Calculate the pH of 0.30 M NH4Br Solution
Use this interactive chemistry calculator to determine the pH of ammonium bromide solution from equilibrium constants, compare approximation versus exact methods, and visualize how pH changes with concentration.
NH4Br pH Calculator
NH4Br is the salt of a weak base (NH3) and a strong acid (HBr), so the solution is acidic because NH4+ acts as a weak acid in water.
Results
Click Calculate pH to solve the pH of a 0.30 M NH4Br solution and display the equilibrium details.
Chart shows predicted pH versus NH4Br concentration using your selected equilibrium constants.
How to calculate the pH of 0.30 M NH4Br solution
To calculate the pH of a 0.30 M NH4Br solution, begin by recognizing what kind of salt ammonium bromide is. NH4Br dissociates completely in water into NH4+ and Br-. The bromide ion comes from the strong acid HBr, so Br- is essentially neutral in water and does not significantly affect pH. The ammonium ion, however, is the conjugate acid of the weak base ammonia, NH3. That means NH4+ can donate a proton to water and produce hydronium, H3O+, making the solution acidic.
This is the key conceptual step students often miss. Many salt problems look similar, but the pH depends on the parent acid and base. If the cation is the conjugate acid of a weak base, the solution becomes acidic. If the anion is the conjugate base of a weak acid, the solution becomes basic. For NH4Br, the cation controls the pH.
Step 1: Write the dissociation and hydrolysis equations
First, write the complete ionic dissociation of the salt:
- NH4Br → NH4+ + Br-
Then identify the ion that reacts with water:
- NH4+ + H2O ⇌ NH3 + H3O+
Because NH4+ behaves as a weak acid, we need its acid dissociation constant, Ka. Most data tables list the base dissociation constant for ammonia, Kb, instead. So you convert using the water ion product:
- Ka × Kb = Kw
- Ka = Kw / Kb
At 25 degrees C, Kw = 1.0 × 10^-14 and a widely used value for Kb of NH3 is 1.8 × 10^-5. Therefore:
- Ka = (1.0 × 10^-14) / (1.8 × 10^-5)
- Ka = 5.56 × 10^-10
Step 2: Set up the ICE table
Since the NH4Br concentration is 0.30 M, the initial NH4+ concentration is also 0.30 M after complete dissociation. Let x represent the amount of NH4+ that donates a proton to water:
| Species | Initial (M) | Change (M) | Equilibrium (M) |
|---|---|---|---|
| NH4+ | 0.30 | -x | 0.30 – x |
| NH3 | 0 | +x | x |
| H3O+ | ~0 | +x | x |
The equilibrium expression is:
- Ka = [NH3][H3O+] / [NH4+]
- Ka = x^2 / (0.30 – x)
Step 3: Solve for x
For a weak acid, x is usually small relative to the initial concentration, so many chemistry classes use the approximation 0.30 – x ≈ 0.30. Then:
- x^2 / 0.30 = 5.56 × 10^-10
- x^2 = 1.67 × 10^-10
- x = 1.29 × 10^-5 M
Since x equals the hydronium concentration, we get:
- [H3O+] = 1.29 × 10^-5 M
- pH = -log(1.29 × 10^-5)
- pH ≈ 4.89
If you solve the full quadratic equation instead of using the approximation, you obtain essentially the same answer for this concentration. That is why the approximation is acceptable here. The 5 percent rule is strongly satisfied because x is much smaller than 0.30 M.
Why NH4Br is acidic in water
Understanding the chemistry behind the number is more important than memorizing isolated formulas. NH4Br is produced from ammonia and hydrobromic acid. Ammonia is a weak base, meaning it does not completely react with water to generate hydroxide. Its conjugate acid, NH4+, therefore has measurable acidic behavior. Hydrobromic acid is a strong acid, so its conjugate base, Br-, is negligibly basic. The result is a solution whose pH is controlled almost entirely by NH4+ hydrolysis.
This logic helps you classify many salts quickly:
- Strong acid + strong base: neutral solution near pH 7 at 25 degrees C
- Strong acid + weak base: acidic solution
- Weak acid + strong base: basic solution
- Weak acid + weak base: depends on relative Ka and Kb values
Exact method versus approximation
For most classroom NH4Br problems, the weak acid approximation is accurate because Ka is tiny and the initial concentration is relatively large. Still, exact calculation is useful in a premium calculator because it avoids hidden assumptions. The exact equation from the acid equilibrium expression is:
- x^2 + Kax – KaC = 0
Solving gives:
- x = (-Ka + √(Ka^2 + 4KaC)) / 2
Here, C is the formal concentration of NH4+. With C = 0.30 M and Ka = 5.56 × 10^-10, x still comes out near 1.29 × 10^-5 M. Because the approximation and exact methods are so close, student answer keys usually accept pH 4.89.
| Method | Expression Used | [H3O+] for 0.30 M NH4Br | Calculated pH | Practical Comment |
|---|---|---|---|---|
| Approximation | x ≈ √(KaC) | 1.29 × 10^-5 M | 4.889 | Fast, highly accurate here |
| Exact quadratic | x = (-Ka + √(Ka^2 + 4KaC)) / 2 | 1.29 × 10^-5 M | 4.889 | Best when concentration is low or precision matters |
Reference equilibrium data used in NH4Br pH calculations
The following values are standard data points commonly used in general chemistry and analytical chemistry. The numbers matter because slight changes in Kb or Kw can shift the final pH by a few hundredths of a unit. That is why calculators that expose the constants are more transparent and more useful for lab work or homework checking.
| Parameter | 20 degrees C | 25 degrees C | 30 degrees C | Why it matters |
|---|---|---|---|---|
| Kw | 6.81 × 10^-15 | 1.00 × 10^-14 | 1.47 × 10^-14 | Changes Ka when Kb is known |
| Kb of NH3 | Commonly tabulated near 1.8 × 10^-5 at 25 degrees C | Sets the acidity of NH4+ | ||
| Ka of NH4+ | 3.78 × 10^-10 | 5.56 × 10^-10 | 8.17 × 10^-10 | Higher Ka gives lower pH |
Worked example in plain language
- Recognize NH4Br as a salt containing NH4+, the conjugate acid of NH3.
- Ignore Br- for pH purposes because it is the conjugate base of a strong acid.
- Use Kb for NH3 to find Ka for NH4+ using Ka = Kw / Kb.
- Set the ammonium concentration equal to the NH4Br concentration, 0.30 M.
- Apply the weak acid equilibrium expression.
- Solve for hydronium concentration and then convert to pH.
This workflow is standard and can be applied to other ammonium salts such as NH4Cl, NH4NO3, and NH4I, provided the anion is the conjugate base of a strong acid and does not hydrolyze significantly.
How concentration affects pH
As the concentration of NH4Br increases, the pH decreases because more NH4+ is available to generate H3O+. However, the decrease is not linear because pH is logarithmic and because weak acid equilibria scale with the square root of concentration in the common approximation. For example, very dilute ammonium bromide solutions are only mildly acidic, while concentrated solutions are noticeably more acidic but still far from the behavior of strong acids.
The chart in the calculator illustrates this concentration effect. It computes pH over a concentration range while keeping your selected Kb and Kw values fixed. This makes it easy to see not only the answer for 0.30 M, but also how sensitive the result is if the solution were diluted in the lab.
Common mistakes when solving NH4Br pH problems
- Treating NH4Br as neutral. It is not neutral because NH4+ is acidic.
- Using Kb directly in the acid equilibrium expression. You must convert to Ka for NH4+.
- Including Br- in the equilibrium calculation. Bromide does not significantly react with water.
- Forgetting complete dissociation of the salt. A 0.30 M NH4Br solution gives 0.30 M NH4+ initially.
- Using the wrong logarithm sign. pH = -log[H3O+], not log[H3O+].
- Confusing M with m. In many homework statements, capitalization matters. This calculator assumes molarity in solution.
When would the exact calculation be more important?
The exact quadratic method becomes more important when the concentration is extremely low, when Ka is larger, or when high precision is required for reporting. In those cases, the simplification C – x ≈ C may no longer hold sufficiently well. For 0.30 M NH4Br, however, approximation error is negligible, so both classroom and professional checks land at roughly pH 4.89.
Lab and academic relevance
Ammonium salts appear in analytical chemistry, buffer preparation, environmental chemistry, fertilizer chemistry, and biological systems involving nitrogen compounds. While NH4Br itself is not the most common ammonium salt in introductory examples, it is ideal for teaching salt hydrolysis because the bromide ion is spectatorial with respect to acid-base behavior. That makes the chemistry cleaner and the equilibrium easier to isolate.
In laboratory reporting, always state the constants and temperature assumptions you used. A pH reported as 4.89 is meaningful only when tied to equilibrium data. If a textbook uses Kb = 1.76 × 10^-5 instead of 1.80 × 10^-5, your result may differ in the third decimal place. That is normal scientific variation, not an error.
Authoritative references for acid-base data and pH concepts
- U.S. Environmental Protection Agency: What is pH?
- National Institute of Standards and Technology: NIST Chemistry WebBook
- University of Wisconsin Chemistry: Acid-Base Equilibria Tutorial
Bottom line
If you are asked to calculate the pH of 0.30 M NH4Br solution, the chemistry is straightforward once you classify the salt correctly. NH4+ is a weak acid, Br- is neutral, and the solution is acidic. Using Kb of ammonia equal to 1.8 × 10^-5 and Kw equal to 1.0 × 10^-14 at 25 degrees C gives Ka for NH4+ equal to 5.56 × 10^-10. Solving the weak acid equilibrium yields a hydronium concentration of about 1.29 × 10^-5 M and a final pH of 4.89. The interactive calculator above performs the exact same logic instantly and also lets you explore how temperature assumptions and concentration changes affect the answer.