15.67

[MCracchiolo 1C]

Would someone be able to explain why 15.67 uses the ratio of activation energies? i.e. How would I have known to substitute Ea(cat) without looking at the solution manual?

[Curtis Tam 1J]

They're using the ratios to see how the rate changes with respect to activation energy. I believe you could have plugged in the actual values given in the problem but simply keeping the Ea as a variable makes the calculation easier.

[Ahmed Mahmood 4D]

Think about it like this: You have two reaction rates, and you want to compare how the factor is affected by the addition of a catalyst. You know that adding a catalyst changes the activation energy; you know that changing the activation energy changes the reaction rate; you know the formula for the reaction rate. Therefore, in order to calculate the factor by which adding a catalyst changes the reaction rate, you must calculate the ratio of the catalyzed/uncatalyzed reaction rates (Aexp(-Ea[cat]/RT)/Aexp(-Ea[uncat]/RT)). A cancels out.