The rate of a reaction increases 4-fold when concentration of reactant is increased 16 times. If the rate of reaction is 4 × 10^–6 mole L–1 S–1 mole L–1 when concentration of the reactant is 4 × 10^–4, the rate constant of the reaction will be

Q:  The rate of a reaction increases 4-fold when concentration of reactant is increased 16 times. If the rate of reaction is 4 × 10–6 mole L–1 S–1 mole L–1 when concentration of the reactant is 4 × 10–4, the rate constant of the reaction will be

(A) 2 × 10–4 mole1/2 L–1/2 S–1

(B) 1 × 10–2 S–1

(C) 2 × 10–4 mole–1/2, L1/2 S–1

(D) 25 mole–1 L min–1

Solution: $Rate \propto \sqrt{Concen}$

$Rate = k\sqrt{Concen}$

$k = \frac{Rate}{(Concen)^{1/2}} = \frac{4 \times 10^{-6}}{(4 \times 10^{-4})^{1/2}}$

= 2 × 10–4 mole1/2 L-1/2 S–1

Ans: (A)