A buffer solution is made with a pH of 5.000. Solid sodium ethanoate, CH3COONa, is added to 400 cm^3 of 0.200 mol dm^–3 ethanoic acid (Ka = 1.75 × 10^–5 mol dm^–3). Calculate the mass of sodium acetate that must be dissolved in the acid to prepare this

There are three steps:
Calculate [CH₃COO^–] using the equation for K_aCalculate the moles of CH₃COO^– using the equation concentration = moles/volumeCalculate the mass of CH₃COONa using the equation moles = mass/RFM
Here's the situation:
CH₃COOH <–> CH₃COO^– + H⁺
K_a = [CH₃COO^–][H⁺]/[CH₃COOH]
To calculate the mass of CH₃COONa, we must first calculate [CH₃COO^–]. Luckily we have been given the three other variables in the K_a equation.
K_a = 1.75 × 10^–5 (given in the question)
[CH₃COOH] = 0.200 mol dm^–3 (again, given in question)
[H⁺] = 10^–5.000 mol dm^–3 (since pH = –log₁₀[H⁺])
Using the rearrangement [CH₃COO^–] = K_a[CH₃COOH]/[H⁺],
[CH₃COO^–] = 1.75 × 10^–5 x 0.200 / 10^–5.000 = 0.350 mol dm^–3
Use concentration = moles/volume to calculate the moles of CH₃COO^–:
moles = 0.350 x 400/1000 = 0.140 (remember to convert cm³ into dm³ to keep the units consistent)
Use moles = mass/RFM to calculate the mass. RFM of CH₃COONa can be obtained from the periodic table as 82.0:
mass = 0.140 x 82.0 = 11.48 g