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[H3O+] |
| pOH=−log[OH−] |
| [H3O+]=10−pH |
| [OH−]=10−pOH |
| pH+pOH=pKw=14.00at25°C |
Chemistry End of Chapter Exercises
Explain why a sample of pure water at 40 °C is neutral even though [H3O+] = 1.7×10−7M. Kw 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=3.051×10−7M = [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+] = 3.0×10−7M; [OH−] = 3.3×10−8M
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+] = 1×10−2M; [OH−] = 1×10−12M
The hydronium ion concentration in a sample of rainwater is found to be 1.7×10−6M at 25 °C. What is the concentration of hydroxide ions in the rainwater?
The hydroxide ion concentration in household ammonia is 3.2×10−3M at 25 °C. What is the concentration of hydronium ions in the solution?
Solution
[OH−] = 3.1×10−12M