The relationship between the acid dissociation constant (Ka) of a conjugate acid and the base dissociation constant (Kb) of its corresponding base can be determined using the equation:
Ka × Kb = Kw
where Kw is the ion product of water at 25°C, which equals 1.0 x 10^-14.
Given that the Kb of NH3 (ammonia) is 1.8 x 10^-5, we can rearrange the equation to solve for Ka:
Ka = Kw / Kb
Substituting the known values:
Ka = (1.0 x 10^-14) / (1.8 x 10^-5)
Calculating this gives:
Ka ≈ 5.56 x 10^-10
Therefore, the Ka of NH4+ (the conjugate acid of NH3) is approximately 5.56 x 10^-10. This low value indicates that NH4+ is a weak acid, which is consistent with the behavior of its conjugate base, NH3.