Calculate the pH of a 1.60 m KBrO Solution
This interactive calculator estimates the pH of potassium hypobromite, KBrO, by treating BrO– as a weak base. It can use the common classroom approximation that molality is close to molarity, or convert molality to molarity when solution density is known.
KBrO pH Calculator
Click the button to estimate the pH of the 1.60 m KBrO solution. With the standard approximation at 25 C, the answer is expected to be a basic pH near 11.4.
Expert Guide: How to Calculate the pH of a 1.60 m KBrO Solution
To calculate the pH of a 1.60 m KBrO solution, you start by recognizing what kind of salt KBrO actually is. KBrO is potassium hypobromite. It dissociates completely in water to give K+ and BrO–. The potassium ion comes from the strong base KOH, so it does not affect pH in a meaningful way. The hypobromite ion, however, is the conjugate base of hypobromous acid, HOBr, which is a weak acid. That means BrO– behaves as a weak base in water and generates hydroxide ions.
The key chemical idea is simple: salts derived from a strong base and a weak acid create basic solutions. This is exactly the category into which KBrO falls. Therefore, a 1.60 m KBrO solution has a pH greater than 7. Under standard classroom assumptions, its pH is approximately 11.42.
Step 1: Write the relevant equilibrium
After KBrO dissolves, the important equilibrium is the hydrolysis of hypobromite:
This equation shows that BrO– accepts a proton from water, producing OH–. Because hydroxide is formed, the solution becomes basic.
Step 2: Relate Kb for BrO- to Ka for HOBr
Most data tables list the acidity constant for HOBr rather than the basicity constant for BrO–. So the standard approach is to convert using:
At 25 C, the ion product of water is:
If the pKa of HOBr is 8.65, then:
Now calculate the base constant:
Step 3: Set up the equilibrium expression
If the concentration of BrO– is treated as 1.60 M, the equilibrium table is:
- Initial: [BrO–] = 1.60, [HOBr] = 0, [OH–] = 0
- Change: -x, +x, +x
- Equilibrium: 1.60 – x, x, x
The equilibrium expression becomes:
Step 4: Solve for hydroxide concentration
Because Kb is small relative to the initial concentration, many classes use the weak-base approximation:
Substitute the values:
So:
The exact quadratic solution gives nearly the same answer because x is much smaller than 1.60.
Step 5: Convert hydroxide concentration to pOH and pH
Now calculate pOH:
Then use:
Depending on rounding and the exact pKa selected for HOBr, you will usually report the pH as 11.42 to 11.43.
Why the solution is basic
Students often memorize that salts can be acidic, basic, or neutral, but it is more useful to understand why. KBrO comes from:
- KOH, a strong base
- HOBr, a weak acid
The cation from the strong base is neutral in water, while the anion from the weak acid reacts with water to make OH–. That pattern predicts a basic solution every time. This logic also helps with similar salts such as NaF, NaOCl, and CH3COONa.
Molality versus molarity: why the notation matters
The problem states 1.60 m, which formally means molality, not molarity. Molality is moles of solute per kilogram of solvent. Strictly speaking, equilibrium calculations are usually written in terms of molarity. In many textbook exercises, however, a concentration written as molality is treated approximately as molarity when no density is provided. That is what produces the familiar pH near 11.42.
If a density value is available, you can convert molality to molarity more carefully. For 1.00 kg of solvent, a 1.60 m solution contains 1.60 mol KBrO. Using the molar mass of KBrO, 135.0013 g/mol, the solute mass is about 216.00 g. The total solution mass is then about 1216.00 g. If the density were known, the solution volume could be estimated and used to calculate molarity. The calculator above handles both cases.
| Quantity | Value | Why it matters |
|---|---|---|
| Molar mass of KBrO | 135.0013 g/mol | Needed to convert molality to molarity when density is used. |
| pKa of HOBr at 25 C | 8.65 | Used to obtain Ka for hypobromous acid. |
| Ka of HOBr | 2.24 × 10^-9 | Shows that HOBr is a weak acid. |
| Kb of BrO- | 4.47 × 10^-6 | Controls the hydrolysis of hypobromite. |
| Approximate [OH-] in 1.60 M KBrO | 2.67 × 10^-3 M | Directly determines pOH and pH. |
| Approximate pH | 11.42 to 11.43 | Final reported answer under standard assumptions. |
Exact solution versus approximation
The square-root shortcut is useful, but it is worth knowing when it works. The approximation assumes that x is small compared with the initial concentration. Here, x is only about 0.00267 while the starting concentration is 1.60, so the percent change is well under 1%. That makes the approximation excellent. The exact quadratic formula confirms it:
For this problem, the exact and approximate answers differ only in the third or fourth decimal place of pH.
Comparison with other salts
One of the fastest ways to improve your acid-base intuition is to compare KBrO with other salts. The table below uses standard 25 C assumptions and idealized equilibrium calculations for 1.60 M solutions.
| Salt | Parent acid or base | Expected behavior in water | Approximate pH at 1.60 M |
|---|---|---|---|
| KCl | HCl + KOH | Neutral salt from strong acid and strong base | 7.00 |
| NaF | HF + NaOH | Basic because F- is the conjugate base of a weak acid | 8.96 |
| NaOCl | HOCl + NaOH | Basic weak-base anion in water | 10.87 |
| KBrO | HOBr + KOH | Basic weak-base anion in water | 11.42 |
Common mistakes students make
- Treating KBrO as neutral. It is not neutral because BrO– hydrolyzes.
- Using Ka directly instead of converting to Kb. Since BrO– is a base, Kb is the constant needed.
- Forgetting to use pOH first. Hydroxide concentration gives pOH, and only then do you convert to pH.
- Ignoring the notation m versus M. If density is not given, approximation is common, but it should still be acknowledged.
- Assuming the potassium ion changes pH. K+ is a spectator ion.
How to explain this answer on homework or an exam
If you need a compact, high scoring explanation, write something like this:
Practical interpretation
A pH around 11.4 means the solution is distinctly basic. In real laboratory work, highly concentrated electrolyte solutions can show nonideal behavior, and activity corrections may shift the value somewhat. Temperature also matters because both Kw and acid dissociation constants vary with temperature. But for general chemistry, analytical chemistry homework, and most classroom problem sets, the standard result is entirely appropriate.
Authoritative references for deeper study
Final answer
Using the standard assumption that the 1.60 m KBrO solution can be treated as approximately 1.60 M at 25 C, and taking pKa(HOBr) = 8.65, the calculated pH is about 11.42 to 11.43. The solution is basic because BrO– is the conjugate base of the weak acid HOBr.