The temperature coefficient of the rate of a reaction is $2.3.$ How many times will the rate of the reaction increase if the temperature is raised by $25 K$ ?
$(8.02 t i m e s)$

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Solution

$C =$ temperature coefficient $= 2.3$
If Temperature is $T$ , let the rate is $R$ .
Temp Rate
$T K$ $R$
$(T + 10) K$ $C R$
$(T + 20) K$ $C^{2} R$
$(T + 30) K$ $C^{3} R$
If $T$ is increased by $20 K$ , $R a t e_{1} = (2.3)^{2} R$
If $T$ is increased by $30 K$ , $R a t e_{2} = (2.3)^{3} R$
At intermediate temperature, temperature is increased by $25 K$
Rate $= \frac{R a t e_{1} + R a t e_{2}}{2} = \frac{(2.3)^{2} R + (2.3)^{2} R}{2}$
$= \frac{5.29 R + 12.167 R}{2} = 8.72 R$
$∴$ Rate will be increased by $8.72$ times

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