Calculate the pH of a 0.10 M NH4CN Solution
Use this premium calculator to estimate the pH of ammonium cyanide by combining the acid behavior of NH4+ with the base behavior of CN-. The tool computes an exact numerical solution and compares it with the standard weak-acid weak-base salt approximation.
How to calculate the pH of a 0.10 M NH4CN solution
To calculate the pH of a 0.10 M NH4CN solution, you need to recognize that ammonium cyanide is not a simple neutral salt. It dissociates into NH4+ and CN-, and both ions react with water. The ammonium ion behaves as a weak acid, while the cyanide ion behaves as a weak base. Because the salt contains the conjugate acid of a weak base and the conjugate base of a weak acid, the final pH depends on a competition between those two hydrolysis reactions.
That is why this problem is more interesting than something like NaCl, which is neutral, or NH4Cl, which is acidic. In NH4CN, the cyanide ion tends to generate hydroxide ions, pushing the pH upward, while the ammonium ion tends to generate hydronium ions, pushing the pH downward. The stronger of the two effects wins. Under common textbook constants at 25 degrees C, the basicity of CN- is much stronger than the acidity of NH4+, so the solution ends up basic.
Step 1: Write the ions produced by NH4CN
When ammonium cyanide dissolves in water, it dissociates essentially completely:
NH4CN(aq) → NH4+(aq) + CN-(aq)
If the original concentration is 0.10 M, then the initial concentration of each ion is also 0.10 M. At this point, you have equal amounts of a weak acid species and a weak base species.
Step 2: Identify the acid and base behavior
Ammonium ion as a weak acid
The ammonium ion is the conjugate acid of ammonia:
NH4+ + H2O ⇌ NH3 + H3O+
Its acid dissociation constant is calculated from the base constant of ammonia:
Ka(NH4+) = Kw / Kb(NH3)
If Kb(NH3) = 1.8 × 10^-5 and Kw = 1.0 × 10^-14, then:
Ka(NH4+) = 5.56 × 10^-10
Cyanide ion as a weak base
The cyanide ion is the conjugate base of hydrocyanic acid:
CN- + H2O ⇌ HCN + OH-
Its base dissociation constant is calculated from the acid constant of HCN:
Kb(CN-) = Kw / Ka(HCN)
If Ka(HCN) = 6.2 × 10^-10, then:
Kb(CN-) = 1.61 × 10^-5
Step 3: Compare Kb of CN- to Ka of NH4+
Now compare the two hydrolysis strengths:
- Ka(NH4+) = 5.56 × 10^-10
- Kb(CN-) = 1.61 × 10^-5
The cyanide ion is much stronger as a base than ammonium is as an acid. Because the base hydrolysis dominates, the solution must have a pH above 7.
Step 4: Use the weak-acid weak-base salt formula
For a salt where the cation is a weak acid and the anion is a weak base at the same formal concentration, the classic approximation is:
pH = 7 + 0.5 log(Kb / Ka)
Substitute the values:
pH = 7 + 0.5 log((1.61 × 10^-5) / (5.56 × 10^-10))
The ratio is about 2.90 × 10^4. The log of that ratio is about 4.46. Half of that is about 2.23.
So the estimated pH is:
pH ≈ 7 + 2.23 = 9.23
This is the result many chemistry instructors expect for the standard form of the problem. Depending on the exact constants supplied by a textbook, you may see an answer in the range of 9.2 to 9.3.
Why the concentration often seems to cancel out
Students sometimes expect the 0.10 M concentration to strongly influence the answer. In many weak-acid weak-base salt calculations, however, the approximate pH formula does not explicitly contain concentration because the cation and anion start at the same concentration. Their effects oppose one another, and under the derivation of the approximation, the shared concentration terms cancel. That does not mean concentration never matters. It means concentration matters less in the idealized derivation than the relative strengths of the acid and base hydrolysis constants.
In an exact numerical treatment, especially at very low concentrations, water autoionization and nonideal effects can shift the result slightly. Still, for a 0.10 M classroom problem, the approximation is generally excellent.
Exact calculation versus approximation
The calculator above performs an exact numerical charge-balance solution instead of relying only on the compact textbook formula. It models the species distributions for both ammonium and cyanide, then solves for the hydronium concentration that balances total positive and negative charge in solution. This gives you a more rigorous answer while still displaying the common shortcut used in many general chemistry courses.
For NH4CN, the exact and approximate values are typically very close because the system is well behaved and the hydrolysis constants are separated by several orders of magnitude. That is good news on an exam, because it means the shortcut is usually reliable.
Key equilibrium data used in this problem
| Species or constant | Typical value at 25 degrees C | Role in calculation | Interpretation |
|---|---|---|---|
| NH4CN concentration | 0.10 M | Sets initial [NH4+] and [CN-] | Both ions begin at equal concentration after dissolution. |
| Kb of NH3 | 1.8 × 10^-5 | Used to find Ka of NH4+ | Shows ammonia is a weak base. |
| Ka of NH4+ | 5.56 × 10^-10 | Acid strength of ammonium | NH4+ is a weak acid, but not a very strong one. |
| Ka of HCN | 6.2 × 10^-10 | Used to find Kb of CN- | HCN is a weak acid. |
| Kb of CN- | 1.61 × 10^-5 | Base strength of cyanide | CN- is much stronger as a base than NH4+ is as an acid. |
| Predicted pH | About 9.23 | Final answer | The solution is basic. |
Comparison with other weak-acid weak-base salts
One of the best ways to understand NH4CN is to compare it with other salts that also contain hydrolyzing ions. The table below uses typical 25 degrees C constants and the same approximation logic to show how the relative acid and base strengths control the pH direction.
| Salt | Acidic ion | Basic ion | Dominant effect | Typical pH trend |
|---|---|---|---|---|
| NH4CN | NH4+ | CN- | Base hydrolysis dominates strongly | Basic, usually around 9.2 to 9.3 |
| NH4CH3COO | NH4+ | CH3COO- | Acid and base strengths are relatively similar | Near neutral, often close to 7 |
| Aluminum ammonium salts | Hydrated metal cation | Weakly basic anion | Acidic cation dominates | Acidic, often well below 7 |
| Sodium cyanide | None significant | CN- | Base hydrolysis only | Strongly basic relative to NH4CN |
Common mistakes students make
- Treating NH4CN as neutral. It is not a neutral salt because both ions hydrolyze.
- Using only NH4+ or only CN-. You must consider both ions to understand the net pH.
- Confusing Ka and Kb conversions. Remember that conjugate pairs are related through Kw = Ka × Kb.
- Assuming concentration alone determines pH. In this type of salt, the relative acid and base strengths usually matter more.
- Ignoring the exact constants given in the problem. Different textbooks may use slightly different values for Ka(HCN), so final pH can vary by a few hundredths.
Exam strategy for solving this quickly
Fast conceptual route
- Identify NH4+ as a weak acid and CN- as a weak base.
- Convert Kb(NH3) into Ka(NH4+).
- Convert Ka(HCN) into Kb(CN-).
- Compare the magnitudes.
- If Kb of CN- is much larger than Ka of NH4+, predict a basic pH.
Fast numerical route
- Calculate Ka(NH4+) = 1.0 × 10^-14 / 1.8 × 10^-5 = 5.56 × 10^-10.
- Calculate Kb(CN-) = 1.0 × 10^-14 / 6.2 × 10^-10 = 1.61 × 10^-5.
- Use pH = 7 + 0.5 log(Kb / Ka).
- Report pH ≈ 9.23.
Why NH4CN is basic even though it contains NH4+
This is one of the most important conceptual takeaways. Many students see ammonium and immediately think the solution must be acidic. That would be true for salts such as NH4Cl, where the anion is neutral. But in NH4CN, the cyanide ion is the conjugate base of a weak acid and is substantially basic in water. Since the basic hydrolysis of CN- is much stronger than the acidic hydrolysis of NH4+, the overall solution shifts toward hydroxide production. The presence of ammonium does not disappear, but it is not strong enough to overcome cyanide’s base effect.
Authoritative references for equilibrium constants and acid-base behavior
If you want to verify acid-base relationships, hydrolysis concepts, or cyanide chemistry from high-quality sources, these references are useful:
- Acid-base properties of salts, University-level chemistry reference
- U.S. Environmental Protection Agency cyanide resources
- National Center for Biotechnology Information overview of cyanide chemistry and toxicity
Final answer for the standard problem
Using common constants at 25 degrees C, the pH of a 0.10 M NH4CN solution is approximately 9.23. The solution is basic because CN- acts as a stronger base than NH4+ acts as an acid. If your course uses a slightly different value for the acid constant of HCN, you may obtain a result closer to 9.28, but the overall conclusion remains the same: NH4CN produces a basic aqueous solution.
Use the calculator above if you want to test alternate constant sets, compare the exact solution to the shortcut formula, or visualize how the predicted pH changes over a range of NH4CN concentrations.