Identify the false statement among the following (a) The rate of hydrolysis of tert-butyl chloride does not change by increasing the concentration of \(\mathrm{OH}^{-}\). (b) 1 -phenylethanol reacts with thionyl chloride to give a chloro compound with almost complete retention of configuration. (c) Polar solvents generally increase the rate of \(\mathrm{S}_{\mathrm{N}} 1\) reactions. (d) \(\mathrm{S}_{\mathrm{N}} 2\) reaction of optically active substrate leads to racemization if the leaving group is attached to the chiral carbon.

The rate of hydrolysis of tert-butyl chloride does not change by increasing the concentration of \(\mathrm{OH}^{-}\). This statement is true. The hydrolysis of tert-butyl chloride is an \(\mathrm{S}_{\mathrm{N}}1\) reaction, which means it's a unimolecular nucleophilic substitution reaction. In an \(\mathrm{S}_{\mathrm{N}}1\) reaction, the reaction rate depends only on the concentration of the substrate (tert-butyl chloride in this case), not the concentration of the nucleophile (\(\mathrm{OH}^{-}\)). Therefore, increasing the concentration of \(\mathrm{OH}^{-}\) does not affect the rate of hydrolysis of tert-butyl chloride.

1-phenylethanol reacts with thionyl chloride to give a chloro compound with almost complete retention of configuration. This statement is true. Reaction of 1-phenylethanol with thionyl chloride is an example of an \(\mathrm{S}_{\mathrm{N}}2\) reaction, in which the nucleophile attacks the carbon attached to the leaving group (in this case the hydroxyl group) from the opposite side of the leaving group. Since the configuration at the chiral center is determined by the three-dimensional arrangement of the groups, an attack from the opposite side will lead to retention of configuration. Therefore, 1-phenylethanol reacts with thionyl chloride to give a chloro compound with almost complete retention of configuration.

Polar solvents generally increase the rate of \(\mathrm{S}_{\mathrm{N}} 1\) reactions. This statement is true. In \(\mathrm{S}_{\mathrm{N}}1\) reactions, the reaction rate depends on the formation of a carbocation intermediate. Polar solvents are capable of stabilizing the charged species (the carbocation) and hence lower the activation energy required for the reaction to occur. As a result, polar solvents generally increase the rate of \(\mathrm{S}_{\mathrm{N}}1\) reactions.

\(\mathrm{S}_{\mathrm{N}} 2\) reaction of optically active substrate leads to racemization if the leaving group is attached to the chiral carbon. This statement is false. In an \(\mathrm{S}_{\mathrm{N}}2\) reaction, the nucleophile attacks the substrate from the opposite side of the leaving group, leading to inversion of configuration at the chiral center. There is no intermediate formation where two enantiomers can be formed, as seen in the \(\mathrm{S}_{\mathrm{N}}1\) reaction. Hence, there is no racemization in \(\mathrm{S}_{\mathrm{N}}2\) reactions of optically active substrates. In conclusion, statement (d) is the false statement among the given options.