Question

A buffer with pH = 10.15 is to be prepared by addition solid sodium hydrogen carbonate to 1.00 L of 0.300 M sodium carbonate. What mass is required assuming the volume does not change? For carbonic acid, Ka1 = 4.45 x 10-7 and Ka2 = 5.69 x 10-11

Answer 1

The balanced chemical equation is : HCO₃^- (aq) $\rightleftharpoons$ CO₃^2- (aq) + H⁺ (aq) : K_a2 = 5.69 x 10^-11

pK_a2 = -log(K_a2)

pK_a2 = -log(5.69 x 10^-11)

pK_a2 = 10.24

According to Henderson - Hasselbalch equation,

pH = pK_a2 + log([conjugate base] / [weak acid])

pH = pK_a2 + log([CO₃^2-] / [HCO₃^-])

10.15 = 10.24 + log(0.300 M / [HCO₃^-])

log(0.300 M / [HCO₃^-]) = 10.15 - 10.24

log(0.300 M / [HCO₃^-]) = -0.09

0.300 M / [HCO₃^-] = 10^-0.09

0.300 M / [HCO₃^-] = 0.804

[HCO₃^-] = (0.300 M) / 0.804

[HCO₃^-] = 0.373 M

moles HCO₃^- = (concentration HCO₃^-) * (volume of solution in Liter)

moles HCO₃^- = (0.373 M) * (1.00 L)

moles HCO₃^- = 0.373 mol

moles NaHCO₃ = moles HCO₃^-

moles NaHCO₃ = 0.373 mol

mass NaHCO₃ = (moles NaHCO₃) * (molar mass NaHCO₃)

mass NaHCO₃ = (0.373 mol) * (84.0 g/mol)

mass NaHCO₃ = 31.3 g