Question

Consider the given acid ionization constants. identify the strongest conjugate base.

Answer 1

The question is incomplete. Complete question is:
Consider the given acid ionization constants. identify the strongest conjugate base.
HNO2(aq) 4.6×10−4
HCHO2(aq) 1.8×10−4
HClO(aq) 2.9×10−8
HCN(aq) 4.9×10−10
.........................................................................................................................
Correct Answer: option 4: HCN(aq) 4.9×10−10

Reason: 
According to Lowry and Bronsted theory of acid and base. Stronger the acid, weaker will be the conjugate base.

In present case, ionization constant is highest of HCN i.e. 4.9×$10^{-10}$. This signifies that, it is the strongest acid. Hence, conjugate base associated with this acid (i.e. $CN^{-}$) is the weakest. 

Answer 2

Missing question:
HNO2(aq) 4.6×10−4
HCHO2(aq) 1.8×10−4
HClO(aq) 2.9×10−8
HCN(aq) 4.9×10−10
Answer is: the strongest conjugate base is CN⁻(aq), because it has highest base ionization constant.
Chemical reaction: HCN(aq) ⇄ CN⁻(aq) + H⁺(aq).
Ka(HCN) = 4,9·10⁻¹⁰.
Ka · Kb = Kw; ionic product of water.
Kb = Kw ÷ Ka.
Kb(CN⁻) = 1·10⁻¹⁴ 4,9·10⁻¹⁰.
Kb(CN⁻) = 2,04·10⁻⁵.