Ratio of pH buffer

Question

What ratio of CH₃NH₂ to CH₃NH₃⁺ is needed to prepare a pH 10.10 buffer? (Kb for CH₃NH₂ is 4.4 × 10⁻⁴)

Answer 1

Most people only know the acid Henderson- Hesselbalch equation for buffers: pK_A = pH + log([acid]/[base]) but I think this is done more easily from the equilibrium constant (The HH equation is derived from it)

K_B = [CH₃NH₃⁺]/{[H⁺][CH₃NH₂]} and let x be the ratio of base over conj. acid: (I'm not sure whether this is what is required or its inverse)

K_B = 1/(x[H⁺]) or x = 1/(K_B[H⁺]) where [H⁺] is 10^-pH