Buffer pH Calculation What is the pH of a phosphate buffer solution containing 1.0 mol/L of sodium dihydrogen phosphate, NaH2PO4, and 0.50 mol/L of sodium hydrogen phosphate, Na2HPO4? Strategy Use the Henderson-Hasselbalch equation to determine the pH. You must know either the number of moles of

Question

Buffer pH Calculation

What is the pH of a phosphate buffer solution containing 1.0 mol/L of sodium dihydrogen phosphate, [latex]NaH _{2} PO _{4}[/latex], and 0.50 mol/L of sodium hydrogen phosphate, [latex]Na _{2} HPO _{4}[/latex]?

Strategy

Use the Henderson-Hasselbalch equation to determine the pH. You must know either the number of moles of both the conjugate acid and base or the concentrations of the conjugate acid or base. Divide the conjugate base by the conjugate acid, take the log of that ratio and add it to the [latex]p K_{ a }[/latex] of the conjugate acid.

Accepted Answer

Solution The weak acid in this problem is [latex]H _{2} PO _{4}^{-}[/latex]; its ionization produces [latex]HPO _{4}{ }^{2-}[/latex].

The [latex]p K_{ a }[/latex] of this acid is 7.21 (from Table 8.3). Under the weak acid and its conjugate base are shown their concentrations.

TABLE 8.3 [latex]K_{ s } ext { and } p K_{ a }[/latex] Values for Some Weak Acids
Formula	Name	[latex]K_{a}[/latex]	[latex]p K _{a}[/latex]
[latex]H _{3} PO _{4}[/latex]	Phosphoric acid	[latex]7.5 imes 10^{-3}[/latex]	2.12
HCOOH	Formic acid	[latex]1.8 imes 10^{-4}[/latex]	3.75
[latex]CH _{3} CH ( OH ) COOH[/latex]	Lactic acid	[latex]1.4 imes 10^{-4}[/latex]	3.86
[latex]CH _{3} COOH[/latex]	Acetic acid	[latex]1.8 imes 10^{-5}[/latex]	4.75
[latex]H _{2} CO _{3}[/latex]	Carbonic acid	[latex]42 imes 1 n^{-7}[/latex]	6.37
[latex]H _{2} PO _{4}^{-}[/latex]	Dihydrogen phosphate ion	[latex]6.2 imes 10^{-8}[/latex]	7.21
[latex]H _{3} BO _{3}[/latex]	Boric acid	[latex]7.3 imes 10^{-10}[/latex]	9.14
[latex]NH _{4}^{+}[/latex]	Ammonium ion	[latex]5.6 imes 10^{-10}[/latex]	9.25
HCN	Hydrocyanic acid	[latex]4.9 imes 10^{-10}[/latex]	9.31
[latex]C _{6} H _{5} OH[/latex]	Phenol	[latex]1.3 imes 10^{-10}[/latex]	9.89
[latex]HCO _{3}^{-}[/latex]	Bicarbonate ion	[latex]5.6 imes 10^{-11}[/latex]	10.25
[latex]HPO _{4}^{2-}[/latex]	Hydrogen phosphate ion	[latex]2.2 imes 10^{-13}[/latex]	12.66

[latex]\begin{array}{l}H _{2} PO _{4}^{-}+ H _{2} O ightleftharpoons HPO _{4}^{2-}+ H _{3} O ^{+} \quad p K_{ a }=7.21\1.0 mol / L \quad 0.50 mol / L\end{array}[/latex][latex]K_{ a }[/latex]

Substituting these values in the Henderson-Hasselbalch equation gives a pH of 6.91.

[latex]\begin{aligned}pH &=7.21+\log \frac{0.50}{1.0} \&=7.21-0.30=6.91\end{aligned}[/latex]

Question 8.10: Buffer pH Calculation What is the pH of a phosphate buffer s...

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