Benzyl bromide reacts with \(\mathrm{H}_{2} \mathrm{O}\) in formic acid solution to yield benzyl alcohol? the rate is independent of \(\left[\mathrm{H}_{2} \mathrm{O}\right]\). Under the same conditions \(\mathrm{p}\) -methylbenzyl bromide reacts 58 times as fast. Benzyl bromide reacts with ethoxide ion in dry alcohol to yield benzyl ethyl ether \(\left(\mathrm{C}_{6} \mathrm{H}_{5} \mathrm{CH}_{2} \mathrm{OC}_{2} \mathrm{H}_{5}\right) ;\) the rate depends upon both \([\mathrm{RBr}]\) and \(\left[\mathrm{OC}_{2} \mathrm{H}_{5}^{-}\right]\). Under the same conditions \(\mathrm{p}\) -methylbenzyl bromide reacts \(1.5\) times as fast. Interpret these results. What do they illustrate concerning the effect of: (a) polarity of solvent, (b) nucleophilic power of the reagent, and (c) electron release by substituents?

Solvent polarity is a critical factor in determining the rate of chemical reactions. A solvent's polarity is essentially a measure of how strongly its molecules pull on electrons—in scientific terms, its dielectric constant. When a solvent is polar, it allows charged particles, like ions, to disperse more readily, which can lower the energy barrier needed for a chemical reaction to occur.

In the exercise provided, formic acid solution is used as a solvent, creating a highly polar environment suitable for the reaction between benzyl bromide and water. The polar environment stabilizes the transition state, facilitating the substitution reaction to produce benzyl alcohol. The significant increase in reaction rate with p-methylbenzyl bromide in the polar formic acid solution (by 58 times) compared to the less polar dry alcohol, implies that the higher polarity of the solvent contributes to a faster rate.

Nucleophilicity represents the propensity of a nucleophile, which is a chemical species with a lone pair of electrons, to form a bond with an electrophile—an electron deficient species. It is contingent on several factors, including charge, electronegativity, steric hindrance, and solvent effects. A highly nucleophilic reagent, such as an ethoxide ion (OC2H5-), is more reactive due to its negative charge as compared to a neutral molecule like water (H2O).

The contrasting reaction rates between water and ethoxide ion in the exercise are indicative of the difference in nucleophilicity. In anhydrous alcohol, the ethoxide ion's reactivity is highlighted as the rate depends on both the concentration of the alkyl bromide and the ethoxide ion. This corresponds to a bimolecular reaction mechanism (SN2), wherein the nucleophilic power greatly influences the reaction's rate, as observed in the faster reaction with p-methylbenzyl bromide.

Substituent effects encompass how the presence of various substituents attached to a molecular framework can influence a molecule's reactivity. Specifically, electron-donating or electron-withdrawing groups can either stabilize or destabilize the transition state of a reaction. In the given exercise, the presence of a methyl substituent on the para position of the benzyl bromide (forming p-methylbenzyl bromide) enhances the electron density around the aromatic ring, thereby facilitating a faster reaction rate.

In an aqueous formic acid solution, the p-methyl group's electron-donating effect enhances the reaction rate significantly, by 58 times compared to benzyl bromide. Yet, in the presence of a less polar solvent and a strong nucleophile (ethoxide ion), the substituent effect is still apparent but not as pronounced (1.5 times faster). This elucidates that while the substituent effect is invariably important, its influence can be modulated by factors like solvent polarity and the strength of the nucleophile.