Calculate The Ph Of A 0.100 M Kbro Solution

Use this premium chemistry calculator to find the pH, pOH, hydroxide concentration, and base dissociation constant for potassium hypobromite solutions. The default setup solves the exact weak-base equilibrium for a 0.100 m KBrO solution at 25 degrees Celsius.

How to calculate the pH of a 0.100 m KBrO solution

If you need to calculate the pH of a 0.100 m KBrO solution, the key idea is that potassium hypobromite is a salt containing the conjugate base of a weak acid. KBrO dissociates essentially completely in water to produce K⁺ and BrO^–. The potassium ion is a spectator ion for acid-base chemistry, while the hypobromite ion reacts with water to produce hydroxide. Because hydroxide forms, the resulting solution is basic, so the pH must be greater than 7 at 25 degrees Celsius.

The full chemistry starts from the hydrolysis reaction:

BrO^– + H₂O ⇌ HOBr + OH^–

This is a classic weak-base equilibrium. To solve it, you first connect the base dissociation constant of BrO^– to the acid dissociation constant of hypobromous acid, HOBr. The relationship is:

K_b = K_w / K_a

At 25 degrees Celsius, K_w is 1.0 × 10^-14. A commonly used value for K_a of HOBr is about 2.3 × 10^-9. Substituting gives:

K_b = (1.0 × 10^-14) / (2.3 × 10^-9) = 4.35 × 10^-6

Now set up an ICE table for a 0.100 concentration of BrO^– in water:

• Initial BrO^– = 0.100
• Initial HOBr = 0
• Initial OH^– ≈ 0
• Change = -x, +x, +x
• Equilibrium = 0.100 – x, x, x

That leads to the equilibrium expression:

K_b = x² / (0.100 – x)

Because K_b is relatively small, many textbooks first use the approximation 0.100 – x ≈ 0.100. Then:

x = square root of (K_b × C) = square root of (4.35 × 10^-6 × 0.100) ≈ 6.60 × 10^-4 M

This x value is the hydroxide concentration. From there:

1. pOH = -log[OH^–]
2. pOH = -log(6.60 × 10^-4) ≈ 3.18
3. pH = 14.00 – 3.18 = 10.82

So the pH of a 0.100 m KBrO solution is approximately 10.82 at 25 degrees Celsius, assuming dilute behavior and a K_a for HOBr of 2.3 × 10^-9. The exact quadratic solution gives nearly the same result, which confirms that the approximation is valid for this concentration.

Why KBrO gives a basic solution

Understanding the origin of the basic pH helps you remember the method rather than just memorizing one answer. KBrO is the salt of a strong base and a weak acid:

• KOH is a strong base.
• HOBr is a weak acid.

When a salt forms from a strong base and a weak acid, the anion acts as a weak base in water. Here, BrO^– accepts a proton from water to make HOBr and OH^–. The newly generated OH^– raises the pH above neutrality. In practical classroom chemistry, this is one of the most common “salt hydrolysis” patterns tested in general chemistry and AP-level acid-base problems.

Quick decision rule for salt pH problems

• Strong acid + strong base salt: neutral solution
• Strong acid + weak base salt: acidic solution
• Weak acid + strong base salt: basic solution
• Weak acid + weak base salt: compare K_a and K_b

KBrO falls in the weak acid plus strong base category, so a basic pH is expected before you even start calculating.

Exact calculation versus approximation

In many chemistry courses, you are allowed to approximate when x is small compared with the initial concentration. For a 0.100 solution of BrO^–, the approximation works extremely well. Still, the exact quadratic form is more rigorous:

x = (-K_b + square root of (K_b² + 4K_bC)) / 2

Using K_b = 4.35 × 10^-6 and C = 0.100 gives x very close to 6.58 × 10^-4 M. The exact pOH is about 3.182, and the exact pH is about 10.818. Rounded to two decimal places, both methods give 10.82.

This is a good illustration of why approximation is accepted: the percent ionization is low.

Method	[OH^–] produced	pOH	pH	Difference from exact pH
Exact quadratic	6.58 × 10^-4	3.182	10.818	0.000
Approximation	6.60 × 10^-4	3.180	10.820	0.002

The numerical difference is tiny, which is why most instructional solutions report pH ≈ 10.82.

Does 0.100 m mean the same thing as 0.100 M?

Strictly speaking, no. Molality, written as m, is moles of solute per kilogram of solvent. Molarity, written as M, is moles of solute per liter of solution. In highly precise physical chemistry, these are not identical units. However, for a relatively dilute aqueous solution like 0.100 m KBrO, the difference is usually small enough that introductory pH calculations treat them as effectively equivalent unless the problem specifically asks for activity corrections or density-based conversion.

That is why this calculator accepts 0.100 m and applies the standard weak-base equilibrium framework used in general chemistry. If you were doing analytical chemistry at higher ionic strength, you might need activity coefficients, exact temperature-dependent values, and a careful conversion between concentration scales. For classroom and most routine problem-solving, the dilute approximation is appropriate.

When the approximation is especially safe

• The solution is dilute and mostly water.
• The weak acid or weak base has a small dissociation constant.
• The percent ionization is under about 5 percent.
• The problem is framed as a standard general chemistry exercise.

Step-by-step expert method you can reuse

1. Write the ions produced when the salt dissolves.
2. Identify whether the cation or anion hydrolyzes.
3. Determine whether the solution should be acidic, basic, or neutral.
4. Find K_b or K_a using K_w if needed.
5. Set up an ICE table for the hydrolysis reaction.
6. Solve for x using either the approximation or quadratic formula.
7. Convert x into pOH or pH.
8. Check whether your answer is chemically reasonable.

For KBrO, that process leads quickly to a basic pH near 10.82. If you got something acidic, that would immediately indicate a sign or setup error.

Comparison data: how concentration changes the pH of KBrO

Because KBrO behaves as a weak base, increasing the concentration raises the hydroxide concentration and therefore raises the pH. The trend is not linear on the pH scale because pH is logarithmic. The following table uses the same K_a value for HOBr and an exact equilibrium solution at 25 degrees Celsius.

KBrO concentration	Kb for BrO^–	[OH^–] from hydrolysis	pOH	pH
0.0100	4.35 × 10^-6	2.06 × 10^-4	3.686	10.314
0.0500	4.35 × 10^-6	4.64 × 10^-4	3.334	10.666
0.100	4.35 × 10^-6	6.58 × 10^-4	3.182	10.818
0.200	4.35 × 10^-6	9.30 × 10^-4	3.031	10.969
0.500	4.35 × 10^-6	1.47 × 10^-3	2.833	11.167

These figures show why pH rises more slowly than concentration. Doubling concentration does not double pH because pH depends on the logarithm of hydroxide concentration.

Common mistakes students make

1. Treating KBrO as a neutral salt

This mistake happens when the student notices potassium is from a strong base and assumes the whole salt is neutral. You must also consider the acid-base behavior of the anion. BrO^– is basic.

2. Using K_a directly instead of converting to K_b

HOBr is the weak acid, but BrO^– is the species in solution. Since BrO^– acts as a base, you need K_b, not K_a. Convert using K_w / K_a.

3. Forgetting to convert pOH to pH

Because the hydrolysis equation gives OH^–, your first log result is pOH. You still need pH = 14.00 – pOH at 25 degrees Celsius.

4. Assuming percent ionization is too large for approximation without checking

For this problem the approximation is fine, but it is still good practice to check x/C. Here, 6.58 × 10^-4 divided by 0.100 is about 0.66 percent, well below 5 percent.

What the final answer means chemically

A pH of about 10.82 means the solution is mildly to moderately basic. It is not nearly as basic as a strong base of the same formal concentration, but it is clearly above neutral water. The difference comes from incomplete hydrolysis. Only a small fraction of BrO^– reacts with water to generate OH^–, which is exactly what weak-base behavior predicts.

You can also estimate the extent of hydrolysis from the hydroxide concentration. With [OH^–] around 6.58 × 10^-4 M and an initial concentration of 0.100, only a small percentage of the available BrO^– has reacted. This aligns with the weak basicity of hypobromite.

Authoritative chemistry and water-quality references

For additional background on pH, aqueous equilibria, and water chemistry, consult these authoritative sources:

• USGS: pH and Water
• U.S. EPA: Aquatic Life Criteria for pH
• Chemistry LibreTexts

Bottom line

To calculate the pH of a 0.100 m KBrO solution, treat KBrO as a fully dissociated salt that delivers the weak base BrO^–. Convert the acid constant of HOBr into a base constant for BrO^–, solve the hydrolysis equilibrium, and then convert hydroxide concentration into pOH and pH. Using a standard K_a for hypobromous acid at 25 degrees Celsius, the result is:

pH of 0.100 m KBrO ≈ 10.82

If you want to verify the result instantly or explore how concentration changes the pH, use the calculator above. It applies both the exact and approximate methods so you can compare the chemistry, the math, and the final answer in one place.