Weak acids do not fully dissociate in water, so their pH cannot usually be found by treating the acid concentration as the hydrogen ion concentration. Instead, the pH depends on the acid dissociation constant, Ka, and the equilibrium concentrations of the acid and its ions. This matters in biology, environmental chemistry, medicine, and food science, where many important acids are weak acids.
An ICE table gives a clear way to organize the starting amount, the change, and the final equilibrium amounts.
Understanding Chemistry: The pH of Weak Acid Solutions
An equilibrium constant is a measure of how far a reaction proceeds before the forward and reverse reactions balance. A larger Ka means an acid produces more hydronium ions at the same starting concentration. It does not mean every sample of that acid has the same pH.
Concentration still matters. Two solutions of the same weak acid can have different pH values if one is more dilute. Ka is fixed for a particular acid at a particular temperature, while the equilibrium concentrations change from sample to sample.
The ICE table works because the reaction changes the amounts in a fixed ratio. Begin by writing the concentration of the acid in the initial row. Hydronium and the negative ion are often treated as zero initially in a basic calculation.
In the change row, the acid decreases by x. Hydronium increases by x, and the negative ion increases by x. The equilibrium row then gives the values used in the Ka expression.
The unknown x represents the hydronium ion concentration made by the acid. Once x is known, take the negative logarithm of x to find pH.
The small x approximation saves time, but it needs to be checked. After calculating x, divide x by the original acid concentration and multiply by one hundred. If the result is five percent or less, treating the remaining acid concentration as nearly unchanged is usually acceptable.
If it is larger than five percent, use the full equilibrium equation and solve the quadratic equation. Skipping this check can give a noticeably wrong pH, especially for a relatively strong weak acid or a very dilute solution.
Keep extra digits during calculations, then round the final pH sensibly. The number of digits after the decimal in pH should match the significant figures in the hydronium concentration.
Percent ionization reveals an important pattern. A weak acid may ionize only a small fraction in a concentrated solution, yet a greater fraction ionizes when the solution is diluted. This does not necessarily mean the dilute solution has more hydronium ions overall.
Dilution lowers the total amount of acid per litre, even while the ionized percentage rises. Students often confuse acid strength with acid concentration. Strength refers to Ka and the tendency to ionize.
Concentration refers to how much acid was added to the water. Household vinegar, fruit juices, and many biological fluids contain weak acids, so both ideas affect their acidity. In later work, the same equilibrium reasoning explains buffer solutions, where a weak acid and its negative ion resist large pH changes.
Key Facts
- For a weak acid HA: HA(aq) + H2O(l) ⇌ H3O+(aq) + A−(aq)
- Ka = [H3O+][A−]/[HA]
- pH = −log[H3O+]
- For initial acid concentration C and change x: Ka = x^2/(C − x)
- Small-x approximation: if x is much smaller than C, then Ka ≈ x^2/C and x ≈ sqrt(KaC)
- Percent ionization = ([H3O+]eq / initial [HA]) × 100%
Vocabulary
- Weak acid
- A weak acid is an acid that only partially donates protons to water at equilibrium.
- Ka
- Ka is the acid dissociation constant that measures how strongly a weak acid produces ions in water.
- ICE table
- An ICE table organizes the Initial, Change, and Equilibrium concentrations for a reaction.
- Small-x approximation
- The small-x approximation treats a very small concentration change as negligible compared with the initial concentration.
- Percent ionization
- Percent ionization is the percentage of the original weak acid molecules that form ions at equilibrium.
Common Mistakes to Avoid
- Using the initial weak acid concentration as [H3O+] is wrong because weak acids only partially ionize, so the equilibrium [H3O+] is usually much smaller.
- Forgetting to subtract x from [HA] in the ICE table is wrong because acid molecules are consumed as H3O+ and A− form.
- Using the small-x approximation without checking it is risky because it is only valid when percent ionization is small, often less than about 5%.
- Confusing Ka with pH is wrong because Ka measures equilibrium strength, while pH is calculated from the hydronium ion concentration.
Practice Questions
- 1 A 0.100 M solution of acetic acid has Ka = 1.8 × 10^-5. Use the small-x approximation to calculate [H3O+] and pH.
- 2 A 0.250 M solution of a weak acid HA has Ka = 6.4 × 10^-6. Calculate the approximate pH and percent ionization.
- 3 Two weak acids have the same initial concentration, but acid A has a larger Ka than acid B. Explain which solution has the lower pH and why.