Question

Account for the following:
${{p}}{{{K}}_{{a}}}$ value of $4 -$nitrobenzoic acid is lower than that of benzoic acid.

Answer 1

Acid dissociation constant, ${{{K}}_{{a}}}$ measures the strength of an acid in solution quantitatively. If the value of ${{p}}{{{K}}_{{a}}}$ value is small, then the acid will be stronger. Acidity of an organic compound depends upon several factors like inductive effect, resonance effect, etc.

Complete step by step solution:
Consider the dissociation of a compound ${{HA}}$.
${{HA}} \rightleftharpoons {{{H}}^ + } + {{{A}}^ - }$
The acid dissociation constant can be expressed as:
${{{K}}_{{a}}} = \dfrac{{\left[ {{{{A}}^ - }} \right]\left[ {{{{H}}^ + }} \right]}}{{\left[ {{{HA}}} \right]}}$
${{p}}{{{K}}_{{a}}}$ is used because using ${{{K}}_{{a}}}$ will be inconvenient practically. ${{p}}{{{K}}_{{a}}}$ is the negative logarithm of ${{{K}}_{{a}}}$. ${{p}}{{{K}}_{{a}}}$ is expressed as negative logarithm of ${{{K}}_{{a}}}$.
The structure of $4 -$nitrobenzoic acid and benzoic acid is given below:

Acids donate protons, ${{{H}}^ + }$. Benzoic acid is an acid from the name itself. This gives a base by donating a proton. When this occurs, it forms carboxylate ions. The negative charge in the carboxylate ion is involved in resonance. Resonance structures are the ones in which the position of valence electrons are different. It stabilizes the molecule. Thus it is said to be a strong acid.
When electron withdrawing groups are added to the benzoic acid, it makes the carboxylate ion more stable. Thus the charge of the carboxylate ion will be delocalized.
Some examples of electron withdrawing groups are $- {{CN}}, - {{N}}{{{O}}_2}, - {{CHO}},$ etc.
When these groups are present, it decreases the electron density of the molecule, thus it is able to accept electrons. This makes the molecule more acidic. This is called $- {{I}}$ effect or negative inductive effect. When the number of electron withdrawing groups is more, then more stronger will be the acid. $- {{N}}{{{O}}_2}$ is an electron withdrawing group. Thus it is obvious that the $4 -$nitrobenzoic acid is more acidic than benzoic acid.

Note:
Similarly, when electron donating groups are present, it increases the electron density of the molecule, thus it is able to donate electrons. This makes it more basic. This is called ${{ + I}}$ effect. ${{p}}{{{K}}_{{a}}}$ of $4 -$nitrobenzoic acid is $3.41$ and benzoic acid is $4.19$.