The esterification of acetic anhydride by ethyl alcohol can be represented by the following balanced equation:
`underset(A)((CH_(3)CO)_(2)O) + underset(B)(C_(2)H_(5)OH) rarrCH_(3)COOC_(2)H_(5) + CH_(3)COOH`
When the reaction is carried out in dilute hexane solution, the rate may be represented by `k[a][b]`. When ethyl alcohol `(B)` is the solvent, the rate may be represented by `k[A]` the values of `k` are not the same in the two cases). Explain the difference in the apparent order of the reaction.

Explanation

To explain the difference in the apparent order of the reaction for the esterification of acetic anhydride by ethyl alcohol when carried out in dilute hexane solution versus when ethyl alcohol is the solvent, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Reaction**:
The reaction can be represented as:
\[
(CH_3CO)_2O + C_2H_5OH \rightarrow CH_3COOC_2H_5 + CH_3COOH
...