What change would you expect on the rate of the reaction of ethanol with 2-iodo-2-methylbutane if the nucleophile concentration is halved by adding diethyl ether as an inert solvent and the alkyl halide concentration is unchanged

The rate of reaction is unchanged

Explanation:

The rate of reaction of tertiary alkyl halides with a nucleophile is independent of the nucleopohile concentration but depends only on the initial concentration of the alkyl halide since tertiary alkyl halides reacts via SN1 mechanism.

The nucleophile concentration does not come into the rate equation for the reaction hence any change in its concentration is inconsequential in determining the overall rate of reaction, hence the rate of reaction is unchanged when the nucleophile concentration is halved.