Example 13.8b: The Product \(K_{\mathrm{a}} \cdot K_{\mathrm{b}} = K_{\mathrm{w}}\)

We can determine the relative acid strengths of \(\ce{NH4+}\) and \(\ce{HCN}\) by comparing their ionization constants. The ionization constant of \(\ce{HCN}\) is given in Appendix H as \(4.9\times 10^{-10}\). The ionization constant of \(\ce{NH4+}\) is not listed, but the ionization constant of its conjugate base, \(\ce{NH3}\), is listed as \(1.8\times 10^{-5}\). Determine the ionization constant of \(\ce{NH4+}\), and decide which is the stronger acid, \(\ce{HCN}\) or \(\ce{NH4+}\).