Calculate The Ph Of A 1.7M Solution Of Hypobromous Acid

Use this premium weak-acid calculator to determine the exact hydrogen ion concentration, percent ionization, and pH for hypobromous acid, HBrO, using its acid dissociation constant at 25°C.

Hypobromous Acid pH Calculator

Equilibrium Visualization

The chart compares initial concentration, equilibrium concentration of undissociated HBrO, hydrogen ion produced, and percent ionization.

For a weak acid such as HBrO, only a very small fraction ionizes in water. That is why a solution can be highly concentrated yet still have a pH in the acidic but not ultra-low range.

How to Calculate the pH of a 1.7 M Solution of Hypobromous Acid

Calculating the pH of a 1.7 M solution of hypobromous acid requires weak-acid equilibrium chemistry rather than the direct complete-dissociation approach used for strong acids like hydrochloric acid. Hypobromous acid, written as HBrO or sometimes HOBr, is a weak acid. That means only a small portion of the dissolved acid molecules donate a proton to water. Because ionization is incomplete, the hydrogen ion concentration is not equal to the starting acid molarity. Instead, you must use the acid dissociation constant, Ka, and solve the equilibrium expression.

For hypobromous acid at 25°C, a commonly cited Ka value is approximately 2.3 × 10^-9. When the initial concentration is 1.7 M, the equilibrium can be represented as:

HBrO ⇌ H⁺ + BrO^–
Ka = [H⁺][BrO^–] / [HBrO]

If the initial concentration of HBrO is 1.7 M and the amount that dissociates is x, then at equilibrium:

• [HBrO] = 1.7 – x
• [H⁺] = x
• [BrO^–] = x

Substituting these into the Ka expression gives:

2.3 × 10^-9 = x² / (1.7 – x)

Because Ka is extremely small relative to the starting concentration, x is much smaller than 1.7. That means the classic weak-acid approximation is justified for quick work:

x² / 1.7 ≈ 2.3 × 10^-9
x ≈ √(1.7 × 2.3 × 10^-9)
x ≈ 6.25 × 10^-5 M

Since x represents [H⁺], the pH becomes:

pH = -log[H⁺] = -log(6.25 × 10^-5) ≈ 4.20

Using the exact quadratic solution yields essentially the same value because the ionization is so small. Therefore, the pH of a 1.7 M hypobromous acid solution is about 4.20 when Ka = 2.3 × 10^-9.

Ka used 2.3 × 10^-9

[H⁺] at equilibrium 6.25 × 10^-5 M

Final pH ≈ 4.20

Step-by-Step Weak Acid Setup

The easiest way to stay organized is to use an ICE table, which stands for Initial, Change, and Equilibrium. This method helps you translate the chemistry into a solvable algebra problem.

1. Write the balanced dissociation equation. For hypobromous acid: HBrO ⇌ H⁺ + BrO^–.
2. Enter the initial concentrations. Start with 1.7 M HBrO and essentially zero product ions from the acid itself.
3. Assign the change. Let x be the amount that dissociates.
4. Write equilibrium concentrations. HBrO becomes 1.7 – x, while H⁺ and BrO^– each become x.
5. Substitute into the Ka expression. Ka = x² / (1.7 – x).
6. Solve for x. Use the weak-acid approximation or the quadratic formula.
7. Convert hydrogen ion concentration to pH. Apply pH = -log[H⁺].

Exact vs Approximate Calculation

In many chemistry classes and laboratory settings, students are taught to check whether the weak-acid approximation is valid. The rule of thumb is that if x is less than about 5% of the initial concentration, then replacing 1.7 – x with 1.7 is acceptable. Here, x is roughly 6.25 × 10^-5 M, and the percent ionization is tiny, so the approximation is excellent.

Method	Expression Used	[H^+] Result	pH Result	Practical Comment
Weak-acid approximation	x ≈ √(KaC)	6.25 × 10^-5 M	4.204	Fast and accurate here
Exact quadratic solution	x = (-Ka + √(Ka^2 + 4KaC)) / 2	6.25 × 10^-5 M	4.204	Best for precision and verification

Why a 1.7 M Weak Acid Does Not Have an Extremely Low pH

This is one of the most important conceptual points. Concentration alone does not determine pH. The strength of the acid matters just as much. A 1.7 M solution of a strong monoprotic acid would have a hydrogen ion concentration close to 1.7 M and a pH near zero or even slightly negative depending on activity effects. Hypobromous acid is different because its Ka is very small. Only a tiny fraction of the 1.7 moles per liter actually dissociates. That leaves most of the acid still present as neutral HBrO molecules rather than free hydrogen ions.

In this case, the equilibrium hydrogen ion concentration is on the order of 10^-5 M, not 10⁰ M. That gap of roughly five powers of ten is exactly why the pH is about 4.20 instead of near 0.

Percent Ionization of 1.7 M Hypobromous Acid

Percent ionization is often calculated to evaluate how much acid actually dissociates:

% ionization = ([H⁺] / initial concentration) × 100

Substituting values gives:

% ionization = (6.25 × 10^-5 / 1.7) × 100 ≈ 0.0037%

This means more than 99.996% of the hypobromous acid remains undissociated under the assumptions of this idealized equilibrium model. That is a hallmark of a very weak acid at relatively high concentration.

Important Chemical Context for Hypobromous Acid

Hypobromous acid is part of the oxyacid family of bromine and is chemically related to bromine-based oxidizing systems used in water treatment, disinfection chemistry, and environmental oxidation reactions. In practical systems, pH affects the distribution between hypobromous acid and hypobromite ion, and that distribution strongly influences reactivity and disinfection performance. Although this calculator focuses on the acid dissociation problem for a defined concentration, the broader chemistry of HBrO is relevant in environmental and analytical science.

Because acid-base constants can vary somewhat depending on source, ionic strength, and temperature, your exact textbook or laboratory reference may list a Ka that is slightly different from 2.3 × 10^-9. If you use a different accepted value, the pH will shift slightly. However, for ordinary coursework the result remains close to pH 4.2.

Comparison with Other Common Acids

To put the result in perspective, it helps to compare hypobromous acid with stronger and weaker acids. The table below uses representative values to show how acid strength changes pH behavior. These figures are intended for educational comparison at 25°C and may vary slightly by source.

Acid	Representative Ka	Relative Strength	Behavior at Similar Formal Concentration
Hydrochloric acid, HCl	Very large, effectively complete dissociation	Strong acid	pH driven by near-total ionization
Hypochlorous acid, HClO	About 3 × 10^-8	Weak acid	More ionized than HBrO but still partial dissociation
Hypobromous acid, HBrO	About 2.3 × 10^-9	Very weak acid	Only a tiny fraction ionizes
Acetic acid, CH3COOH	About 1.8 × 10^-5	Weak acid	Much greater ionization than HBrO

When You Should Use the Quadratic Formula

Although the approximation works beautifully here, not every weak-acid problem behaves so cleanly. You should use the exact quadratic solution when:

• The Ka is not very small compared with the acid concentration.
• The concentration is low enough that ionization is not negligible.
• Your instructor, lab manual, or report format requires exact values.
• You want to verify the validity of the 5% approximation rule.

For this calculator, both the exact and approximate methods are available. In this specific problem, the two methods agree to essentially the same pH value.

Common Mistakes in This Problem

• Assuming HBrO is a strong acid. If you set [H⁺] = 1.7 M, the answer will be completely wrong.
• Using the wrong Ka. Similar acids like HClO and HIO have different dissociation constants.
• Forgetting that x is [H⁺]. The quantity x from the ICE table is what you convert into pH.
• Skipping the percent ionization check. It is useful for validating the approximation.
• Mixing concentration with activity. Introductory calculations typically use concentration, not corrected thermodynamic activity.

Authoritative Reference Sources

If you want to explore acid-base chemistry and aqueous equilibrium data in more depth, these authoritative educational and government resources are useful starting points:

• LibreTexts Chemistry for detailed acid-base equilibrium tutorials.
• U.S. Environmental Protection Agency for water chemistry and disinfectant context involving bromine species.
• NIST Chemistry WebBook for chemical reference data and thermodynamic context.

Final Answer

Using Ka = 2.3 × 10^-9 for hypobromous acid at 25°C, the equilibrium hydrogen ion concentration in a 1.7 M solution is approximately 6.25 × 10^-5 M. Therefore, the pH of a 1.7 M solution of hypobromous acid is about 4.20.

Educational note: real laboratory pH measurements at high ionic strength can differ slightly from idealized textbook values because pH meters respond to hydrogen ion activity rather than simple molar concentration.