Based on their activation energies and energy changes and assuming that all collision factors are the same, which of the following reactions would be fastest? (a) ea = 57 kj/mol , δe = 13 kj/mol (b) ea = 47 kj/mol , δe = -29 kj/mol (c) ea = 34 kj/mol , δe = -10 kj/mol .

C is the fastest reaction.

Explanation:

Let us consider a generic reaction aA ⇄ bB.

The reaction rate would be:

  [1]

where,

r is the reaction rate

k is the rate constant

n is the reaction order

So we can see that the reaction rate depends on the rate constant. We can find out this constant using the Arrhenius equation:

   [2]

where,

A is the collision factor

R is the universal gas constant

T is the absolute temperature

If A and T are the same for different reactions, k will only depend on Ea. According to [2], the lower Ea, the higher the k. According to [1], the higher the k, the higher the r. And when r is higher the reaction is faster. All in all, C has the lowest Ea (34 kJ/mol), so it is the fastest reaction.