Suppose you are given solutions of 1.00 M acetic acid and 1.00 M sodium acetate and are asked to make 100.00 mL of buffer at pH 5.00 using only these two solutions. What volume, in milliliters, of acid would you need? The pKa of acetic acid is 4.75

Since acetic acid is a weak acid, it would be represented as HA:

Given:

pH = 5

pKa = 4.75

Total volume = 100 mL

= 0.1 L

Using Henderson-Hasselbalch equation:

pH = pKa + log[A-]/[HA]

[A-]/[HA] = 10^ (pH/pKa)

[A-]/[HA] = 11.2884

Remember [A-] = 11.2884 * [HA]

[HA] + 11.2884[HA] = 1.00

Solving for [HA],

[HA] = 1/12.2884

= 0.0814 M

[A-] = 11.2884 * [HA]

= 11.2884 * 0.0814

= 0.9189 M

Molar concentration = number of moles/volume

Number of moles, nA - = 0.9189 * 0.1

= 0.0919 moles

Number of moles, nHA = 0.0814 * 0.1

= 0.00814 moles

Volume of the acid, VHA = 0.00814/1

= 0.00814 L

= 8.14 mL