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Chemical Kinetics

Question

In the Arrhenius equation for a certain reaction, the value of A and Ea (activation energy) are 4 x 10¹³ sec^–1 and 98.6 mol^–1 respectively, If the reaction is of first order, at what temperature will its half life period be the minutes?

Solution

By using the half life reaction equation

k = \frac{0.693}{t_{1 / 2}} = \frac{0.693}{10 \times 60} = 1.155 \times 10^{- 3}

According to Arrhenius equation

\log k = \log A - \frac{Ea}{2.303 RT}

\log 1.155 \times 10^{- 3} = \log 4 \times 10^{13} - \frac{98.6}{2.303 \times 8.314 \times T} or T = 311.65 K