Ammonium chloride ($NH_4Cl$) is a salt formed by a strong acid ($HCl$) and a weak base ($NH_4OH$). In an aqueous solution, the ammonium ion ($NH_4^+$) undergoes hydrolysis to form $NH_4OH$ and $H^+$. The hydrolysis constant ($K_h$) for a salt of a weak base and strong acid is given by the expression: $K_h = \frac{K_w}{K_b}$ where $K_w$ is the ionic product of water ($1.0 \times 10^{-14}$ at 298 K) and $K_b$ is the ionization constant of the weak base. Given $K_b = 1.77 \times 10^{-5}$. Substituting the values: $K_h = \frac{1.0 \times 10^{-14}}{1.77 \times 10^{-5}} \approx 0.5649 \times 10^{-9} = 5.65 \times 10^{-10}$.