Question 15.6: Finding the pH of a Weak Acid Solution Find the pH of a 0.20...

Finding the pH of a Weak Acid Solution

Find the pH of a 0.200 M HNO_{2} solution.

1. Write the balanced equation for the ionization of the acid and use it as a guide to prepare an ICe table showing the given concentration of the weak acid as its initial concentration. Leave room in the table for the changes in concentrations and for the equilibrium concentrations. (Note that the [H_{3}O^{+}] concentration is listed as approximately zero because the autoionization of water produces a negligibly small amount of [H_{3}O^{+}].)

2. Represent the change in the concentration of H_{3}O^{+} with the variable x. Define the changes in the concentrations of the other reactants and products in terms of x, always keeping in mind the stoichiometry of the reaction.

3. Sum each column to determine the equilibrium concentrations in terms of the initial concentrations and the variable x.

4. Substitute the expressions for the equilibrium concentrations (from step 3) into the expression for the acid ionization constant (K_{a}).

In many cases, you can make the approximation that x is small (as discussed in Section 14.8). Substitute the value of the acid ionization constant (from Table 15.5) into the K_{a} expression and solve for x.

TABLE 15.5 Acid Ionization Constants (K_{a}) for Some Monoprotic Weak Acids at 25 °C
Acid	Formula	Structural Formula	Ionization Reaction	K_{a}	pK*_{a}
Chlorous acid	HCIO_{2}	H—O—Cl=O	HClO_{2}(aq)+H_{2}O(l)\xrightleftharpoons[]{}H_{3}O^{+}(aq)+ClO_{2}^{-}9aq)	1.1×10^{-2}	1.96
Nitrous acid	HNO_{2}	H—O—N=O	HNO_{2}(aq)+ H_{2}O(l)\xrightleftharpoons[]{}H_{3}O^{+}(aq) + NO_{2}^{–}(aq)	4.6×10^{-4}	3.34
Hydrouoric acid	HF	H—F	HF(aq)+ H_{2}O(l)\xrightleftharpoons[]{}H_{3}O^{+}(aq) + F^{–}(aq)	3.5×10^{-4}	3.46
Formic acid	HCHO_{2}	H—O—\overset{O}{\underset{C}{\parallel } } —H	HCHO_{2}(aq)+ H_{2}O(l)\xrightleftharpoons[]{}H_{3}O+(aq) + CHO_{2}^{–}(aq)	1.8×10^{-4}	3.74
Benzoic acid	HC_{7}H_{5}O_{2}		HC_{7}H_{5}O_{2}(aq)+ H_{2}O(l)\xrightleftharpoons[]{}H_{3}O^{+}(aq) + C_{7}H_{5}O_{2}^{–}(aq)	6.5×10^{-5}	4.19
Acetic acid	HC_{2}H_{3}O_{2}	H—O\overset{O}{\underset{C}{\parallel } } —CH_{3}	HC_{2}H_{3}O_{2}(aq)+ H_{2}O(l)\xrightleftharpoons[]{}H_{3}O^{+}(aq) + C_{2}H_{3}O_{2}^{–}(aq)	1.8×10^{-5}	4.74
Hypochlorous acid	HCIO_{2}	H—O—CI	HClO(aq)+ H_{2}O(l)\xrightleftharpoons[]{}H_{3}O^{+}(aq) + ClO^{–}(aq)	2.9×10^{-8}	7.54
Hydrocyanic acid	HCN	H—C≡N	HCN(aq)+ H_{2}O(l)\xrightleftharpoons[]{}H_{3}O^{+}(aq)+CN^{–}(aq)	4.9×10^{-10}	9.31
Phenol	HC_{6}H_{5}O		HC_{6}H_{5}O(aq)+ H_{2}O(l)\xrightleftharpoons[]{}H_{3}O^{+}(aq)+C_{6}H_{5}O^{–}(aq)	1.3×10^{-10}	9.89
*pK_{a} = –logK_{a} (See the discussion at the end of Section 15.5)

Confirm that the x is small approximation is valid by calculating the ratio of x to the number it was subtracted from in the approximation. The ratio should be less than 0.05 (or 5%).

5. Determine the H_{3}O^{+} concentration  from the calculated value of x and calculate the pH if necessary.

6. Check your answer by substituting the calculated equilibrium values into the acid ionization expression.The calculated value of K_{a} should match the given value of K_{a}. Note that rounding errors and the x is small approximation could cause a difference in the least significant digit when comparing values of K_{a}.