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 = 3.59; pOH = 10.4; (b) pH = 13; pOH = 0.68; (c) pH = 10; pOH = 3.9; (d) pH = 14; pOH = -0.40
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−] = $3.1×10^{−12}\;M$