The rate of a reaction increases four-fold when the concentration of reactant is increased 16 times. If the…

The rate of a reaction increases four-fold when the concentration of reactant is increased 16 times. If the rate of reaction is $4 \times 10^{-6} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$ when the concentration of the reactant is $4 \times 10^{-4} \mathrm{~mol}$ $\mathrm{L}^{-1} .$ The rate constant of the reaction will be
  1. $2 \times 10^{-4} \mathrm{~mol}^{1 / 2} \mathrm{~L}^{-1 / 2} \mathrm{~s}^{-1}$
  2. $1 \times 10^{-2} \mathrm{~s}^{-1}$
  3. $2 \times 10^{-4} \mathrm{~mol}^{-1 / 2} \mathrm{~L}^{1 / 2} \mathrm{~s}^{-1}$
  4. $25 \mathrm{~mol}^{-1} \mathrm{~L} \mathrm{~min}^{-1}$

Solution

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

Asked in: JEE-TOPICTESTS-CHEMISTRY

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