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Question: In the Arrhenius equation for a certain reaction, the values of A and \(E_{a}\) are \(4 \times 10^{1...

In the Arrhenius equation for a certain reaction, the values of A and EaE_{a} are 4×1013sec⁡−14 \times 10^{13}\sec^{- 1}{} and 9.86kJmol−19.86kJmol^{- 1}

respectively. If the reaction is of first order, at what temperature will its half life period be 10 minute

A

311.34 K

B

31.134 K

C

411.34 K

D

41.134 K

Answer

311.34 K

Explanation

Solution

According to Arrhenius equation, k=Ae−Ea/RTk = Ae^{- E_{a}/RT} or

log⁡kA=−EaRT×12.303\log\frac{k}{A} = - \frac{E_{a}}{RT} \times \frac{1}{2.303}

k=0.693t1/2=0.69310×60=1.155×10−3k = \frac{0.693}{t_{1/2}} = \frac{0.693}{10 \times 60} = 1.155 \times 10^{- 3}

∴log⁡1.155×10−34×1013=−98.6×1038.314×T×2.303\therefore\log\frac{1.155 \times 10^{- 3}}{4 \times 10^{13}} = - \frac{98.6 \times 10^{3}}{8.314 \times T \times 2.303}

or −16.54=−986008.314×2.303T- 16.54 = - \frac{98600}{8.314 \times 2.303T}

or T=986008.314×2.303×16.54=311.34K.T = \frac{98600}{8.314 \times 2.303 \times 16.54} = 311.34K.