Question

How is the speed of a chemical reaction related to the spontaneity of the reaction?

Answer 1

It's not. Spontaneity is a thermodynamic phenomenon, and the rate/speed of a reaction is a kinetic phenomenon.

The rate of a chemical reaction can be written in a rate law as

`r(t) = k[A]`

where

• `r(t)` is the rate of reaction.
• `k` is the rate constant for that reaction at a given temperature.
• `[A]` is the concentration of `A` in `"M"`.

for a simple unimolecular reaction

`A -> B`,

which has activation energy `E_a`. Reactions also have a Gibbs' free energy of reaction, `DeltaG_"rxn"`.

Both are on the same reaction coordinate diagram, but they do not influence each other.

Modifying the rate `r(t)` modifies the rate constant `k` when `[A]` is held constant (such as changing the temperature, pressure, etc).

From the Arrhenius equation

`k = Ae^(-E_a"/RT")`,

increasing `k` increases `e^(-E_a"/RT")`, which means `E_a` is decreased. Hence, a lower activation energy indicates a faster reaction.

Yes, `DeltaG_"rxn"` indicates a reaction is spontaneous when `DeltaG_"rxn" < 0`, but it doesn't matter.

When you modify `E_a`, you do not modify the free energy of the reactants or products, so you do not touch `DeltaG_"rxn"` for the overall reaction. If you raise/lower the peak of the hill, you have not raised/lowered the bottom of the hill.

• If the overall reaction was spontaneous without a catalyst, it is still spontaneous with a catalyst.
• If it is also slow without a catalyst, it is now fast with a catalyst, but not additionally and suddenly possible/spontaneous.