The rate of a chemical reaction doubles for every $10^{\circ} \mathrm{C}$ rise of temperature. If the…

The rate of a chemical reaction doubles for every $10^{\circ} \mathrm{C}$ rise of temperature. If the temperature is raised by $50^{\circ} \mathrm{C}$, the rate of the reaction increases by about :
  1. 24 times
  2. 32 times
  3. 64 times
  4. 10 times

Solution

Temperature coefficient $\mu=2$; $ \begin{aligned} & \mu^{\frac{\Delta \mathrm{T}}{10}}=\frac{\mathrm{k}_2}{\mathrm{k}_1} \\ & 2^{\frac{50}{10}}=2^5=32=\frac{\mathrm{k}_2}{\mathrm{k}_1} \end{aligned} $ Therefore $32 \mathrm{k}_1=\mathrm{k}_2$

Asked in: JEE Main 2011

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