Calculate the pH of 100 mL of 0.10 M HClO
Use this premium weak-acid calculator to solve hypochlorous acid pH with full equilibrium logic, formatted steps, and a live concentration chart.
HClO pH Calculator
With 100 mL of 0.10 M HClO, the pH is expected to be mildly acidic because HClO is a weak acid that only partially dissociates.
What this tool shows
- Exact pH from the weak-acid equilibrium equation
- Hydrogen ion concentration, [H+]
- Percent dissociation of HClO
- Total moles of HClO present in 100 mL
- A live chart comparing initial acid, remaining acid, and ionized amount
HClO ⇌ H+ + ClO–
Ka = [H+][ClO–] / [HClO]
For initial concentration C and change x:
Ka = x2 / (C – x)
Expert Guide: 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 need to recognize that hypochlorous acid is a weak acid, not a strong acid. That single fact changes the entire method. A strong monoprotic acid such as HCl would fully dissociate, so a 0.10 M solution would have a hydrogen ion concentration of 0.10 M and a pH of 1.00. HClO behaves differently. It only partially ionizes in water, so you must use an equilibrium expression and the acid dissociation constant, Ka, rather than assuming complete dissociation.
For hypochlorous acid, the accepted Ka value at room temperature is commonly taken as approximately 3.0 × 10-8. The equilibrium is:
HClO ⇌ H+ + ClO–
If the initial concentration of HClO is 0.10 M, then the standard ICE setup is:
- Initial: [HClO] = 0.10, [H+] = 0, [ClO–] = 0
- Change: [HClO] decreases by x, [H+] increases by x, [ClO–] increases by x
- Equilibrium: [HClO] = 0.10 – x, [H+] = x, [ClO–] = x
Substituting into the Ka expression gives:
Ka = x2 / (0.10 – x)
Using 3.0 × 10-8 for Ka:
3.0 × 10-8 = x2 / (0.10 – x)
Because Ka is very small compared with the initial concentration, the weak-acid approximation usually works well here. That means you can treat 0.10 – x as approximately 0.10, leading to:
x2 = (3.0 × 10-8)(0.10) = 3.0 × 10-9
x = √(3.0 × 10-9) ≈ 5.48 × 10-5 M
Since x represents the equilibrium hydrogen ion concentration, [H+] ≈ 5.48 × 10-5 M. Therefore:
pH = -log(5.48 × 10-5) ≈ 4.26
Why the 100 mL volume does not change the pH in this case
Students often wonder why the problem specifies 100 mL if the pH calculation seems to use only molarity and Ka. The reason is that pH depends on concentration, not simply on the total amount of acid by itself. If the solution is already stated to be 0.10 M, then the concentration is known. Whether you have 100 mL, 250 mL, or 1.0 L of that same undiluted 0.10 M solution, the pH remains the same at the same temperature because the equilibrium concentrations are the same.
However, the volume does matter if you want to know the number of moles present. In this problem:
- Convert 100 mL to liters: 100 mL = 0.100 L
- Use moles = M × L
- Moles HClO = 0.10 mol/L × 0.100 L = 0.0100 mol
So the sample contains 0.0100 mol of HClO, but its pH still comes from the concentration equilibrium, not from the total moles alone.
When to use the quadratic equation instead of the shortcut
The approximation method is popular because it is quick, but technically the exact equilibrium solution is the quadratic form:
x2 + Ka x – KaC = 0
Where C is the initial concentration. Solving for the physically meaningful positive root gives:
x = [-Ka + √(Ka2 + 4KaC)] / 2
For C = 0.10 and Ka = 3.0 × 10-8, the exact value of x is nearly identical to the approximation. That is because the percent ionization is tiny and x is much smaller than 0.10. A common rule is to verify that x is less than 5% of the initial concentration. Here:
(5.48 × 10-5 / 0.10) × 100 ≈ 0.0548%
That is far below 5%, so the approximation is fully justified.
| Quantity | Value for 100 mL of 0.10 M HClO | How it is obtained |
|---|---|---|
| Volume | 0.100 L | 100 mL ÷ 1000 |
| Initial concentration, C | 0.10 M | Given in the problem |
| Ka of HClO | 3.0 × 10-8 | Typical literature value near room temperature |
| Moles of HClO | 0.0100 mol | 0.10 × 0.100 |
| [H+] | 5.48 × 10-5 M | √(KaC) or exact quadratic |
| pH | 4.26 | -log[H+] |
| Percent dissociation | 0.0548% | (x/C) × 100 |
Weak acid behavior of HClO compared with strong acids
Hypochlorous acid is often discussed in water chemistry, sanitation chemistry, and disinfection contexts. It is important chemically because it is the protonated form related to the hypochlorite system. Even though it is a useful oxidizing and antimicrobial species, it remains a weak acid in aqueous equilibrium. That means the concentration of hydrogen ions generated is much smaller than the starting acid concentration.
This is easiest to see by comparing HClO with a strong acid at the same formal concentration. A 0.10 M strong monoprotic acid gives pH 1.00, while 0.10 M HClO gives about pH 4.26. A difference of over 3 pH units corresponds to more than a thousand-fold difference in hydrogen ion concentration. This is exactly why identifying acid strength before starting calculations is so important.
| Acid solution | Acid type | Typical formula used | Estimated [H+] | Approximate pH |
|---|---|---|---|---|
| 0.10 M HCl | Strong acid | [H+] = 0.10 | 1.0 × 10-1 M | 1.00 |
| 0.10 M HClO | Weak acid | [H+] ≈ √(KaC) | 5.48 × 10-5 M | 4.26 |
| 0.10 M CH3COOH | Weak acid | [H+] ≈ √(KaC) | 1.34 × 10-3 M | 2.87 |
Step by step method you can reuse on exams
- Identify acid strength. HClO is a weak acid, so do not assume complete dissociation.
- Write the balanced dissociation reaction. HClO ⇌ H+ + ClO–.
- Set up an ICE table. Start with 0.10 M HClO and 0 for both ions.
- Write the Ka expression. Ka = x2 / (0.10 – x).
- Use the approximation or quadratic solution. Since Ka is tiny, x is small.
- Find x = [H+]. x ≈ 5.48 × 10-5 M.
- Calculate pH. pH = -log(5.48 × 10-5) = 4.26.
- Check the approximation. Percent ionization is about 0.0548%, so the shortcut was valid.
Common mistakes to avoid
- Treating HClO like HCl. This is the most common error. HClO is weak.
- Using moles directly for pH. pH is based on equilibrium concentration, not just total moles.
- Ignoring Ka. Weak-acid calculations require Ka or pKa.
- Forgetting the volume conversion. 100 mL is 0.100 L if you need moles.
- Using too few significant figures in intermediate steps. Keep enough precision until the final pH.
- Not checking if the approximation is valid. Use the 5% rule.
Why HClO matters in real chemistry
Hypochlorous acid is important far beyond textbook equilibrium problems. It plays a major role in disinfection chemistry, aqueous chlorine systems, and biological oxidative processes. In water treatment and sanitation science, the distribution between HClO and ClO– depends strongly on pH. Lower pH generally favors HClO, while higher pH favors hypochlorite ion. Because HClO is typically the more effective disinfecting species, pH control can change practical performance in real systems. This is one reason chemistry students are frequently asked to calculate pH and understand weak-acid equilibria involving HClO.
Even in this simple problem, the result tells a deeper story: only a very small fraction of the 0.10 M HClO dissociates. Most of the acid remains in molecular form at equilibrium. That is exactly what the small Ka value means quantitatively.
Authoritative references for further study
PubChem: Hypochlorous Acid
MIT OpenCourseWare Chemistry Resources
USGS: pH and Water
Bottom line
If you are asked to calculate the pH of 100 mL of 0.10 M HClO, the correct approach is a weak-acid equilibrium calculation using Ka. With Ka ≈ 3.0 × 10-8, the hydrogen ion concentration is about 5.48 × 10-5 M and the pH is approximately 4.26. The given 100 mL volume is useful for finding total moles, which equal 0.0100 mol, but it does not alter the pH so long as the concentration remains 0.10 M.