Question

The rate constant of a reaction at ${27}^{o}C$ is $2.3\times {10}^{-3}mi{n}^{-1}$ and at this temperature $0.001$ % of the reactant molecules are able to cross over the energy barrier existing between the reactants and the products. What can the maximum value of rate constant be achieved by raising the temperature?

• A. $23.0mi{n}^{-1}$
• B. $2.3\times {10}^{-2}min$
• C. $115.0mi{n}^{-1}$
• D. $230.0mi{n}^{-1}$

Answer 1

The correct option is D $230.0mi{n}^{-1}$

$k=A{e}^{-Ea/RT},$

$k=2.3\times {10}^{-3}mi{n}^{-1}$

$e^{-Ea/RT}=$ Fraction of molecules crossing over energy barrier

$=\frac{0.001}{100}$

$=1.0\times {10}^{-5}$

Hence $2.3\times {10}^{-3}=A\times 1.0\times {10}^{-5};$

$A=230mi{n}^{-1}$

$k_{max}=A$ when

$T=\infty .$

Hence $k_{max}=230mi{n}^{-1}$.