For the reaction 2A -> P the rate of reaction is defined as r = -(1)/(2)(d[A])/(dt) and r = k[A]^2 with k = 5.0x10^-3 L mol^-1 s^-1. For [A]_0 = 0.80 mol L^-1 the half-life of A is

JEE Advanced levelSingle correct optionDifficulty 3 of 3ck091

For the reaction $2 A P$ the rate of reaction is defined as $r = - \frac{1}{2} \frac{d [ A ]}{d t}$ and $r = k [A]^{2}$ with $k = 5.0 \times 1 0^{- 3} L mo l^{- 1} s^{- 1}$ . For $[A]_{0} = 0.80 mol L^{- 1}$ the half-life of $A$ is

With this definition

- d [A] / d t = 2 k [A]^{2}

, so

1/ [A] = 1/ [A]_{0} + 2 k t

and

t_{1/2} = 1/ (2 k [A]_{0}) = 1/ (2 \times 5.0 \times 1 0^{- 3} \times 0.80) = 125 s

. Taking

- d [A] / d t = k [A]^{2}

instead would wrongly give 250 s.