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Factors Affecting the Rate of a Chemical Reaction

A first order...

Question

A first order reaction occuring at 300 K has an activation energy of 2.484 $k c a l / m o l$ . When the temperature is doubled then the rate of the reaction is increased by n times. Find the value of n. (Take ln 2 = 0.69 and R = 2 $c a l / m o l . K$ )

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Solution

$l n \frac{k_{2}}{k_{1}} = \frac{E_{a}}{R} (\frac{1}{T_{1}} - \frac{1}{T_{2}})$
$= \frac{2484}{2} (\frac{1}{300} - \frac{1}{600})$
$= 1242 \times \frac{1}{600} = 2.07$
$= 3 \times 0.69 = 3 l n 2 = l n 2^{3}$

$\Rightarrow \frac{k_{2}}{k_{1}} = 8$
$\Rightarrow k_{2} = 8 k_{1}$
On doubling the temperature, k increases and since rate $\propto$ k, n = 8

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