Ammonium chloride ($NH_4Cl$) is a salt of a strong acid ($HCl$) and a weak base ($NH_4OH$). For a salt of a strong acid and a weak base, the hydrolysis constant ($K_h$) is given by the relation: $K_h = \frac{K_w}{K_b}$ Where $K_w$ is the ionic product of water ($10^{-14}$ at $298 \text{ K}$) and $K_b$ is the ionization constant of the weak base. Given: $K_b = 1.77 \times 10^{-5}$ $K_w = 1.0 \times 10^{-14}$ Substituting the values, we get: $K_h = \frac{10^{-14}}{1.77 \times 10^{-5}} = 0.5649 \times 10^{-9} = 5.65 \times 10^{-10}$