find the ratio for the solution

Question

What ratio of CH₃NH₂ to CH₃NH₃⁺ is needed to prepare a pH 10.00 buffer? (Kb for CH₃NH₂ is 4.4 × 10⁻⁴)

Answer 1

pOH = pKb + log [conj.acid] / [base]

pOH = 14 - pH = 14 - 10 = 4.00

pKb = -log Kb = -log 4.4x10^-4 = 3.36

conj.acid = CH₃NH₃⁺

base = CH₃NH₂

The question asks for the ratio of base to conj.acid, so we will solve the equation and take the reciprocal:

pOH = pKb + log [conj.acid] / [base]

4.00 = 3.36 + log [conj.acid] / [base]

log [conj.acid] / [base] = 0.64

[conj.acid] / [base] = 4.37

[base] / [conj.acid] = 1/4.37 = 0.229

Alternate metod:

pH = pKa + log [base]/[acid]

pH = 10.00

Ka = 1x10^-14 / Kb = 1x10^-14 / 4.4x10^-4 = 2.27x10^-11

pKa = -log Ka = 10.64

10.00 = 10.64 + log [base]/[acid]

log [base]/[acid] = -0.64

[base]/[acid] = 0.229