Chemistry

Problem

In the Arrhenius equation for a certain reaction, the values of

A

and

E_a

(energy of activation) are

4 \times 10^{13} \text{ sec}^{-1}

and

98.6 \text{ kJ mol}^{-1}

respectively. If the reaction is of first order, at what temperature will its half-life period be 10 minute? (IIT 1990)

Intuitive explanation

The Arrhenius equation connects temperature to the rate constant, and for a first-order reaction, half-life depends only on that rate constant through $t_{1/2} = \frac{\ln 2}{k}$ . Your strategy is to work backward: use the given half-life to find $k$ , then use the Arrhenius equation $k = Ae^{-E_a/RT}$ to solve for the temperature where that rate constant occurs. This links macroscopic reaction timing to molecular collision energy.

Intuitive explanation

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