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Question

The time required for 5% completion of a reaction at 300 K is equal to that required for its 20% completion at 320 K. If the pre -exponential factor for the reaction is 3.56×109 sec1. Then which of the following is correct.(given log95 = 1.98, log80 = 1.90, log5 =0.7, R=253JK1mol1)

A
The reaction follows first order kinetics
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B
The activation energy of the reaction is 64.48 kJ/mol
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C
The activation energy for the reaction is 7.19 kJ/mol
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D
The reaction follows second order kinetics
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Solution

The correct options are
A The reaction follows first order kinetics
B The activation energy of the reaction is 64.48 kJ/mol
a) Since unit of pre exponential factor is sec1, so it is a first order reaction.
b)We know that,
k=2.303tlogaax
So at 300 K ,
k300=2.303tlog10095----(1)
At 320 K ,
k320=2.303tlog10080------(2)
Dividing equation (2) by (1),
k320k300=5
From Arrhenius equation,
log5=Ea×32.303×25(13001320)
0.7=Ea×3276360
Ea= 64484J/mol = 64.48 kJ/mol

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