Calculate the pH of a 100m KBrO Solution
Use this premium calculator to estimate the pH of potassium hypobromite, KBrO, from concentration and the acid strength of hypobromous acid, HBrO. The default setup interprets “100m” as 100 mM, which is 0.100 M.
Enter the numeric concentration value.
Default is mM because many students mean 100 mM when they write 100m.
KBrO is basic because BrO- is the conjugate base of HBrO.
A commonly used pKa for HBrO at 25 C is about 8.65.
This affects the value of Kw used in the hydrolysis calculation.
Volume is optional for pH, but it helps estimate total moles of KBrO.
pH depends on concentration, not on total volume alone.
For very high concentrations such as 100 M, real solutions deviate strongly from ideal behavior.
Expert guide: how to calculate the pH of a 100m KBrO solution
To calculate the pH of a KBrO solution, you need to recognize what KBrO is doing in water. Potassium hypobromite dissociates into K+ and BrO–. The potassium ion is essentially neutral in ordinary acid-base calculations, but the hypobromite ion is not. BrO– is the conjugate base of hypobromous acid, HBrO, which means it reacts with water to produce hydroxide ions. That is why a KBrO solution is basic and has a pH above 7 under standard assumptions.
The phrase “100m KBrO” is slightly ambiguous in informal writing. In classroom and lab settings, many people use it to mean 100 mM, which equals 0.100 M. In formal chemistry notation, however, uppercase M usually indicates molarity. Because the difference matters dramatically for the answer, the calculator above lets you choose the unit explicitly. If you mean 100 mM, the predicted pH is much lower than if you literally mean 100 M.
Core idea: KBrO is a salt of a weak acid and a strong base. Therefore, the anion hydrolyzes water:
BrO– + H2O ⇌ HBrO + OH–
The hydroxide formed in this equilibrium determines the pOH and then the pH.
Step 1: Convert the concentration into molarity
If your concentration is written as 100 mM, convert it to molarity by dividing by 1000:
100 mM = 0.100 M
If you truly mean 100 M, then the concentration is already in molarity. That value is extraordinarily high and not physically realistic for many salts, but it is still possible to show the ideal mathematical treatment. In practical chemistry, activity effects and solubility limits would become very important long before 100 M.
Step 2: Relate the base constant of BrO- to the acid constant of HBrO
The easiest way to calculate pH is to start with the acid dissociation constant of hypobromous acid. A commonly used classroom value is a pKa near 8.65 at 25 C. That means:
Ka = 10-8.65 ≈ 2.24 × 10-9
Next use the relationship:
Kb = Kw / Ka
At 25 C, Kw = 1.0 × 10-14, so:
Kb ≈ 1.0 × 10-14 / 2.24 × 10-9 ≈ 4.47 × 10-6
Step 3: Set up the equilibrium expression
For a starting concentration C of BrO–, the hydrolysis reaction is:
BrO– + H2O ⇌ HBrO + OH–
If x mol/L of hydroxide is produced, then the equilibrium concentrations are:
- [BrO–]eq = C – x
- [HBrO]eq = x
- [OH–]eq = x
So the base equilibrium expression is:
Kb = x2 / (C – x)
For many weak-base problems, students estimate C – x ≈ C, which gives x ≈ √(KbC). The calculator on this page uses the more exact quadratic form to improve accuracy.
Worked example for 100 mM KBrO
Assume the phrase 100m KBrO means 100 mM, or 0.100 M, and use pKa = 8.65 for HBrO.
- Convert concentration: 100 mM = 0.100 M
- Compute Ka = 10-8.65 = 2.24 × 10-9
- Compute Kb = 1.0 × 10-14 / 2.24 × 10-9 = 4.47 × 10-6
- Approximate hydroxide: [OH–] ≈ √(4.47 × 10-6 × 0.100) ≈ 6.69 × 10-4 M
- Find pOH: pOH = -log[OH–] ≈ 3.17
- Find pH: pH = 14.00 – 3.17 = 10.83
That means a 0.100 M KBrO solution is predicted to be moderately basic, with a pH of about 10.83 at 25 C under ideal assumptions.
Worked example if you literally mean 100 M KBrO
If you instead plug in 100 M using the same pKa value, then:
[OH–] ≈ √(4.47 × 10-6 × 100) ≈ 2.11 × 10-2 M
pOH ≈ 1.68
pH ≈ 12.32
This is the ideal-equilibrium answer, but it comes with a major warning: a 100 M salt solution is not a realistic dilute aqueous system. At concentrations this extreme, ionic strength, activity coefficients, and even whether the stated concentration is physically achievable all become serious issues. So the arithmetic result is educational, but not a dependable real-world measurement.
Why the solution is basic
Students often wonder why KBrO does not stay neutral the way KCl does. The answer lies in the parent acid. Chloride is the conjugate base of a strong acid, HCl, so Cl– barely reacts with water. By contrast, hypobromite is the conjugate base of a weak acid, HBrO. Because HBrO does not completely dissociate, its conjugate base has enough strength to pull a proton from water and create OH–. More hydroxide means higher pH.
| Conjugate acid | Approximate pKa at 25 C | Approximate Ka | Conjugate base | Approximate Kb from Kw/Ka |
|---|---|---|---|---|
| HOCl | 7.53 | 2.95 × 10-8 | OCl– | 3.39 × 10-7 |
| HOBr | 8.65 | 2.24 × 10-9 | BrO– | 4.47 × 10-6 |
| HOI | 10.4 | 3.98 × 10-11 | IO– | 2.51 × 10-4 |
This comparison shows why BrO– is more basic than OCl– but less basic than IO–. The weaker the conjugate acid, the stronger the conjugate base.
Predicted pH values across common KBrO concentrations
The following table uses pKa = 8.65 for HBrO and assumes ideal behavior at 25 C. These are useful benchmark values when checking homework or preparing a lab report.
| KBrO concentration | Molarity used in calculation | Approximate [OH-] at equilibrium | Predicted pOH | Predicted pH |
|---|---|---|---|---|
| 1 mM | 0.001 M | 6.46 × 10-5 M | 4.19 | 9.81 |
| 10 mM | 0.010 M | 2.09 × 10-4 M | 3.68 | 10.32 |
| 100 mM | 0.100 M | 6.66 × 10-4 M | 3.18 | 10.82 |
| 1.0 M | 1.000 M | 2.11 × 10-3 M | 2.68 | 11.32 |
| 100 M | 100.0 M | 2.11 × 10-2 M | 1.68 | 12.32 |
Common mistakes when calculating the pH of KBrO
- Treating KBrO as neutral. The K+ ion is neutral, but BrO– is a weak base.
- Using Ka directly as if it were Kb. You must convert with Kb = Kw/Ka.
- Confusing 100 mM with 100 M. This changes the pH by roughly 1.5 units in the ideal calculation.
- Forgetting that pH depends on temperature. If temperature changes, Kw changes too.
- Ignoring non-ideal behavior at high concentration. Above dilute ranges, activity effects matter.
When the shortcut works and when it does not
The weak-base shortcut x ≈ √(KbC) is usually fine when the extent of reaction is small relative to the starting concentration. For 0.100 M KBrO, the ionization fraction is under 1 percent, so the shortcut works well. For broad educational use, it is acceptable. Still, the calculator above solves the quadratic expression directly, which avoids approximation error and gives a cleaner result when you explore more extreme concentrations.
Interpreting the chemistry in a practical way
In a laboratory context, KBrO solutions are of interest because hypobromite chemistry appears in oxidation, halogen equilibrium, and water-treatment discussions. Even though many textbook problems ask only for pH, the number is really telling you about the position of an equilibrium. A pH around 10.8 for 100 mM KBrO means only a small fraction of BrO– converts into HBrO and OH–, but that fraction is still enough to make the solution clearly basic.
If you are comparing KBrO with other oxyhalogen salts, remember that their pH values depend strongly on the pKa of the corresponding acid. That is why potassium hypochlorite and potassium hypoiodite do not all land at exactly the same pH when prepared at the same molarity. Their conjugate acids differ in strength, and the conjugate bases inherit that difference.
Authoritative references for deeper study
If you want to verify acid-base concepts or explore bromine oxy-compounds in greater depth, these resources are useful:
- PubChem, U.S. National Library of Medicine: Hypobromous Acid
- U.S. Environmental Protection Agency: National Primary Drinking Water Regulations
- NCBI Bookshelf: acid-base and solution chemistry references
Final takeaway
To calculate the pH of a 100m KBrO solution, first decide what “100m” means. If it means 100 mM, then the concentration is 0.100 M and the pH is about 10.8 at 25 C using a typical pKa of 8.65 for HBrO. If you literally mean 100 M, the ideal calculation gives a pH near 12.3, though that result should be treated cautiously because such a concentrated solution is not realistically described by simple dilute-solution equilibrium theory. The key chemistry is always the same: BrO– is the conjugate base of a weak acid, so it hydrolyzes water and makes the solution basic.