Calculate the pH of 0.14 M NH4Br Solution
Use this interactive weak-acid calculator to determine the pH of ammonium bromide solution from concentration and ammonia base constant data. The tool applies the conjugate-acid relationship for NH4+ and solves the equilibrium with a premium step-by-step summary.
Calculated Results
Enter values and click Calculate pH. For the default 0.14 M NH4Br setup, the expected pH is slightly acidic.
How to calculate the pH of 0.14 M NH4Br solution
To calculate the pH of a 0.14 M NH4Br solution, the key idea is to identify which ion actually affects acid-base behavior in water. Ammonium bromide dissociates almost completely into NH4+ and Br-. The bromide ion is the conjugate base of the strong acid HBr, so Br- does not hydrolyze to any meaningful extent. The ammonium ion, however, is the conjugate acid of the weak base ammonia, NH3. That makes NH4+ a weak acid in water, and the solution becomes acidic.
The chemistry can be summarized in two simple steps. First, write the dissociation of the salt:
NH4Br(aq) → NH4+(aq) + Br-(aq)
Second, write the hydrolysis of ammonium in water:
NH4+(aq) + H2O(l) ⇌ NH3(aq) + H3O+(aq)
Because hydronium is produced, the pH drops below 7. At 25°C, ammonia has a base dissociation constant Kb of about 1.8 × 10^-5. The acid dissociation constant for ammonium is found from:
Ka = Kw / Kb = 1.0 × 10^-14 / 1.8 × 10^-5 = 5.56 × 10^-10
Once you know Ka and the initial ammonium concentration, you can compute the hydronium concentration and then the pH. For a 0.14 M NH4Br solution, the exact equilibrium result gives a pH of about 5.05. That means the solution is mildly acidic, not strongly acidic.
Step-by-step equilibrium setup
Students often lose points on this problem because they classify the salt incorrectly. NH4Br is not neutral. It is a salt formed from a weak base and a strong acid, which generally yields an acidic aqueous solution. The correct strategy is to treat NH4+ as a weak acid and ignore Br- for acid-base purposes.
1. Determine the acidic species
- NH4+ is the conjugate acid of NH3, a weak base.
- Br- is the conjugate base of HBr, a strong acid.
- Therefore, NH4+ controls the pH.
2. Calculate Ka for ammonium
Use the conjugate pair relationship:
- Kw = Ka × Kb
- Ka = Kw / Kb
- Ka = 1.0 × 10^-14 / 1.8 × 10^-5
- Ka = 5.56 × 10^-10
3. Set up the ICE table
For the equilibrium NH4+ + H2O ⇌ NH3 + H3O+, let x be the amount that ionizes:
| Species | Initial (M) | Change (M) | Equilibrium (M) |
|---|---|---|---|
| NH4+ | 0.14 | -x | 0.14 – x |
| NH3 | 0 | +x | x |
| H3O+ | 0 | +x | x |
4. Write the Ka expression
Substitute the equilibrium concentrations into the acid dissociation expression:
Ka = [NH3][H3O+] / [NH4+] = x² / (0.14 – x)
Using Ka = 5.56 × 10^-10:
5.56 × 10^-10 = x² / (0.14 – x)
5. Solve for x
Because Ka is very small, the weak-acid approximation usually works well:
x² / 0.14 ≈ 5.56 × 10^-10
x² ≈ 7.78 × 10^-11
x ≈ 8.82 × 10^-6 M
Since x = [H3O+], calculate pH:
pH = -log(8.82 × 10^-6) ≈ 5.05
The exact quadratic solution yields nearly the same value because x is tiny compared with 0.14 M. The percent ionization is far below 5%, so the approximation is valid.
Final answer for the pH of 0.14 M NH4Br
The pH of a 0.14 M NH4Br solution at 25°C is approximately 5.05, assuming Kb for NH3 is 1.8 × 10^-5 and Kw is 1.0 × 10^-14.
Why NH4Br is acidic instead of neutral
A powerful shortcut in salt hydrolysis problems is to classify the parent acid and parent base. NH4Br comes from NH3 and HBr. NH3 is a weak base, while HBr is a strong acid. Salts of a weak base with a strong acid normally produce acidic solutions because the cation hydrolyzes and generates hydronium. By contrast, salts from a strong acid and a strong base are usually neutral, and salts from a weak acid with a strong base are usually basic.
This logic is useful beyond NH4Br. The same pattern applies to NH4Cl, NH4NO3, and other ammonium salts paired with anions that are conjugate bases of strong acids. In all these cases, the anion is essentially a spectator for pH, while NH4+ controls the equilibrium.
Approximation method versus exact quadratic method
Most chemistry courses allow the square root approximation if the acid or base is weak and the initial concentration is much larger than the amount ionized. Still, advanced courses or digital calculators often use the exact quadratic solution because it is more rigorous. For NH4Br at 0.14 M, both methods agree extremely well.
| Method | Equation Used | Calculated [H3O+] (M) | pH | Comment |
|---|---|---|---|---|
| Weak acid approximation | x ≈ √(KaC) | 8.82 × 10^-6 | 5.054 | Fast and highly accurate here |
| Exact quadratic | x² + Kax – KaC = 0 | 8.82 × 10^-6 | 5.054 | Most rigorous method |
The difference is negligible because the equilibrium shift is so small. The percent ionization is approximately:
(8.82 × 10^-6 / 0.14) × 100 ≈ 0.0063%
That is far less than the usual 5% threshold, confirming the validity of the simplification.
Comparison with other common aqueous solutions
It is helpful to compare 0.14 M NH4Br to other familiar solution types. This puts the pH result in context and helps students avoid overestimating acidity. A pH of about 5.05 is acidic, but not remotely close to a strong acid of similar molarity.
| Solution | Typical Classification | Main pH-Controlling Species | Approximate pH at Similar Concentration | Interpretation |
|---|---|---|---|---|
| 0.14 M NH4Br | Acidic salt solution | NH4+ | 5.05 | Mildly acidic due to weak acid hydrolysis |
| 0.14 M NaBr | Neutral salt solution | None significant | 7.00 | Strong acid plus strong base salt |
| 0.14 M NH3 | Weak base solution | NH3 | 11.20 | Basic because ammonia accepts protons |
| 0.14 M HBr | Strong acid solution | H3O+ | 0.85 | Very acidic due to near complete ionization |
Common mistakes when solving NH4Br pH problems
- Assuming the salt is neutral. Not every ionic compound in water gives pH 7. You must check the parent acid and base.
- Using Kb directly for NH4+. Kb belongs to NH3, not NH4+. Convert it to Ka using Ka = Kw/Kb.
- Including Br- in the hydrolysis calculation. Bromide is a negligible base because it is the conjugate base of a strong acid.
- Forgetting the logarithm sign. pH = -log[H3O+], not log[H3O+].
- Rounding too early. Keep several significant digits until the final pH value.
When temperature or constants change
The result pH ≈ 5.05 assumes standard aqueous conditions near 25°C and accepted textbook constants. If temperature changes significantly, Kw changes, and weak acid or weak base constants may also shift. In high precision analytical chemistry, those changes matter. In typical general chemistry homework, however, using Kb = 1.8 × 10^-5 and Kw = 1.0 × 10^-14 is standard practice.
The calculator above lets you modify both Kb and Kw so you can test how sensitive the pH is to different assumptions. That feature is useful in advanced coursework, lab pre-calculations, and solution design tasks.
Practical interpretation of a pH near 5.05
A pH of roughly 5.05 means the hydronium concentration is on the order of 10^-5 M. This is significantly more acidic than pure water, but still a weakly acidic environment compared with mineral acid solutions. In practical terms, an NH4Br solution at this concentration can influence indicator color changes, reaction rates, and some biological or environmental systems, but it is not as corrosive or as low in pH as a strong acid of equal concentration.
In laboratory contexts, ammonium salts are often encountered in buffer systems, ionic strength adjustments, and qualitative analysis. Understanding why ammonium-containing salts acidify water gives students a broader framework for predicting pH without memorizing isolated examples.
Authoritative references for acid-base constants and pH concepts
- U.S. Environmental Protection Agency: Water Quality Criteria and pH background
- Chemistry LibreTexts: Acid-base equilibria and salt hydrolysis
- National Institute of Standards and Technology: Chemistry data and measurement standards
Summary
If you need to calculate the pH of 0.14 M NH4Br solution, treat NH4+ as a weak acid and Br- as a spectator ion. Convert the known Kb of NH3 into Ka for NH4+, set up the hydrolysis equilibrium, solve for hydronium concentration, and then convert to pH. Using Kb = 1.8 × 10^-5 at 25°C, the solution pH is approximately 5.05. This result is consistent whether you use the square root approximation or the exact quadratic equation.