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

The correct option is A $2\times {10}^{-4}$ mol${}^{1/2}$ L${}^{-1/2}$ s${}^{-1}$

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

Hence, the correct option is $\text{A}$