Which of the following statements, for the reaction of type A → B, ar…

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

For a reaction of the type A → B that is second order, the rate is proportional to the square of the concentration of A, and the rate constant has the unit L mol⁻¹ s⁻¹:

    \( \displaystyle r = k[\mathrm{A}]^{2} \)

Integrating this rate law gives the half-life:

    \( \displaystyle \frac{1}{[\mathrm{A}]} - \frac{1}{[\mathrm{A}]_0} = kt \Rightarrow t_{1/2} = \frac{1}{k[\mathrm{A}]_0} \)

• (A) The initial rates for a second order reaction depend on the square of the concentration of the reactant — Correct. With \( r = k[\mathrm{A}]^2 \), doubling the initial concentration makes the initial rate four times.

• (B) The half-life is the time for half of the reactant to be consumed — Correct. This is the definition of half-life: the time in which the concentration falls to half its initial value.

• (C) The expression for rate of second order reaction is \(r = k[2A]^2\) — Incorrect. The rate law contains the concentration of A, \( r = k[\mathrm{A}]^2 \); “[2A]” has no meaning as a concentration, and a coefficient in a balanced equation does not enter the brackets.

• (D) The half-life of a second-order reaction depends on the initial concentration — Correct. \( t_{1/2} = 1/(k[\mathrm{A}]_0) \): the larger the initial concentration, the shorter the half-life. Only for a first order reaction is \( t_{1/2} \) independent of concentration.