Temperature coefficient of a reaction is 2 . When temperature is increased from \(30^{\circ} \mathrm{C}\) to \(90^{\circ} \mathrm{C}\), the rate of reaction is increased by

Temperature coefficient
\((n)=\frac{\text { Rate constant at } T+10^{\circ} \mathrm{C}}{\text { Rate constant at } T^{\circ} \mathrm{C}}=2\)
i.e., For each \(10^{\circ} \mathrm{C}\) rise in temperature, rate becomes two times for the reaction
\(\begin{array}{cc}\text { Temperature } & \text { Rate of reaction } \\ 30^{\circ} \mathrm{C} & R_{1} \\ 40^{\circ} \mathrm{C} & 2 R_{1} \\ 50^{\circ} \mathrm{C} & (2)^{2} R_{1} \\ 60^{\circ} \mathrm{C} & (2)^{3} R_{1} \\ 70^{\circ} \mathrm{C} & (2)^{4} R_{1} \\ 80^{\circ} \mathrm{C} & (2)^{5} R_{1} \\ 90^{\circ} \mathrm{C} & (2)^{6} R_{1}\end{array}\)
\(\therefore\) Rate of reacation at \(90^{\circ} \mathrm{C}\) will become \((2)^{6}=64\) times.