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Arrhenius Equation

The rate cons...

Question

The rate constants $k_{1}$ and $k_{2}$ of two reactions are in the ratio 2:1 at some temperature and 1:1 at infinite temperature. The corresponding energies of activation of the two reactions will be related by:

A

E_{1} > E_{2}

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B

E_{1} < E_{2}

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C

E_{1} = E_{2}

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D

Can't say

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Solution

The correct option is B $E_{1} < E_{2}$
Given,
$\frac{k_{1}}{k_{2}} = \frac{2}{1}$ or $k_{1} = 2 k_{2}$ i.e., $k_{1} > k_{2}$ According to Arrhenius equation:
$k = A e^{\frac{- E_{a}}{R T}}$
Since, k are equal at infinite temperature, A would be same for both.
Therefore, as k increases, $E_{a}$ must fall.
Hence, $E_{2} > E_{1}$

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