Question

A student wishes to buffer a solution at a pH of 1.8. Which of the following acids is most appropriate, and what is its conjugate base? What ratio of concentrations would be required? How many moles of each should be used to make 1.0L of 0.50M buffer solution? (Hint: buffer concentration refers to all of the species, whether acid or CB, present. In other words, [HA] + [A-] = 0.5M in this case).

Acid	pKa at 25C
trichloroacetic acid (Cl3CCOOH)	0.66
H3PO4	2.12
HF	3.20
HCOOH	3.75
C6H5COOH	4.2
H2PO4-	7.2
NH4+	9.24

Note: do not worry if pKa values here differ from pKa values for the same acid elsewhere on the worksheet; don’t forget that all Keq values are temperature-dependent! If I give you a Keq, I’m giving you the value for the temperature of interest.

Answer 1

The pKa value of H3PO4 is closer to the required pH.

Hence, H3PO4 is most appropriate and its conjugate base is H2PO4^-.

According to the Henderson-Hasselbulch equation:

pH = pKa + Log([conjugate base]/[weak acid])

Here, 1.8 = 2.12 + Log([H2PO4^-]/[H3PO4])

i.e. Log([H3PO4]/[H2PO4^-]) = 0.32

i.e. [H3PO4]/[H2PO4^-] = 2.089 ~ 2.1 ----> equation 1

Here, [H3PO4] + [H2PO4^-] = 0.5 M

i.e. [H3PO4] = 0.5-[H2PO4^-] ----> equation 2

From equations 1 and 2:

(0.5-[H2PO4^-])/[H2PO4^-] = 2.089

i.e. 0.5/[H2PO4^-] = 3.089

i.e. [H2PO4^-] = 0.162 M

Therefore, [H3PO4] = 0.5-0.162 = 0.338 M

Hence no.of moles of H2PO4^- = 0.162 mol/L × 1 L = 0.162 mol

And the no.of moles of H3PO4 = 0.338 mol/L × 1 L = 0.338 mol