Calculate the pH of 2M Solution of NH4Br
Use this premium ammonium bromide pH calculator to solve the acidity of an NH4Br solution at 25°C. The tool applies weak acid equilibrium chemistry for NH4+ and gives pH, hydrogen ion concentration, Ka, pKa, and percent ionization.
NH4Br pH Calculator
Default is 2.0 M, matching the requested calculation.
Typical textbook value for ammonia is 1.8 × 10-5.
Enter values and click Calculate pH to see the full ammonium bromide equilibrium results.
Expert Guide: How to Calculate the pH of a 2M Solution of NH4Br
To calculate the pH of a 2M solution of NH4Br, you need to recognize what kind of salt ammonium bromide is and which ion actually affects acidity. NH4Br is composed of NH4+ and Br-. The bromide ion is the conjugate base of the strong acid HBr, so Br- does not significantly react with water. The ammonium ion, however, is the conjugate acid of the weak base NH3. That means NH4+ donates protons to water to a small extent, producing H3O+ and making the solution acidic.
This is the key idea: the pH of ammonium bromide is controlled by the hydrolysis of NH4+, not by bromide. Because NH3 is a weak base, its conjugate acid NH4+ is weakly acidic. At 25°C, the accepted base dissociation constant for ammonia is commonly taken as 1.8 × 10-5. Using the relationship between a conjugate acid and base, we can find the acid dissociation constant of NH4+:
Ka = Kw / Kb = 1.0 × 10-14 / 1.8 × 10-5 = 5.56 × 10-10
Once you have Ka, you can treat NH4+ as a weak acid in water. For a 2.0 M NH4Br solution, the initial concentration of NH4+ is also 2.0 M, assuming complete dissociation of the salt. The equilibrium is:
Ka = [NH3][H3O+] / [NH4+]
Step-by-step setup
- Write the equilibrium reaction for NH4+ acting as a weak acid.
- Set the initial concentration of NH4+ equal to the salt concentration, which is 2.0 M.
- Let x be the amount of NH4+ that ionizes.
- At equilibrium, [H3O+] = x, [NH3] = x, and [NH4+] = 2.0 – x.
- Substitute into the Ka expression: Ka = x2 / (2.0 – x).
Using the exact value of Ka:
Because Ka is very small compared with the concentration, x will be tiny relative to 2.0. That means the standard weak acid approximation is valid:
Since x is the hydronium concentration:
pH = -log(3.33 × 10-5) ≈ 4.48
So, the pH of a 2M solution of NH4Br is approximately 4.48 at 25°C when Kb for NH3 is 1.8 × 10-5. If you solve the equilibrium exactly with the quadratic formula, the answer is essentially the same because the degree of ionization is extremely small.
Why NH4Br is acidic
Students often wonder why a salt made from ions can produce a non-neutral pH. The answer lies in the acid-base strengths of the parent acid and base:
- HBr is a strong acid, so Br- is an extremely weak base and does not affect pH much.
- NH3 is a weak base, so NH4+ is a weak acid that does hydrolyze in water.
- Therefore, NH4Br solutions are acidic, often with pH values in the 4 to 6 range depending on concentration.
As concentration increases, the hydronium concentration also increases, but not linearly. Because weak acid equilibria typically follow a square-root dependence on concentration, the pH decreases gradually rather than crashing dramatically. That is why a 2.0 M NH4Br solution is only moderately acidic and not anywhere close to the pH of a strong acid at the same concentration.
Exact versus approximate method
For classroom chemistry, the approximation x ≈ √(KaC) is usually acceptable if the percent ionization is less than 5%. In this case, the percent ionization is extremely small:
That is far below the 5% rule, so the approximation is excellent. Still, high-quality calculators often report both methods. The exact quadratic expression for a weak acid concentration C is:
For NH4Br at 2.0 M, this exact expression still returns [H3O+] very close to 3.33 × 10-5 M and a pH of about 4.48.
Comparison table: NH4Br pH at different concentrations
| NH4Br Concentration (M) | Ka of NH4+ at 25°C | Approximate [H3O+] (M) | Calculated pH | Percent Ionization |
|---|---|---|---|---|
| 0.010 | 5.56 × 10-10 | 2.36 × 10-6 | 5.63 | 0.0236% |
| 0.10 | 5.56 × 10-10 | 7.45 × 10-6 | 5.13 | 0.00745% |
| 0.50 | 5.56 × 10-10 | 1.67 × 10-5 | 4.78 | 0.00334% |
| 1.00 | 5.56 × 10-10 | 2.36 × 10-5 | 4.63 | 0.00236% |
| 2.00 | 5.56 × 10-10 | 3.33 × 10-5 | 4.48 | 0.00167% |
The data above show a practical trend: doubling or tripling concentration does lower pH, but weak acid behavior means the change is moderate. That is why NH4Br remains a weakly acidic salt even at high molarity. In laboratory work, this matters when using ammonium salts in buffers, ionic strength control, or analytical preparation.
Comparison with other ammonium salts
Another useful perspective is to compare NH4Br with other ammonium salts. If the anion comes from a strong acid, the pH is dominated by NH4+ and tends to be similar at the same concentration. If the anion is basic, it can offset acidity. This is why NH4Cl, NH4NO3, and NH4Br behave similarly, while salts like ammonium acetate are much less acidic because acetate is a weak base.
| Salt | Parent Acid of Anion | Anion Basicity in Water | Main pH Driver | Expected 0.10 M Solution Behavior |
|---|---|---|---|---|
| NH4Br | HBr, strong acid | Negligible | NH4+ acidity | Acidic, around pH 5.1 |
| NH4Cl | HCl, strong acid | Negligible | NH4+ acidity | Acidic, similar to NH4Br |
| NH4NO3 | HNO3, strong acid | Negligible | NH4+ acidity | Acidic, similar to NH4Br |
| NH4CH3COO | CH3COOH, weak acid | Moderate | Competition between NH4+ and acetate | Closer to neutral |
Common mistakes when solving this problem
- Treating NH4Br as neutral. Many salts are neutral, but only those formed from a strong acid and a strong base. NH4Br is not one of them.
- Using Br- in the equilibrium calculation. Bromide is a spectator for pH purposes here.
- Using Kb directly instead of converting to Ka. Since NH4+ is the acid species, Ka is the appropriate constant.
- Forgetting the 25°C assumption. If temperature changes, Kw and equilibrium constants change too.
- Assuming strong acid behavior. NH4+ is a weak acid, so its pH is not remotely as low as that of a 2.0 M strong acid solution.
Short answer for exams and homework
If you need the fastest correct solution, this compact format works well:
- NH4Br dissociates completely to NH4+ and Br-.
- Br- is neutral because it is the conjugate base of strong acid HBr.
- NH4+ is a weak acid with Ka = Kw/Kb = 1.0 × 10-14 / 1.8 × 10-5 = 5.56 × 10-10.
- For C = 2.0 M, [H3O+] ≈ √(KaC) = √[(5.56 × 10-10)(2.0)] = 3.33 × 10-5 M.
- pH = -log(3.33 × 10-5) = 4.48.
Final answer: the pH of a 2M NH4Br solution is about 4.48 at 25°C.
Authoritative references
- PubChem (.gov): Ammonium bromide compound profile
- U.S. EPA (.gov): What is pH?
- University of Wisconsin (.edu): Acid-base equilibrium tutorial
Note: Reported values assume aqueous solution behavior near 25°C and idealized introductory chemistry constants. In highly concentrated real solutions, activity effects can shift measured pH slightly from ideal calculations.