Question

Set the following in increasing order of their ${{p}^{{{K}_{a}}}}$ values
(x) $C{{H}_{3}}S{{(O)}_{2}}OH$ (y) $C{{H}_{3}}C(O)OH$ (z) $C{{H}_{3}}OH$ :
(A) $y > x > z$
(B) $x < y < z$
(C) $y > z > x$
(D) $x < z < y$

Answer 1

The $K_a$ value is directly proportional to the acidity of the compound. The ${{p}^{{{K}_{a}}}}$ value is negative of the log of Ka. Thus, the ${{p}^{{{K}_{a}}}}$ values give the basicity of the acid. Higher is the basicity of an acid, higher will be the ${{p}^{{{K}_{a}}}}$ values.

Complete step by step solution:
This question can be answered on the basis of inductive effect. The induction of polarity between two atoms where one is more electronegative and the other is less electronegative is known as inductive effect. The ${{p}^{{{K}_{a}}}}$ values give the basicity of the acid. Higher is the basicity of an acid, higher will be the ${{p}^{{{K}_{a}}}}$ values.
A covalent is known to be formed by sharing if electrons between two atoms. If the electronegativity of two atoms that are sharing a bond between them are different A covalent is known to be formed by sharing if electrons between two atoms. If the electronegativity of two atoms that are sharing a bond between them are different. The electron pair forming the sigma bond is not equally shared between the two atoms.
Here, the electron pair gets displaced towards the more electronegative of the two. Due to this displacement a partial negative charge on the more electronegative atom and an equivalent partial positive charge on the other atom. This induction of polarity in a covalent bond and this is called the inductive effect. Higher the value of ${{p}^{{{K}_{a}}}}$ lower is the acidity.
In the given compounds $C{{H}_{3}}OH~$ is least acidic due to less stability of $C{{H}_{3}}{{O}^{-}}~$ ion ( $+I$ effect of $C{{H}_{3}}$ ) therefore has highest ${{p}^{{{K}_{a}}}}$ , In $C{{H}_{3}}CO{{O}^{-}}~$ and $C{{H}^{3}}SO_{3}^{-}~$ the negative charge is in conjugation with π bond making them strong acids. $C{{H}_{3}}S{{O}_{3}}H~$ is strongest acid as the highly electron negative group $S{{O}_{3}}$ ​ makes the hydrogen highly acidic.
Therefore correct answer is option B i.e. $x < y < z$ .

Note:
It must be noted that the nitro group is the electron withdrawing group. They can strongly attract the electrons toward themselves. As a result, the $O-H$ bond gets weakened. So, the hydrogen can be easily donated. Thus, they are strong acids.