15.1 Applications of inductive effect

  General Organic Chemistry

Inductive effect is useful in correlating structure with reactivity.

(a). Acid strength of aliphatic carboxylic acids: The strength of an acid depends on the extent of its ionization. The greater the ionization, the stronger is the acid. The strength of an acid is denoted by the numerical value of p$K_a$ (${\text{p}}{K_a} = - {\log _{10}}{K_a}$, where $K_a$ is the acidity constant).

Smaller the numerical value stronger is the acid.

In acetic acid, the electron-releasing inductive effect of methyl group hinders the breaking of $O-H$ bond; consequently reduces the ionization. This effect is absent in formic acid.

Greater ionization in formic acid over acetic acid makes formic acid (p$K_a=3.77$) stronger than acetic acid (p$K_a=4.76$).

Monochloroacetic acid (p$K_a=2.86$) is stronger than formic acid since -I effect of chlorine promotes ionization. As this effect is additive, trichloroacetic acid (p$K_a=0.66$) is still a stronger acid.

When an unsaturated carbon is conjugated with the carboxyl group, the acid strength is increased. This is because with the increasing $s$ contribution to the hybrid orbitals, the electrons are progressively drawn closer to the nucleus of the carbon resulting in the increase in -I effect.

Since the $s$ contributions in $sp$, $sp^2$ and $sp^3$ orbitals are respectively 50%, 33.3% and 25%, the order of -I effect of hybrid orbitals is $sp\ >\ sp^2\ >\ sp^3$. This is reflected in the p$K_a$ values of the following acids.

(b). Aromatic carboxylic acids: The $\alpha$ carbon of benzoic acid is $sp^2$-hybridized. Hence benzoic acid (p$K_a=4.20$) is a stronger acid than its saturated analogue, cyclohexane carboxylic acid (p$K_a=4.87$).

Electron-withdrawing groups substituted at $o-$ and $p-$ positions enhances the acid strength.

(c). Dioic acids: Since carboxyl group is itself an electron-withdrawing group, the dioic acid are in general stronger than their monocarboxyl analogues, e.g.,

The electron-withdrawing effect of one carboxyl group over the other falls off sharply on separating the two carboxyl groups by at least two saturated carbons.

(d). Aliphatic bases: The strength of nitrogenous bases depends on the ease of availability of the unshared electron pair on the nitrogen atom to the proton. Due to the increasing +I effect in amines, the order of base strength should be $NH_3<MeNH_2<Me_2NH<Me_3N$.

However, the p$K_a$ values are 9.25 ($NH_3$), 10.64 ($MeNH_2)$, 10.77 ($Me_2NH$) and 9.80 ($Me_3N$).

The p$K_a$ value for the base $B:$ is a measure of the acid strength of its conjugate acid ${B^ \oplus }:H.$.

Stronger the acid ${B^ \oplus }H$, weaker is the base $B:$. In other words, smaller the numerical value of p$K_a$ for the acid ${B^ \oplus }H$, the weaker is the base $B$.

From the p$K_a$ values it is seen that $2^\circ $ amine (10.77) is a stronger base than $3^\circ $ amine (9.80). This is because of the base strength of an amine in water depends not only on the ease of availability of lone pair but also on the extent of solvation of the protonated amine by hydrogen bonding. The protonated $3^\circ $ amine has one and protonated $2^\circ $ amine has two hydrogens on the nitrogen for hydrogen bonding.

Hence, $2^\circ $ amine is a stronger base than $3^\circ $ amine. Solvation is an important factor for the determination of the base strength. This is supported by the fact that the order of base strength of amines is $3^\circ > 2^\circ > 1^\circ $ in chlorobenzene in which hydrogen bonding is absent.

(e). Aromatic bases: An aniline is a weaker base (p$K_a=4.62$) than its saturated analogue, cyclohexylamine (p$K_a=10.68$). This is because the nitrogen atom in aniline is bonded to an $sp^2$ carbon which pulls the unshared electron pair on nitrogen. This results in the delocalization of the lone pair with the $\pi$ electrons of the ring. Thus, the lone pair is not easily available for protonation.

Hence, aniline is a weaker base than ammonia or cyclohexylamine. Electron-withdrawing substituents at $o-$ and $p-$ positions have marked base-weakening effect.