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Question

For a first order reaction AP, the tem[erature (T) dependent rate constant (k) was found to follow the equation logk=(2000)1T+6. The pre exponential factor A and the activation energy Ea respectively, are:

A
1.0×106 s1 and 9.7 kJ mol1
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B
6.0× s1 and 16.6 kJ mol1
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C
1.0×106 s1 and 16.6 kJ mol1
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D
1.0×106 s1 and 38.29 kJ mol1
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Solution

The correct option is D 1.0×106 s1 and 38.29 kJ mol1
According to Arrhenius equation,
k=AeEaRT
lnk=lnAEaRT
logk=logAEa2.303RT ...(1)
Given,
logk=6.0(2000)1T ...(2)
On comparing equation (1) and (2),
logA=6.0A=106 s1
and Ea2.303R=2000Ea=2000×2.303×8.314=38.29 kJ mol1

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