Calculate the pH of a 0.020 M HOBr Solution
Use this premium weak-acid calculator to find the hydronium concentration, percent ionization, and pH of hypobromous acid using either the exact quadratic solution or the standard weak-acid approximation.
HOBr pH Calculator
Expert Guide: How to Calculate the pH of a 0.020 M HOBr Solution
If you need to calculate the pH of a 0.020 M HOBr solution, you are dealing with a classic weak-acid equilibrium problem from general chemistry. HOBr is hypobromous acid, a weak acid that only partially ionizes in water. That single fact explains why you cannot simply take the negative logarithm of 0.020 as if it were a strong monoprotic acid. Instead, you need to use the acid dissociation constant, usually written as Ka, along with an equilibrium model.
The most common value used for hypobromous acid near room temperature is about 2.3 × 10-9, corresponding to a pKa close to 8.64 to 8.65. Because Ka is small, HOBr ionizes only slightly. For a 0.020 M solution, the hydronium concentration is much lower than 0.020 M, and the pH ends up mildly acidic rather than strongly acidic. In fact, the result is about pH 5.17 when Ka = 2.3 × 10-9.
Step 1: Write the Dissociation Equation
The acid equilibrium for hypobromous acid in water is:
HOBr ⇌ H+ + OBr–
Some textbooks write hydronium explicitly as H3O+, but the algebra is the same for this calculation. The equilibrium expression is:
Ka = [H+][OBr–] / [HOBr]
Because we start with 0.020 M HOBr and essentially no products, an ICE setup is the most straightforward method:
- Initial: [HOBr] = 0.020, [H+] = 0, [OBr–] = 0
- Change: [HOBr] decreases by x, [H+] increases by x, [OBr–] increases by x
- Equilibrium: [HOBr] = 0.020 – x, [H+] = x, [OBr–] = x
Step 2: Substitute into the Ka Expression
Substitute the equilibrium concentrations into the acid dissociation expression:
Ka = x2 / (0.020 – x)
If Ka = 2.3 × 10-9, then:
2.3 × 10-9 = x2 / (0.020 – x)
At this point, there are two standard solution paths:
- Use the weak-acid approximation, assuming x is very small compared with 0.020.
- Solve the quadratic exactly.
Step 3: Use the Weak-Acid Approximation
Because HOBr is weak and the starting concentration is relatively large compared with Ka, the approximation is excellent. If x is tiny, then 0.020 – x is approximately 0.020. That gives:
Ka ≈ x2 / 0.020
So:
x ≈ √(Ka × 0.020)
x ≈ √((2.3 × 10-9)(0.020))
x ≈ √(4.6 × 10-11) ≈ 6.78 × 10-6 M
Since x represents [H+], the pH is:
pH = -log(6.78 × 10-6) ≈ 5.17
Step 4: Confirm with the Exact Quadratic Method
For the exact method, start from:
Ka(0.020 – x) = x2
x2 + Ka x – Ka(0.020) = 0
Substituting Ka = 2.3 × 10-9:
x = [-Ka + √(Ka2 + 4KaC)] / 2
Using C = 0.020 M gives an x value essentially identical to the approximation for practical reporting, so the pH remains about 5.17. This is a useful teaching point: for a weak acid with a very small Ka and a modest initial concentration, the approximation usually works extremely well.
Why You Cannot Treat HOBr as a Strong Acid
A common mistake is to assume that every monoprotic acid fully dissociates. If HOBr were a strong acid, then [H+] would be 0.020 M and the pH would be:
pH = -log(0.020) ≈ 1.70
That result is completely wrong for hypobromous acid because HOBr does not ionize anywhere near 100 percent. The actual pH is around 5.17, more than three pH units higher. Since each pH unit represents a tenfold concentration difference in hydronium ion, that is a major error.
Percent Ionization of 0.020 M HOBr
Percent ionization tells you how much of the acid dissociates:
% ionization = (x / C) × 100
Using x = 6.78 × 10-6 and C = 0.020:
% ionization ≈ (6.78 × 10-6 / 0.020) × 100 ≈ 0.034%
That very small percentage confirms that the weak-acid approximation is valid and also explains why the pH is not extremely low.
Key Chemical Data for Understanding HOBr Acidity
| Property | Symbol | Typical value | Why it matters |
|---|---|---|---|
| Initial hypobromous acid concentration | C | 0.020 M | Sets the starting amount of weak acid available to dissociate. |
| Acid dissociation constant | Ka | 2.3 × 10-9 | Measures how strongly HOBr donates a proton in water. |
| Acid strength on pKa scale | pKa | About 8.64 to 8.65 | Higher pKa means weaker acid and less dissociation. |
| Calculated hydronium concentration | [H+] | 6.78 × 10-6 M | Directly determines pH. |
| Calculated pH | pH | About 5.17 | Shows the solution is acidic, but only mildly so compared with strong acids. |
| Percent ionization | % ionization | About 0.034% | Confirms that dissociation is very limited. |
How pH Changes with HOBr Concentration
One useful way to develop intuition is to compare pH at several concentrations while holding Ka constant. Because HOBr is weak, lowering concentration raises pH, but not in the same simple one-to-one way seen with strong acids.
| HOBr concentration | Assumed Ka | Calculated [H+] | Calculated pH |
|---|---|---|---|
| 0.200 M | 2.3 × 10-9 | 2.14 × 10-5 M | 4.67 |
| 0.020 M | 2.3 × 10-9 | 6.78 × 10-6 M | 5.17 |
| 0.0020 M | 2.3 × 10-9 | 2.14 × 10-6 M | 5.67 |
| 0.00020 M | 2.3 × 10-9 | 6.78 × 10-7 M | 6.17 |
This table reveals a practical trend: every tenfold decrease in weak-acid concentration raises the pH by roughly 0.5 units when the square-root approximation is valid. That is because [H+] depends approximately on the square root of concentration, not directly on concentration itself.
Comparison with Other Acids
Students often understand HOBr more clearly when comparing it to familiar acids. Acetic acid, for example, has a Ka around 1.8 × 10-5, so it is much stronger than HOBr. Strong acids like HCl effectively dissociate completely. HOBr, by contrast, is weak enough that only a tiny fraction dissociates under these conditions.
- HCl: strong acid, essentially complete dissociation in dilute solution
- Acetic acid: weak acid, but far stronger than HOBr
- HOBr: weak acid with very small Ka, limited dissociation
- HOCl: typically stronger than HOBr, so an equivalent concentration of HOCl usually has a lower pH
When the Approximation Works and When It Does Not
The five-percent rule is commonly used to justify the approximation. If x is less than 5 percent of the initial concentration, then replacing 0.020 – x with 0.020 is considered acceptable. Here, x is only about 0.034 percent of 0.020 M, which is far below 5 percent. Therefore, the approximation is extremely safe.
However, you should avoid relying blindly on the approximation when:
- The acid is much stronger, so Ka is not very small.
- The initial concentration is very low.
- You need high-precision reporting.
- The problem explicitly asks for an exact quadratic solution.
Common Student Errors in HOBr pH Problems
- Treating HOBr as a strong acid. This leads to a pH around 1.70, which is incorrect.
- Using pKa directly without converting when necessary. If you are given pKa, compute Ka = 10-pKa.
- Forgetting equilibrium stoichiometry. Both H+ and OBr– increase by the same amount x.
- Mixing logs and natural logs incorrectly. pH uses base-10 logarithms.
- Ignoring significant figures. Report pH with a sensible number of decimal places based on the data provided.
Practical Context: Why HOBr Matters
Hypobromous acid is relevant in water chemistry, disinfection chemistry, and oxidation systems that involve bromine species. In practical systems, HOBr often exists in equilibrium with OBr–, and the surrounding pH strongly affects speciation. Even though this calculator focuses on a straightforward weak-acid pH calculation, the same equilibrium ideas are foundational in environmental chemistry and sanitation chemistry.
For example, if a treatment process or water sample contains bromine-based oxidants, knowing the pH helps predict which species dominate. That matters because the acid form and conjugate base can differ in disinfecting strength and reactivity.
Authoritative Resources for Further Study
If you want to go deeper into acid-base chemistry, pH concepts, and bromine-related chemical data, these authoritative sources are useful:
- U.S. Environmental Protection Agency: pH overview and water chemistry context
- PubChem (.gov): chemical property database for bromine-related compounds and acid-base data
- Michigan State University (.edu): acid-base strength and equilibrium fundamentals
Final Answer Summary
To calculate the pH of a 0.020 M HOBr solution, model HOBr as a weak acid and use its dissociation constant. With Ka = 2.3 × 10-9, set up the equilibrium expression:
Ka = x2 / (0.020 – x)
Because x is very small, use the standard approximation:
x ≈ √(KaC) = √((2.3 × 10-9)(0.020)) ≈ 6.78 × 10-6
Then:
pH = -log(6.78 × 10-6) ≈ 5.17
So the accepted chemistry answer is:
This result is robust, chemically sensible, and fully supported by weak-acid equilibrium theory.