Which of the following statements, for the reaction of type A → B, are correct?

(A) The initial rates for a second order reaction depend on the square of the concentration of the reactant
(B) The half-life is the time for half of the reactant to be consumed
(C) The expression for rate of second order reaction is $r = k[2A]^2$
(D) The half-life of a second-order reaction depends on the initial concentration

Choose the correct answer from the options given below:

(A), (B) and (D) only

The correct answer is Option (1) → (A), (B) and (D) only

A second-order reaction is a chemical process where the reaction rate is proportional to the square of the concentration of one reactant ($2A \rightarrow P$) or the product of the concentrations of two different reactants ($A + B \rightarrow P$). The rate law is $r = k[A]^2$ or $r = k[A][B]$, and the reaction rate quadruples if the reactant concentration doubles.

Key Characteristics and Equations

• Rate Law: $\text{Rate} = -\frac{d[A]}{dt} = k[A]^2$.
• Integrated Rate Equation: $\frac{1}{[A]_t} = kt + \frac{1}{[A]_0}$, where $[A]_t$ is concentration at time $t$, and $[A]_0$ is initial concentration.
• Half-Life ($t_{1/2}$): The half-life is inversely proportional to the initial concentration.

$t_{1/2} = \frac{1}{k[A]_0}$

Statement A

For a second order reaction:

$\text{Rate} = k[A]^2$

Thus, the initial rate depends on the square of the concentration of reactant. Hence, this statement is correct.

Statement B

Half-life is defined as the time required for the concentration of reactant to reduce to half of its initial value. This definition is valid for all reaction orders. Hence, correct.

Statement C

The correct rate expression for a second order reaction is:

$\text{Rate} = k[A]^2$

The given expression $r = k[2A]^2$ is incorrect because concentration is not multiplied by $2$ in the rate law. Hence, incorrect.

Statement D

For second order reaction:

$t_{1/2} = \frac{1}{k[A]_0}$

Thus, half-life depends on initial concentration. Hence, correct.