Question

The rate constant of a first-order reaction is ${10}^{–3}{\text{min}}^{–1}$ at $300\text{K}$. The temperature coefficient of the reaction is $2$. What is the rate constant of the reaction at $350\text{K}$ approximately?

• A. $16\times {10}^{-3}$
• B. $64\times {10}^{-3}$
• C. $32\times {10}^{-3}$
• D. $2^{50}$

Answer 1

The correct option is C $32\times {10}^{-3}$

Given rate constant $={10}^{–3}$
Temperature Coefficient $=2$
Temperature Coefficient $=\frac{k_{T+10}}{k_T}=2$
$k_{T+10}=2\times k_T=2\times {10}^{-3}$
So when temperature increases ${10}^{\circ }\text{C}$ rate of reaction increase $2$ time.
$\therefore {10}^{\circ }\text{C}\Rightarrow 2$ time
$\because 300\text{k}$ to $350\text{k}={50}^{\circ }\text{C}\Rightarrow (2{)}^5$ times or $32$ times
Rate constant at $\left(k_{{50}^{\circ }\text{C}}\right)350\text{k}=32\times {10}^{-3}$