Question

One difference between first- and second-order reactions is that ________. One difference between first- and second-order reactions is that ________. 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 rate of both first-order and second-order reactions do not depend on reactant concentrations the rate of a first-order reaction depends on reactant concentrations; the rate of a second-order reaction does not depend on reactant concentrations a first-order reaction can be catalyzed; a second-order reaction cannot be catalyzed None of the above are true.

Answer 1

Answer:

(first choice)

One difference between first- and second-order reactions is that the half-life of a first-order reaction does not depend on [Ao]; the half-life of a second-order reaction does depend on [Ao].

Explanation:

1) First order reactions' model

This is a brief deduction of the first order reactions' half-life

• Equation: aA +b B → cC + dD

• rate: r = - d[A]/dt = k[A]

• Integration:

       - d[A]/[A] = kdt ⇒ - ln { [A]/[Ao] } = kt

• Half-life:

       t half-life = T

       [A] = (1/2) [Ao] ⇒- ln { [A]/[Ao] } = - ln (1/2) = ln(2) = kT

       ⇒ T = ln(2) / T

• Conclusion:

        * The half-life of a first order reaction is a constant; it does not depend on the initial concentration of the reactants, it only depend on the rate constant.

2) Second order reaction's model:

This is a brief deduction of the second order reactions' half-life

• Equation: aA +b B → cC + dD

• rate: r = - d[A]/dt = k[A]²

• Integration:

       - d[A]/[A]² = kdt ⇒ 1/[Ao] - 1/[A] = kt

• Half-life:

       t half-life = T

       [A] = (1/2) [Ao] ⇒ 1 / [Ao] - 1 / {2[Ao]} = 1 / {2[Ao]} = kT

       ⇒ T =   1 / {2k[Ao] }

• Conclusion:

        * The half-life of a second order reaction depends on the initial concentration and the rate constant.

3) Final conclusion:

We have found that while the half life of a first order reaction is does not depend on the initial concentration, the half-life of a second order reaction does depends on the initial concentration. Hence, the correct answer to the question is:

One difference between first- and second-order reactions is that the half-life of a first-order reaction does not depend on [Ao]; the half-life of a second-order reaction does depend on [Ao].