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Question

The rate constant for two parallel reactions were found to be 1.0×102 dm3 mol1 s1 and 3.0×102 dm3 mol1 s1. If the corresponding energies of activation of the parallel reactions are 60.0 kJ mol1 and 70.0 kJ mol1 respectively, what is the apparent overall energy of activation?


A
130.0 kJ mol1
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B
67.5 kJ mol1
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C
100.0 kJ mol1
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D
65.0 kJ mol1
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Solution

The correct option is B 67.5 kJ mol1
We know that, the overall energy of activation for the parallel reaction can be calculated as:

Ea=Ea1×k1+Ea2×k2(k1+k2)

Given,
Ea1=60 kJ mol1
Ea2=70 kJ mol1
k1=1.0×102 dm3 mol1 s1
k2=3.0×102 dm3 mol1 s1

Ea     =1.0×102×60+3×102×70[1.0×102+3.0×102]

Ea=67.5 kJ mol1

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