What is the pH of a buffer solution containing equimolar quantities of:
(a) $H_{3}PO_{4} and NaH_{2}PO_{4}?$ $(b) H_{2}CO_{3} and NaHCO_{3}$ ?

Question

What is the pH of a buffer solution containing equimolar quantities of:
(a)[latex] H_{3}PO_{4} and NaH_{2}PO_{4}?[/latex] [latex](b) H_{2}CO_{3} and NaHCO_{3}[/latex]?

Strategy
When there are equimolar quantities of a weak acid and its conjugate base in a buffer solution, the pH is always the same as the [latex]pK_{a}[/latex] of the weak acid. Look up the [latex]pK_{a}[/latex] of the weak acid in Table 8.3.

Accepted Answer

Because we are adding equimolar quantities of a weak acid and its conjugate base, the pH is equal to the [latex]pK_{a}[/latex] of the weak acid, which we find in Table 8.3:
(a) pH =2.12 (b) pH = 6.37

Formula	Name	[latex]K_{a}[/latex]	[latex]pK_{a}[/latex]
[latex]H_{3}PO_{4}[/latex]	Phosphoric acid	[latex]7.5× 10^{-3}[/latex]	2.12
HCOOH	Formic acid	[latex]1.8 × 10^{-4}[/latex]	3.75
[latex]CH_{3}CH(OH)COOH[/latex]	Lactic acid	[latex] 1.4 × 10^{-4}[/latex]	3.86
[latex]CH_{3}COOH[/latex]	Acetic acid	[latex] 1.8 × 10^{-5}[/latex]	4.75
[latex]H_{2}CO_{3}[/latex]	Carbonic acid	[latex]4.3× 10^{-7}[/latex]	6.37
[latex] H_{2}PO_{4}^{-}[/latex]	Dihydrogen phosphate ion	[latex]6.2 × 10^{-8}[/latex]	7.21
[latex]H_{3}BO_{3}[/latex]	Boric acid	[latex] 7.3 × 10^{-10}[/latex]	9.14
[latex] NH_{4}^{+}[/latex]	Ammonium ion	[latex]5.6 × 10^{-10}[/latex]	9.25
HCN	Hydrocyanic acid	[latex]4.9 × 10^{-10}[/latex]	9.31
[latex]C_{6}H_{5}OH[/latex]	Phenol	[latex]1.3 × 10^{-10}[/latex]	9.89
[latex]HCO_{3}^{-}[/latex]	Bicarbonate ion	[latex] 5.6 × 10^{-11}[/latex]	10.25
[latex]HPO_{4}^{2-}[/latex]	Hydrogen phosphate ion	[latex]2.2 × 10^{-13}[/latex]	12.66

Question 8.9: What is the pH of a buffer solution containing equimolar qua...

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