Question

Which of the following acid/base reaction is most difficult to proceed in forward direction ?

• A. BCl$_3$ + NMe$_3$ $\longrightarrow$ Cl$_3$B$\leftarrow$NMe$_3$
• B. BF$_3$ + NH$_3$ $\longrightarrow$ F$_3$B$\leftarrow$NH$_3$
• C. NH$_3$ + H$_2$O $\longrightarrow$ NH$_4^+$ + OH$^-$
• D. PH$_3$ + H$_2$O $\longrightarrow$ PH$_4^+$ + OH$^-$

Answer 1

Answer: (D)

D

Answer 2

The difficulty of a reaction proceeding in the forward direction can be assessed by considering the strengths of the reactants (acid and base) and the stability of the products, which is reflected in the equilibrium constant (K) of the reaction. A reaction that is difficult to proceed forward will have a small equilibrium constant.

Let's analyze each reaction:

(A) BCl$_3$ + NMe$_3$ $\longrightarrow$ Cl$_3$B$\leftarrow$NMe$_3$

This is a Lewis acid-base reaction. BCl$_3$ is a Lewis acid, and NMe$_3$ is a Lewis base. They form a stable adduct. BCl$_3$ is a relatively strong Lewis acid, and NMe$_3$ is a relatively strong Lewis base. This reaction proceeds readily.

(B) BF$_3$ + NH$_3$ $\longrightarrow$ F$_3$B$\leftarrow$NH$_3$

This is also a Lewis acid-base reaction. BF$_3$ is a Lewis acid, and NH$_3$ is a Lewis base. They form a stable adduct. BF$_3$ is a weaker Lewis acid than BCl$_3$ due to backbonding from F to B. NH$_3$ is a weaker Lewis base than NMe$_3$ due to the absence of inductive effect from methyl groups. This reaction also proceeds readily.

(C) NH$_3$ + H$_2$O $\longrightarrow$ NH$_4^+$ + OH$^-$

This is a Brønsted-Lowry acid-base reaction where water acts as an acid and ammonia acts as a base. Ammonia is a weak base, and its reaction with water establishes an equilibrium. The base dissociation constant (K$_b$) for NH$_3$ is approximately $1.8 \times 10^{-5}$. While the equilibrium lies towards the reactants, the forward reaction occurs to a measurable extent.

(D) PH$_3$ + H$_2$O $\longrightarrow$ PH$_4^+$ + OH$^-$

This is a Brønsted-Lowry acid-base reaction where water acts as an acid and phosphine (PH$_3$) acts as a base. The basicity of group 15 hydrides decreases significantly down the group (NH$_3$ > PH$_3$ > AsH$_3$ > SbH$_3$). PH$_3$ is a very weak base, much weaker than NH$_3$. Its tendency to accept a proton from water is extremely low. The base dissociation constant (K$_b$) for PH$_3$ is reported to be extremely small (on the order of $10^{-27}$). This means the equilibrium for this reaction lies overwhelmingly towards the reactants, and the forward reaction proceeds to a negligible extent.

Comparing the four reactions, reactions (A) and (B) are Lewis acid-base adduct formations that are generally favorable. Reaction (C) is the reaction of a weak base (NH$_3$) with water, which occurs to a small but measurable extent. Reaction (D) is the reaction of an extremely weak base (PH$_3$) with water, which occurs to a negligible extent. Therefore, the reaction that is most difficult to proceed in the forward direction is the one with the smallest equilibrium constant, which is reaction (D).