Question

The rate of a reaction increases four-fold when the concentration of reactant is increased $16$ times. If the rate of reaction is $4 \times 10^{-6} mol\, L ^{-1} s ^{-1}$ when the concentration of the reactant is $4 \times 10^{-4} mol \,L ^{-1}$. The rate constant of the reaction will be

• A. $2 \times 10^{-4} mol ^{1 / 2} L ^{-1 / 2} s ^{-1}$
• B. $1 \times 10^{-2} s ^{-1}$
• C. $2 \times 10^{-4} mol ^{-1 / 2} L ^{1 / 2} s ^{-1}$
• D. $25 \,mol ^{-1} L \,\min ^{-1}$

Answer 1

Answer: (A)

Rate $\propto \sqrt{\text { Concentration }}=k \sqrt{\text { Concentration }}$
$k=\frac{\text { Rate }}{(\text { Concentration })^{1 / 2}}$
$=\frac{4 \times 10^{-6}}{\left(4 \times 10^{-4}\right)^{\frac{1}{2}}}=\frac{4 \times 10^{-6}}{2 \times 10^{-2}} $
$=2 \times 10^{-4} mol ^{1 / 2} L ^{-1 / 2} s ^{-1}$