The correct difference between first and second order reactions is that

Options

A. a first-order reaction can be catalysed , a second-order reaction cannot be catalysed
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. 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
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

B

Explanation

For first order reactions, the rate of reaction is proportional to the first power of the concentration of the first power of the concentration of the reactant.
For, `A to B`
Rate`=-(d[A])/(dt)=k[A] " " ["where,k=constant"]`
Half-life `(t_(1//2)=(0.693)/(k))`
`therefore` Rate of first order reaction depends upon reactant concentrations and half life does not depend upon initial concentration of reactant, `[A]_(0)`.
For second order reactions, the rate of reaction is proportional to the second power of the concentration of the reactant.
For, `2A to B`
Rate `=k[A]^(2)`
Half-life`(t_(1//2)=(1)/(k[A]_(0)))`
`therefore` Rate of second order reaction depends upon reactant concentration and half life also does depend on `[A]_(0)`.