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

Options

A. The rate of a first-order reaction does not depent on reactant concentrations' the rate of a second-order reaction does depend on reactant concentrations
B. The half-life ona 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 first-order reaction does depend on reactant concentrations, the rate of a second-order reaction does not depend on reactant concentrations

Answer

B

Explanation

Relation between half-life `(t_(1//2))` and initial concentration of reactant `([A]_(0))` is as follows:
`t_(1//2) prop (1)/([A]_(0)^(n -1))`
When `n` is the order of reaction.
For first-order reaction
`t_(1//2) prop (1)/([A]_(0)^(1 -1)) prop (1)/([A]_(0)^(0))`
i.e. `t_(1//2)` does depend on initial concentratio of reactant. For second order reaction
`t_(1//2) propk (1)/([A]_(0)^(2 - 1)) prop (1)/([A]_(0))`
i.e., `t_(1//2)` is inversly proportional ot the initial conc. fo reactant.