When t-butyl bromide is treated with `CH_(3)O^(-)` in a mixture of `CH_(3)OHandH_(2)O`, the rate of formation of t-butyl alcohol and t-butyl methyl ether doesn't change appreciably as the concentration of `CH_(3)O^(-)` ion is increased. However, increasing the concentration of `CH_(3)O` caused a marked increase in the rate at which t-butyl bromide disappear from the mixture. Why?

Explanation

To understand the question regarding the reaction of t-butyl bromide with methoxide ion in a mixture of methanol and water, let's break it down step by step.

### Step-by-Step Solution:

1. **Identify the Reaction Type**:
- The reaction between t-butyl bromide (C₄H₉Br) and methoxide ion (CH₃O⁻) is primarily an **SN1 reaction**. In an SN1 reaction, the rate-determining step involves the formation of a carbocation.

2. **Formation of Carbocation**:
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