Calculate the pH of 100 mL of 0.10 M HClO
Use this premium weak-acid calculator to determine the pH of a hypochlorous acid solution using the exact equilibrium expression or the common approximation. For the standard case of 100 mL of 0.10 M HClO at 25 C, the tool shows the pH, hydrogen ion concentration, percent ionization, and initial moles present in solution.
pH of HClO across common concentrations
How to calculate the pH of 100 mL of 0.10 M HClO
To calculate the pH of 100 mL of 0.10 M HClO, you treat hypochlorous acid as a weak acid and solve its acid dissociation equilibrium. The important chemistry idea is that pH depends on concentration and acid strength, not on the total sample volume by itself. The 100 mL detail is still useful because it lets you calculate the total starting moles of acid, but if the concentration remains 0.10 M, the pH is the same whether you have 100 mL, 250 mL, or 1.00 L.
Hypochlorous acid dissociates in water according to the equilibrium:
HClO ⇌ H+ + ClO–
At 25 C, a commonly used acid dissociation constant for HClO is about Ka = 2.95 × 10-8, which corresponds to a pKa near 7.53. Because Ka is much smaller than 1, HClO only partially ionizes in water. That means you cannot treat it like a strong acid such as HCl. Instead, you use an ICE setup, solve for the equilibrium hydrogen ion concentration, and then convert that value into pH with:
pH = -log10[H+]
Step 1: Identify what is given
- Volume = 100 mL = 0.100 L
- Initial concentration of HClO = 0.10 M
- Ka of HClO = 2.95 × 10-8
Before solving the equilibrium, many students like to compute the starting moles:
moles HClO = M × V = 0.10 mol/L × 0.100 L = 0.0100 mol
This moles value is chemically correct and useful, but for pH you still need the equilibrium concentration calculation. Since the acid is already described as 0.10 M, you can proceed directly with concentrations.
Step 2: Set up the ICE table
For the reaction HClO ⇌ H+ + ClO–, let x represent the amount of HClO that dissociates.
| Species | Initial (M) | Change (M) | Equilibrium (M) |
|---|---|---|---|
| HClO | 0.10 | -x | 0.10 – x |
| H+ | 0 | +x | x |
| ClO– | 0 | +x | x |
Plug these equilibrium expressions into the Ka formula:
Ka = [H+][ClO–] / [HClO] = x2 / (0.10 – x)
Step 3: Solve for x, the hydrogen ion concentration
Using the exact equilibrium method:
2.95 × 10-8 = x2 / (0.10 – x)
Rearranging gives the quadratic:
x2 + (2.95 × 10-8)x – 2.95 × 10-9 = 0
Solving this yields:
x = [H+] ≈ 5.43 × 10-5 M
Then:
pH = -log(5.43 × 10-5) ≈ 4.27
So the pH of 100 mL of 0.10 M HClO is approximately 4.27 at 25 C when Ka is taken as 2.95 × 10-8.
Step 4: Check the approximation method
Because HClO is weak and dissociates only slightly, many chemistry courses also use the approximation 0.10 – x ≈ 0.10. Then:
x ≈ √(Ka × C) = √((2.95 × 10-8)(0.10)) = √(2.95 × 10-9) ≈ 5.43 × 10-5 M
This gives nearly the same answer because x is tiny compared with 0.10. In fact, the percent ionization is only around:
(5.43 × 10-5 / 0.10) × 100 ≈ 0.054%
Since the ionization is far below 5%, the approximation is valid. That is why the exact and approximate pH values are almost identical for this problem.
Why the 100 mL volume matters less than many students expect
One of the most common mistakes in acid-base problems is overemphasizing sample volume. In this example, the solution is already stated to be 0.10 M HClO. Molarity means moles per liter, so concentration is already built into the problem. If nothing is added or removed, the pH depends on that concentration and the Ka value, not on whether the sample occupies 100 mL or another volume.
Volume becomes important in cases such as:
- you are asked to calculate the number of moles present
- you dilute the solution and need a new concentration
- you mix the acid with a base or another solution
- you need stoichiometric amounts before an equilibrium step
In the current problem, the 100 mL simply confirms that the sample contains 0.0100 mol HClO at the start. The equilibrium pH remains controlled by the 0.10 M concentration.
Comparison data: HClO versus other weak acids
Looking at HClO alongside other weak acids helps explain its behavior. Lower pKa means a stronger acid. HClO has a relatively high pKa compared with acetic acid or hydrofluoric acid, which tells you it is weaker and produces a lower fraction of ionized molecules at the same formal concentration.
| Acid | Formula | Approximate Ka at 25 C | Approximate pKa | Relative acid strength |
|---|---|---|---|---|
| Hypochlorous acid | HClO | 2.95 × 10-8 | 7.53 | Weak |
| Acetic acid | CH3COOH | 1.8 × 10-5 | 4.76 | Stronger than HClO |
| Hydrofluoric acid | HF | 6.8 × 10-4 | 3.17 | Much stronger than HClO |
| Hydrocyanic acid | HCN | 6.2 × 10-10 | 9.21 | Weaker than HClO |
These values explain why a 0.10 M HClO solution is acidic but not dramatically so. It is nowhere near the behavior of a strong monoprotic acid such as HCl, where 0.10 M would give a pH close to 1.00. By contrast, HClO only ionizes very slightly, producing a pH near 4.27.
How pH changes as HClO concentration changes
Because the weak-acid relationship approximately follows [H+] ≈ √(KaC), increasing the initial concentration of HClO lowers the pH, but not in a one-to-one linear way. The square-root dependence means that a large concentration increase causes a more moderate pH change than many beginners expect.
| Initial HClO concentration (M) | Estimated [H+] (M) | Estimated pH | Percent ionization |
|---|---|---|---|
| 0.001 | 5.43 × 10-6 | 5.27 | 0.543% |
| 0.010 | 1.72 × 10-5 | 4.76 | 0.172% |
| 0.050 | 3.84 × 10-5 | 4.42 | 0.077% |
| 0.100 | 5.43 × 10-5 | 4.27 | 0.054% |
| 0.500 | 1.21 × 10-4 | 3.92 | 0.024% |
A useful pattern appears here: as the solution becomes more concentrated, the pH drops, but the percent ionization decreases. This is a classic property of weak acids. The equilibrium shifts so that a smaller fraction of molecules ionize at higher formal concentration.
Practical chemistry meaning of HClO pH
Hypochlorous acid is an important species in water chemistry, sanitation, and disinfection. In many practical settings, HClO exists in equilibrium with its conjugate base, hypochlorite, ClO–. The ratio between these two species depends strongly on pH. Near neutral pH, a significant fraction may remain as HClO, while at higher pH more converts to ClO–. This matters because the chemical reactivity and disinfecting effectiveness are tied to the exact acid-base speciation.
That practical relevance is one reason weak-acid pH calculations for HClO appear so frequently in chemistry, environmental science, and water treatment coursework. Even a straightforward problem like 100 mL of 0.10 M HClO teaches several foundational lessons:
- volume and concentration are related but not interchangeable
- weak acids require equilibrium treatment
- Ka determines how much ionization occurs
- pH comes from equilibrium [H+], not from initial formal concentration alone
- approximation methods must be justified by low percent ionization
Common mistakes to avoid
- Treating HClO as a strong acid. This would incorrectly predict pH = 1.00 for a 0.10 M solution, which is far too acidic.
- Ignoring Ka. Without Ka, you cannot determine the extent of ionization.
- Using volume as if it changes pH by itself. The 100 mL matters for moles, not for pH when concentration is already specified.
- Forgetting unit conversion. If moles are needed, convert 100 mL to 0.100 L.
- Applying the approximation without checking. It is valid here because percent ionization is well under 5%.
Final answer for the problem
For 100 mL of 0.10 M HClO, using Ka = 2.95 × 10-8 at 25 C:
- Initial moles HClO = 0.0100 mol
- Equilibrium [H+] ≈ 5.43 × 10-5 M
- pH ≈ 4.27
- Percent ionization ≈ 0.054%
If your class uses the rounded value Ka = 3.0 × 10-8, you will still get essentially the same result, about pH 4.26. That small difference comes from rounding the acid dissociation constant.
Authoritative references for deeper study
For more background on hypochlorous acid chemistry, acid-base equilibria, and disinfectant behavior, consult these authoritative resources: