The rate constant of a first-order reaction at 27°C is 10⁻³ min⁻¹. The temperature coefficient of the reaction is 2. What is the rate constant at 17°C for this reaction?

\(5 × 10^{−4}\)

Given, \(T_1 = 17^oC\)

\(T_2 = 27^oC\)

So, \(\Delta T = T_2 − T_1 = (27 − 17)^oC = 10^oC\)

We know,

\(\frac{K_{T_2}}{K_{T_1}} = (2)^{\Delta T / 10}\)

⇒ \(\frac{10^{−3}}{K_{T_1}} = (2)^{10 / 10}\)

⇒ \(K_{T_1} = \frac{10^{−3}}{2}\)

⇒ \(K_{T_1} = 0.5 × 10^{−3}\)

∴ \(K_{T_1} = 5 × 10^{−4} min^{−1}\)