For the mechanism
Step 2 is the rate determining step. The activation energies are $E_{a, 1} = 85$ kJ/mol, $E_{a, - 1} = 60$ kJ/mol and $E_{a, 2} = 150$ kJ/mol. Find the activation energy (kJ/mol) of the overall reaction $2 P + 2 Q \to 2 S + X + Y$ .

Question

For the mechanism

Step 2 is the rate determining step. The activation energies are $E_{a, 1} = 85$ kJ/mol, $E_{a, - 1} = 60$ kJ/mol and $E_{a, 2} = 150$ kJ/mol. Find the activation energy (kJ/mol) of the overall reaction $2 P + 2 Q \to 2 S + X + Y$ .

TestHub · Accepted Answer

Step 2 is slow: rate = k 2 ​ [ R ] 2 . Step 1 is a fast pre-equilibrium: [ R ] = [ S ] K 1 ​ [ P ] [ Q ] ​ ​ with K 1 ​ = k − 1 ​ k 1 ​ ​ . So rate = [ S ] k 2 ​ K 1 ​ [ P ] [ Q ] ​ , and for the overall equation (step 1 taken twice) the effective constant is k 2 ​ K 1 2 ​ . E a ​ = E a , 2 ​ + 2 ( E a , 1 ​ − E a , − 1 ​ ) = 150 + 2 ( 85 − 60 ) = 200 kJ/mol. 175 comes from using one unit of step 1, and 235 from adding E a , 1 ​ without subtracting E a , − 1 ​ . Answer: (C).

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