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Byju's Answer

Standard XII

Chemistry

Arrhenius Equation

Two reactions...

Question

Two reactions of same order have equal exponential factors but their activation energy differ by $24.9 k J m o l^{- 1}$ . If the ratio between the rate constant of these reactions occurs at $27^{o} C$ is $x \times 10^{4}$ . Nearest integer value of $x$ is_________.(R=8.314 $J K^{- 1} m o l^{- 1}$ )

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Solution

Th Arrhenius equation is $k = A e^{- E a / R T}$ .....(1)

The difference in the activation energies of two reactions is $E_{2} - E_{1} = 24900 J / m o l$

The ratio of the rate constants of two reactions is $\frac{k_{2}}{k_{1}} = x \times 10^{4}$

By using equation (1), the ratio $\frac{k_{2}}{k_{1}}$ is

$\frac{k_{2}}{k_{1}} = \frac{A e^{- E_{1} / R T}}{A e^{- E_{2} / R T}} = e^{(E_{2} - E_{1}) / R T} = e^{\frac{24900}{8.314 \times 300}} = e^{9.98} = 2.15 \times 10^{4} = x \times 10^{4}$

Hence, $x = 2$ .

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Two reactions of same order have equal exponential factors but their activation energy differ by 24.9kJmol−1. If the ratio between the rate constant of these reactions occurs at 27oC is x×104. Nearest integer value of x is_________.(R=8.314 JK−1mol−1)

Two reactions of same order have equal exponential factors but their activation energy differ by $24.9 k J m o l^{- 1}$ . If the ratio between the rate constant of these reactions occurs at $27^{o} C$ is $x \times 10^{4}$ . Nearest integer value of $x$ is_________.(R=8.314 $J K^{- 1} m o l^{- 1}$ )