Strongest conjugate base is:
A. ${\text{C}}{{\text{l}}^ - }$
B. ${\text{B}}{{\text{r}}^ - }$
C. ${{\text{F}}^ - }$
D. ${{\text{I}}^ - }$

Hint: The concept of conjugate acid base depends on the Bronsted Lowry theory. The weakest acid has the strongest conjugate base. The strength of an acid is determined based on the stability of the anion.

Complete answer:
According to the Bronsted-Lowery concept, acids are proton donors and bases are proton acceptors. The acid and base react to form conjugate base and conjugate acid.
Acid forms conjugate base and base forms conjugate acid.
The general reaction of acid and base is shown as follows:
Acid + Base $ \to $ conjugate base + conjugate acid
The strength of conjugate acid and base depends upon the strength of base and acid.
A strong acid or base forms the weak conjugate base or conjugate acid.
Weak acid or base forms the strong conjugate base or conjugate acid.
Determine the acidity of the hydrogen halides as follows:
Add protons with each anion to form an acid.
So, acids are, ${\text{HF,}}\,{\text{HCl,}}\,{\text{HBr,}}\,{\text{HI}}$.
The decreasing order of the acidity of the Hodgeon halides is as follows:
${\text{HI}}\,\,\,{\text{ > }}\,\,{\text{HBr}}\,\, > \,\,{\text{HCl}}\,\,{\text{ > }}\,{\text{HF}}$
So, ${\text{HF}}$ is the weakest acid, so its conjugate base ${{\text{F}}^ - }$will be strongest.
$\mathop {{\text{HF}}}\limits_{{\text{acid}}} \, \to \,{{\text{H}}^ + }\, + \,\mathop {{{\text{F}}^ - }}\limits_{{\text{conjugate }}\,{\text{base}}} $

Therefore, option (C) ${{\text{F}}^ - }$ is correct.

Note: The acidity of the hydrogen halides depends upon the two factors: the stability of the anion and stability of the bond. As the fluorine is most electronegative so, the hydrogen-fluorine bond is strongest so it does not dissociate easily, so the ${\text{HF}}$ is the weak acid. The size of fluorine is smaller than other halogens so the electron feels more repulsion in fluoride ion, so ${\text{HF}}$ is the weak acid.