11 Calculate the pH of 0.15 M Acetic Acid
Use this premium weak-acid calculator to compute the pH of 0.15 M acetic acid with either the exact quadratic method or the common weak-acid approximation. Results include hydrogen ion concentration, percent ionization, pOH, and a concentration chart.
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Core chemistry used
- Reaction: CH3COOH + H2O ⇌ H3O+ + CH3COO-
- Acid dissociation constant: Ka = [H3O+][CH3COO-] / [CH3COOH]
- Exact solution for x = [H3O+]: x² + Ka x – Ka C = 0
- Positive root: x = (-Ka + √(Ka² + 4KaC)) / 2
- pH = -log10([H3O+])
Expert Guide: How to Calculate the pH of 0.15 M Acetic Acid
When students first learn pH calculations, strong acids are usually the easiest place to start because they dissociate almost completely in water. Acetic acid is different. It is a weak acid, which means only a small fraction of dissolved molecules donate protons to water. That single fact changes the entire strategy for solving the problem. If you want to calculate the pH of 0.15 M acetic acid correctly, you should not assume that the hydronium concentration is 0.15 M. Instead, you need to use the acid dissociation constant, commonly written as Ka, and solve for the amount of ionization that actually occurs.
Acetic acid, CH3COOH, is the main acidic component of vinegar. At 25 degrees C, a commonly used Ka value for acetic acid is about 1.8 × 10-5. Since this value is much smaller than 1, acetic acid remains mostly undissociated in water. That means the solution is acidic, but not nearly as acidic as a strong acid of the same formal concentration. For a 0.15 M solution, the pH ends up being close to 2.79, not near 0.82 as it would be for a strong monoprotic acid of concentration 0.15 M.
Step 1: Write the acid dissociation equation
For acetic acid in water, the equilibrium reaction is:
CH3COOH + H2O ⇌ H3O+ + CH3COO-
Because acetic acid is weak, the equilibrium lies far to the left. Most dissolved particles remain as CH3COOH, while only a small amount converts into hydronium ions and acetate ions.
Step 2: Set up an ICE table
An ICE table tracks the Initial, Change, and Equilibrium concentrations.
- Initial: [CH3COOH] = 0.15 M, [H3O+] ≈ 0, [CH3COO-] = 0
- Change: -x, +x, +x
- Equilibrium: [CH3COOH] = 0.15 – x, [H3O+] = x, [CH3COO-] = x
Now insert these equilibrium values into the Ka expression:
Ka = x² / (0.15 – x)
Substituting Ka = 1.8 × 10-5 gives:
1.8 × 10-5 = x² / (0.15 – x)
Step 3: Solve for x, the hydronium concentration
You can solve this in two ways. The first is the exact quadratic method. The second is the weak-acid approximation, where you assume x is very small compared with 0.15. Both are useful, but the exact method is the gold standard when precision matters.
Exact quadratic solution
Rearrange the equilibrium expression:
x² + Ka x – KaC = 0
With C = 0.15 and Ka = 1.8 × 10-5:
x² + 1.8 × 10-5x – 2.7 × 10-6 = 0
Using the quadratic formula:
x = (-Ka + √(Ka² + 4KaC)) / 2
The physically meaningful positive root gives:
x ≈ 1.634 × 10-3 M
Since x = [H3O+], calculate pH:
pH = -log10(1.634 × 10-3) ≈ 2.79
Approximation method
Because acetic acid is weak, x is often much smaller than the initial concentration. If x is negligible relative to 0.15, then 0.15 – x ≈ 0.15. The Ka expression simplifies to:
Ka ≈ x² / 0.15
So:
x ≈ √(Ka × C) = √(1.8 × 10-5 × 0.15)
x ≈ √(2.7 × 10-6) ≈ 1.643 × 10-3 M
Then:
pH ≈ -log10(1.643 × 10-3) ≈ 2.78
The approximation is very close to the exact result because the ionization is small. In this case, percent ionization is only a little above 1 percent, so the approximation is excellent.
Why the 5 percent rule matters
In weak-acid chemistry, a common check is the 5 percent rule. If the value of x is less than 5 percent of the initial concentration, the approximation is generally acceptable. For 0.15 M acetic acid, x is around 0.00163 M. Dividing by 0.15 gives roughly 0.0109, or 1.09 percent. Since 1.09 percent is less than 5 percent, the approximation is justified.
| Method | [H3O+] (M) | pH | Percent ionization | Comment |
|---|---|---|---|---|
| Exact quadratic | 1.634 × 10-3 | 2.79 | 1.09% | Most rigorous classroom result |
| Weak-acid approximation | 1.643 × 10-3 | 2.78 | 1.10% | Very accurate here |
| Incorrect strong-acid assumption | 0.15 | 0.82 | 100% | Not valid for acetic acid |
What this number means chemically
A pH of about 2.79 means the solution is clearly acidic, but not extremely acidic compared with a strong acid of similar concentration. The hydronium concentration is in the low millimolar range, even though the formal acid concentration is 0.15 M. This demonstrates the defining trait of weak acids: concentration alone does not determine pH. The equilibrium constant is equally important.
It also helps explain why vinegar, despite being acidic enough to taste sour and react with bases, is still far less hazardous than concentrated strong acids. The acid molecules in vinegar do not release their protons completely, so the hydronium ion concentration stays comparatively lower.
Common mistakes students make
- Treating acetic acid like a strong acid. This leads to a dramatically wrong pH.
- Using pKa incorrectly. If you are given pKa instead of Ka, remember that Ka = 10-pKa.
- Forgetting to verify the approximation. Even if the answer seems reasonable, always check percent ionization.
- Mixing up concentration units. Molarity must be in moles per liter.
- Rounding too early. Keep enough significant figures until the final pH step.
How acetic acid compares with other common acids
To place the result in context, compare acetic acid with stronger and weaker acids. The Ka value determines how far the equilibrium shifts toward products. The larger the Ka, the more hydronium forms and the lower the pH will be at the same starting concentration.
| Acid | Typical Ka at 25 degrees C | Acid strength category | Expected effect at equal concentration |
|---|---|---|---|
| Hydrochloric acid, HCl | Very large, effectively complete dissociation | Strong acid | Much lower pH than acetic acid |
| Formic acid, HCOOH | About 1.8 × 10-4 | Weak acid, stronger than acetic | Lower pH than acetic acid |
| Acetic acid, CH3COOH | About 1.8 × 10-5 | Weak acid | Moderately acidic solution |
| Hydrocyanic acid, HCN | About 6.2 × 10-10 | Very weak acid | Higher pH than acetic acid |
Real-world concentration context
Household vinegar is often sold as roughly 5 percent acidity, commonly corresponding to a molarity near 0.8 to 0.9 M depending on formulation and density. That is significantly more concentrated than 0.15 M acetic acid, so ordinary vinegar usually has a lower pH than the sample calculated here. Still, because acetic acid is weak, even concentrated vinegar is nowhere near as acidic as a similarly concentrated strong acid solution.
Relationship between Ka, pKa, and pH
Acetic acid has a pKa close to 4.76 at 25 degrees C. Since pKa = -log10(Ka), a small Ka becomes a moderate pKa value. The pKa is especially useful in buffer calculations, where the Henderson-Hasselbalch equation is applied. However, for a solution containing only acetic acid and water, the direct equilibrium approach shown above is the more fundamental method.
When to use the exact method instead of the approximation
- When the acid is not very weak
- When the concentration is low enough that x may not be negligible
- When your instructor explicitly requires exact treatment
- When you need to verify the quality of an approximation
- When comparing multiple possible answer choices that are numerically close
Practical summary of the calculation
- Write the balanced weak-acid equilibrium equation.
- Create the ICE table with initial concentration 0.15 M.
- Use Ka = 1.8 × 10-5.
- Solve x from Ka = x² / (0.15 – x), either exactly or by approximation.
- Compute pH from pH = -log10(x).
- Check percent ionization to confirm whether the approximation is valid.
The final result for 0.15 M acetic acid is about pH 2.79. The exact and approximate methods agree very closely, which is exactly what you would expect for a weak acid with only about 1.09 percent ionization under these conditions.
Authoritative chemistry references
For additional verification and deeper study, review authoritative educational resources:
LibreTexts Chemistry educational resources |
U.S. Environmental Protection Agency on acidity concepts |
National Institute of Standards and Technology
Additional university and government sources relevant to acid-base chemistry:
University of Illinois Department of Chemistry |
University of Wisconsin Chemistry