Calculate the pH of 25 mL of 0.15 M Benzoic Acid
Use this interactive weak-acid calculator to find the pH, hydrogen ion concentration, percent ionization, and equilibrium concentrations for benzoic acid. The default setup matches the classic chemistry problem: 25 mL of 0.15 M benzoic acid at 25 degrees Celsius.
Benzoic Acid Calculator
Results
Enter values and click Calculate pH to see the equilibrium solution.
Solution Snapshot
- Weak acid equilibrium: HA ⇌ H+ + A–
- For benzoic acid, a common literature value is pKa ≈ 4.20 at 25 degrees Celsius.
- Exact equation: Ka = x2 / (C – x)
- Approximation when valid: x ≈ √(KaC)
- pH = -log10[H+]
The chart compares the initial acid concentration with the equilibrium concentrations of hydrogen ion, benzoate ion, and undissociated benzoic acid.
How to calculate the pH of 25 mL of 0.15 M benzoic acid
If you need to calculate the pH of 25 mL of 0.15 M benzoic acid, the most important concept is that benzoic acid is a weak acid, not a strong acid. That means it does not fully dissociate in water. Instead, only a small fraction of the dissolved benzoic acid molecules donate a proton to water. Because of that partial ionization, the pH must be found from an equilibrium calculation rather than from the simple strong-acid shortcut pH = -log(concentration).
The standard equilibrium expression for a weak monoprotic acid is based on the reaction HA ⇌ H+ + A–. In this problem, HA is benzoic acid and A– is the benzoate ion. A commonly used value for benzoic acid at 25 degrees Celsius is pKa = 4.20, which corresponds to Ka ≈ 6.31 × 10-5. With an initial concentration of 0.15 M, you can solve for the equilibrium hydrogen ion concentration and then convert that into pH.
Step 1: Write the acid dissociation reaction
Benzoic acid dissociates according to:
For a weak acid, the equilibrium constant expression is:
If the initial concentration of benzoic acid is 0.15 M and x dissociates, then at equilibrium:
- [H+] = x
- [A–] = x
- [HA] = 0.15 – x
Substituting these into the equilibrium expression gives:
Step 2: Convert pKa to Ka
The relationship between pKa and Ka is:
Using pKa = 4.20:
This value is small, which is exactly what you expect for a weak acid. Benzoic acid ionizes only slightly, so the hydrogen ion concentration will be much lower than 0.15 M.
Step 3: Solve the weak-acid equilibrium
There are two common ways to proceed. The first is the classic approximation, where x is assumed to be small relative to the initial concentration. The second is the exact quadratic solution. For this problem, both methods give almost the same answer, but the exact solution is the most rigorous.
Using the approximation:
Since x is the hydrogen ion concentration, pH is:
If you solve exactly with the quadratic expression
you get essentially the same value, x ≈ 3.04 × 10-3 M, which gives a pH of about 2.52. That is the best answer for the pH of 25 mL of 0.15 M benzoic acid at 25 degrees Celsius when pKa = 4.20 is used.
Final answer for the default problem
For 25 mL of 0.15 M benzoic acid, using pKa = 4.20:
- Ka = 6.31 × 10-5
- [H+] ≈ 3.04 × 10-3 M by the exact method
- pH ≈ 2.52
- Percent ionization ≈ 2.03%
- Total moles of benzoic acid in 25 mL = 0.00375 mol
Notice that the volume gives the total amount of acid present, but the pH is governed by the molar concentration and the acid strength. If you prepared a larger or smaller sample at the same 0.15 M concentration, the pH would remain the same, assuming temperature and composition stayed unchanged.
Why the volume appears in the question
Students often wonder why the problem states 25 mL if the pH of a simple weak-acid solution depends mainly on concentration. The answer is that chemistry problems frequently include volume to test whether you understand the distinction between moles and molarity. In this case:
This mole value matters if you are doing a titration, mixing solutions, diluting the sample, or comparing total acid content. But for the pH of the standalone benzoic acid solution, the concentration is the key variable.
Comparison data: benzoic acid versus other common weak acids
The acid strength of benzoic acid is moderate compared with several familiar weak acids used in general chemistry. The table below lists typical 25 degrees Celsius values used in educational and reference settings. These are useful because they show why benzoic acid gives a lower pH than acetic acid at the same concentration but a higher pH than much stronger acids.
| Acid | Typical pKa | Typical Ka | Relative strength at 25 degrees Celsius |
|---|---|---|---|
| Benzoic acid | 4.20 | 6.31 × 10-5 | Stronger than acetic acid |
| Acetic acid | 4.76 | 1.74 × 10-5 | Weaker than benzoic acid |
| Formic acid | 3.75 | 1.78 × 10-4 | Stronger than benzoic acid |
| Hydrofluoric acid | 3.17 | 6.76 × 10-4 | Much stronger weak acid |
Since benzoic acid has a lower pKa than acetic acid, it dissociates more extensively at the same molarity. That means a 0.15 M benzoic acid solution will have a higher hydrogen ion concentration and therefore a lower pH than a 0.15 M acetic acid solution.
How concentration changes the pH of benzoic acid
For a weak acid, increasing concentration usually lowers pH, but not in a one-to-one way. That is because hydrogen ion concentration scales with the square root of KaC under the approximation. The table below shows calculated pH values for benzoic acid using pKa = 4.20 and the exact equilibrium method.
| Benzoic acid concentration (M) | Equilibrium [H+] (M) | Calculated pH | Percent ionization |
|---|---|---|---|
| 0.010 | 7.63 × 10-4 | 3.12 | 7.63% |
| 0.050 | 1.75 × 10-3 | 2.76 | 3.50% |
| 0.100 | 2.48 × 10-3 | 2.61 | 2.48% |
| 0.150 | 3.04 × 10-3 | 2.52 | 2.03% |
| 0.200 | 3.53 × 10-3 | 2.45 | 1.77% |
Two trends stand out. First, pH falls as concentration increases. Second, percent ionization decreases as concentration rises. That behavior is characteristic of weak acids and is an important exam concept.
When is the square-root approximation valid?
In many classroom problems, weak-acid calculations are simplified by assuming x is small compared with the initial concentration C. A common rule of thumb is that the approximation is acceptable if x/C is less than 5%. For this benzoic acid problem, x is only about 2.03% of the starting 0.15 M concentration, so the approximation is valid. That is why the quick method gives nearly the same pH as the exact quadratic method.
- Compute x ≈ √(KaC).
- Check percent ionization as x/C × 100.
- If the result is under 5%, the shortcut is usually acceptable.
- If it is larger, solve the quadratic exactly.
Common mistakes to avoid
- Treating benzoic acid as a strong acid and setting [H+] = 0.15 M.
- Using the 25 mL directly in the pH equation without converting or understanding its purpose.
- Confusing pKa with pH. pKa is an acid strength constant, not the solution pH.
- Forgetting that pH depends on the logarithm of hydrogen ion concentration.
- Dropping the x term without checking whether the approximation is justified.
Why benzoic acid matters in chemistry
Benzoic acid is more than a textbook weak acid. It is an aromatic carboxylic acid commonly discussed in organic chemistry, analytical chemistry, and acid-base equilibrium lessons. Its conjugate base, benzoate, is resonance stabilized, which helps explain its acidity relative to aliphatic carboxylic acids. Benzoic acid and benzoate salts also appear in discussions of food preservation, buffering systems, and laboratory synthesis.
Because the acid strength is moderate and the equilibrium math is manageable, benzoic acid is an excellent example for teaching weak-acid pH calculations. It is strong enough to produce a measurable acidic pH, but weak enough that the distinction between complete and partial dissociation becomes obvious.
Authoritative references for benzoic acid and pH concepts
If you want to verify physical data or review acid-base theory from reliable sources, these references are useful:
- NIST Chemistry WebBook: Benzoic acid data
- Purdue University: Acid-base equilibrium review
- University of Wisconsin: Weak acid equilibrium tutorial
Quick recap
To calculate the pH of 25 mL of 0.15 M benzoic acid, start with benzoic acid as a weak monoprotic acid and use its pKa of about 4.20. Convert pKa to Ka, set up the equilibrium expression Ka = x2 / (C – x), solve for x, and then compute pH from -log[H+]. The exact result is approximately pH = 2.52. The 25 mL sample contains 0.00375 mol of benzoic acid, but the pH is determined by the concentration and acid dissociation equilibrium, not by the total amount alone.
Use the calculator above anytime you want to adjust the volume, concentration, or pKa and instantly recompute the pH. It is especially helpful for homework checking, lab preparation, and comparing exact versus approximate weak-acid methods.