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Arrhenius Equation

Two different...

Question

Two different first order reactions have rate constants $k_{1}$ and $k_{2}$ at $T_{1} (k_{1} > k_{2})$ . If temperature is increased from $T_{1}$ to $T_{2}$ , then new constants become $k_{3}$ and $k_{4}$ respectively. Which among the following relations is correct?

A

k_{1} > k_{2} = k_{3} = k_{4}

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B

k_{1} < k_{3}

and

k_{2} < k_{4}

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C

k_{1} = k_{3} = k_{4}

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D

k_{1} > k_{2} > k_{3} > k_{4}

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Solution

The correct option is D $k_{1} < k_{3}$ and $k_{2} < k_{4}$
From the Arrhenius equation,

$k = A e^{- E_{a} / R T}$

Since $k_{1} > k_{2}$ at $T_{1},$ $k_{1} > k_{2}$ at all temperatures.
However for $T_{1} ⟶ T_{2}$

$k_{1} < k_{3}$ and $k_{2} < k_{4}$ since $k \propto T$ and $T_{1} < T_{2} .$

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