The correct decreasing order of nucleophilicity of the following ions for \(\mathrm{S}_{\mathrm{N}}{ }^{2}\) reactions in protic solvents is (a) \(\mathrm{PhS}^{-}>\mathrm{PhO}^{-}>\mathrm{OH}^{-}>\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}^{-}>\mathrm{CN}^{-}\) (b) \(\mathrm{PhS}^{-}>\mathrm{CN}^{-}>\mathrm{C}_{2} \mathrm{H}_{5} \mathrm{O}^{-}>\mathrm{OH}^{-}>\mathrm{PhO}^{-}\) (c) \(\mathrm{CN}^{-}>\mathrm{OH}^{-}>\mathrm{C}, \mathrm{H}_{5} \mathrm{O}^{-}>\mathrm{PhS}^{-}>\mathrm{PhO}^{-}\) (d) \(\mathrm{C}, \mathrm{H}, \mathrm{O}^{-}>\mathrm{CN}^{-}>\mathrm{OH}^{-}>\mathrm{PhO}^{-}>\mathrm{PhS}^{-}\)

Understanding the role of protic solvents is essential when discussing nucleophilicity in SN2 reactions. Protic solvents are those that contain hydrogen atoms capable of forming hydrogen bonds. Common examples include water (H₂O), alcohols (like ethanol, CH₃CH₂OH), and acids (like acetic acid, CH₃COOH).

In SN2 reactions, the nucleophile must attack the substrate from behind to displace the leaving group. Protic solvents play a pivotal role by stabilizing various ions through hydrogen bonding. This interaction can greatly affect the nucleophilicity of a reacting ion. Typically, smaller and more basic nucleophiles are better stabilized by hydrogen bonds in these solvents, which can sometimes hinder their ability to attack the substrate. Conversely, larger nucleophiles, less subject to solvation, can often react more freely. Hence, the reactivity order can be quite different in protic solvents compared to aprotic solvents.

Basicity is a measure of the ability of a molecule or ion to accept a proton (H+). In other words, a base is a proton acceptor. When comparing basicity across ions, we consider factors such as atomic size, electronegativity, resonance stabilization, and inductive effects.

For instance, sulfur in the phenyl thiolate ion (PhS⁻) is larger and less electronegative than oxygen in the phenyl alkoxide ion (PhO⁻). Hence, PhS⁻ is a weaker base. Alkoxides, like hydroxide (OH⁻) and ethoxide (C₂H₅O⁻), generally act as stronger bases due to their negative charge being localized over a smaller volume and not being stabilized via resonance. However, differences in alkyl substitutions can modulate their basicity, as seen in the enhanced basicity of ethoxide due to the electron-donating effect of the ethyl group.

Nucleophile strength refers to how efficiently a nucleophile can donate its electron pair to form a new bond in a chemical reaction. In SN2 reactions, the strength of the nucleophile is a crucial factor determining the rate of the reaction. More potent nucleophiles will react faster with the electrophilic center, leading to a higher reaction rate.

In protic solvents, the trend in nucleophile strength is sometimes parallel to basicity, but this isn't a universal rule. For example, while phenyl thiolate (PhS⁻) is less basic than ethoxide (C₂H₅O⁻), it is more nucleophilic because it experiences less solvation, freeing it to more effectively attack the substrate. This trend demonstrates the importance of considering all molecular interactions in the reaction environment when predicting the outcome of SN2 reactions.