactants. This answer is incorrect.

*B. 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 - Correct Answer!

Let's look at the equations for half-life (t_1/2) for each type of reaction.

First-order:

t_1/2 = 0.693/k

(you might also see this as ln(2)/k, which is the same thing)

Second-order:

t_1/2 = 1/k[A]₀, where [A]₀ is the initial concentration of reactant A.

Notice how the concentration of A is NOT in the equation for the half-life of a first-order reaction, but the concentration of A IS in the equation for the half-life of a second-order reaction. This means that the half-life of a first-order reaction does not depend on initial concentration ([A]₀), but the half-life of a second-order reaction does depend on initial concentration. This answer is correct.

Please note that the half-life of a zero-order reaction also depends on the initial concentration, [A]₀.

C. a first-order reaction can be catalyzed; a second-order reaction cannot be catalyzed

A catalyst is a substance that increases the rate of reaction without itself being consumed. It does so by providing an alternative, lower-energy pathway (thereby decreasing the activation energy). Second-order reactions can be catalyzed. This answer is incorrect.

D. the rate of a first-order reaction depends on reactant concentrations; the rate of a second-order reaction does not depend on reactant concentrations

As we saw in answer choice A, when looking at the rate laws of first-order and second-order reactions, the rates of both types of reactions do depend on reactant concentrations. Zero-order reactions do not depend on reactant concentrations. This answer is incorrect.

E. None of the above are true.

Answer choice B is true, so this answer is incorrect.

I hope this helps! Please comment if you have any additional questions! :)