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Question

A reaction takes place in three steps with an individual rate constant and activation energy, as given below.
Rate constant Activation energy
Step 1 k1 Ea1=180kJ/mol
Step 2 k2 Ea2=80kJ/mol
Step 3 k3 Ea3=50kJ/mol
And overall rate constant, k=(k1k2k3)2/3.
The overall activation energy of the reaction will be:

A
140 kJ/mol
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B
150 kJ/mol
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C
130 kJ/mol
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D
120 kJ/mol
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Solution

The correct option is A 140 kJ/mol
AeEa/RT=[AeEa1/RT×AeEa2/RTAeEa3/RT]2/3
=[Ae(Ea1Ea2+Ea3)/RT]2/3
Ea=23[Ea1+Ea2Ea3]
=23[180+8050]=140kJ/mol

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