pH and pOH Summary

Concentrations of hydronium and hydroxide ions in aqueous media are often represented as logarithmic pH and pOH values, respectively. At 25 °C, the autoprotolysis equilibrium for water requires the sum of pH and pOH to equal 14 for any aqueous solution. The relative concentrations of hydronium and hydroxide ion in a solution define its status as acidic ([H3O+] > [OH]), basic ([H3O+] < [OH]), or neutral ([H3O+] = [OH]). At 25 °C, a pH < 7 indicates an acidic solution, a pH > 7 a basic solution, and a pH = 7 a neutral solution.

Key Equations

$pH=−log[H_3O^+]$
$pOH =−log[OH^−]$
$[H_3O^+] = 10^{−pH}$
$[OH^−] = 10^{−pOH}$
$pH + pOH = pK_w = 14.00\;at\;25 °C$

Chemistry End of Chapter Exercises

Explain why a sample of pure water at 40 °C is neutral even though [H3O+] = $1.7×10^{−7}\;M$. $K_w$ is $2.9×10^{−14}$ at 40 °C.

Solution

In a neutral solution [H3O+] = [OH]. At 40 °C,
[H3O+] = [OH] = (2.910 × 10−14)1/2 = $1.7×10^{−7}$.

The ionization constant for water (Kw) is $2.9×10^{−14}$ at 40 °C. Calculate [H3O+], [OH], pH, and pOH for pure water at 40 °C.

The ionization constant for water (Kw) is $9.311×10^{−14}$ at 60 °C. Calculate [H3O+], [OH], pH, and pOH for pure water at 60 °C.

Solution

$x= 3.051×10^{−7}\;M$ = [H3O+] = [OH]; $pH =−log3.051×10^{−7} = −(−6.5156) = 6.5156$; pOH = pH = 6.5156

Calculate the pH and the pOH of each of the following solutions at 25 °C for which the substances ionize completely:

(a) 0.200 M HCl

(b) 0.0143 M NaOH

(c) 3.0 M HNO3

(d) 0.0031 M Ca(OH)2

Calculate the pH and the pOH of each of the following solutions at 25 °C for which the substances ionize completely:

(a) 0.000259 M HClO4

(b) 0.21 M NaOH

(c) 0.000071 M Ba(OH)2

(d) 2.5 M KOH

Solution

(a) pH = 3.587; pOH = 10.413; (b) pH = 0.68; pOH = 13.32; (c) pOH = 3.85; pH = 10.15; (d) pH = −0.40; pOH = 14.4

What are the pH and pOH of a solution of 2.0 M HCl, which ionizes completely?

What are the hydronium and hydroxide ion concentrations in a solution whose pH is 6.52?

Solution

[H3O+] = $3.0×10^{−7}\;M$; [OH] = $3.3×10^{−8}\;M$

Calculate the hydrogen ion concentration and the hydroxide ion concentration in wine from its pH. See [link] for useful information.

Calculate the hydronium ion concentration and the hydroxide ion concentration in lime juice from its pH. See [link] for useful information.

Solution

[H3O+] = $1×10^{−2}\;M$; [OH] = $1×10^{−12}\;M$

The hydronium ion concentration in a sample of rainwater is found to be $1.7×10^{−6}\;M at 25 °C. What is the concentration of hydroxide ions in the rainwater?

The hydroxide ion concentration in household ammonia is $3.2×10^{−3}\;M$ at 25 °C. What is the concentration of hydronium ions in the solution?

Solution

[OH] = $3.1×10^{−12}\;M$