For 2A -> P the rate of reaction is defined as r = -(1)/(2)(d[A])/(dt) = k[A]^2 with k = 0.010 L mol^-1 s^-1 and [A]_0 = 0.50 mol L^-1. Select the correct statement(s).

[A] at 300 s is 0.125 mol L^-1.

The initial rate of disappearance of A is 5.0x10^-3 mol L^-1 s^-1.

The initial rate of formation of P is 5.0x10^-3 mol L^-1 s^-1.

[A] at 300 s is 0.125 mol L^-1.

The initial rate of disappearance of A is 5.0x10^-3 mol L^-1 s^-1.

JEE Advanced levelOne or more correct optionsDifficulty 3 of 3ck099

For $2 A P$ the rate of reaction is defined as $r = - \frac{1}{2} \frac{d [ A ]}{d t} = k [A]^{2}$ with $k = 0.010 L mo l^{- 1} s^{- 1}$ and $[A]_{0} = 0.50 mol L^{- 1}$ . Select the correct statement(s).

AThe half-life of $A$ is $100 s$ .
BThe initial rate of formation of $P$ is $5.0 \times 1 0^{- 3} mol L^{- 1} s^{- 1}$ .
C $[A]$ at $300 s$ is $0.125 mol L^{- 1}$ .
DThe initial rate of disappearance of $A$ is $5.0 \times 1 0^{- 3} mol L^{- 1} s^{- 1}$ .

Here

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

, so

1/ [A] = 2 + 0.020 t

. Then

t_{1/2} = 1/ (2 k [A]_{0}) = 100 s

[A]_{300} = 1/ (2 + 6) = 0.125 mol L^{- 1}

and the initial rate of disappearance of

A

2 k [A]_{0}^{2} = 5.0 \times 1 0^{- 3}

. Since one

P

forms per two

A

d [P] / d t = r = k [A]_{0}^{2} = 2.5 \times 1 0^{- 3}

, half of the quoted value.