Calculate the pH of 0.01 Molar Solution of NH4CN
Use this premium acid-base calculator to determine the pH of ammonium cyanide solutions. The tool applies weak acid and weak base hydrolysis relationships using the conjugate acid NH4+ and the conjugate base CN- at 25 degrees Celsius.
NH4CN pH Calculator
Default is 0.01 M for ammonium cyanide.
This calculator uses Kw = 1.0 x 10^-14 at 25 degrees Celsius.
Typical literature value for ammonia base dissociation.
Typical literature value for hydrocyanic acid acid dissociation.
For NH4CN, pH is well estimated using pH = 7 + 0.5 log10(Kb of NH3 / Ka of HCN).
Enter or confirm the constants above, then click Calculate pH.
What this calculator shows
This tool evaluates whether the NH4+ ion or the CN- ion dominates the solution chemistry.
- NH4+ acts as a weak acid.
- CN- acts as a weak base.
- Because CN- is much stronger as a base than NH4+ is as an acid, the solution is basic.
- For standard constants, the pH of 0.01 M NH4CN is about 9.23.
Expert Guide: How to Calculate the pH of 0.01 Molar Solution of NH4CN
To calculate the pH of a 0.01 molar solution of NH4CN, you need to recognize that ammonium cyanide is a salt made from a weak base and a weak acid. Specifically, NH4CN dissociates into NH4+ and CN-. The ammonium ion is the conjugate acid of ammonia, while the cyanide ion is the conjugate base of hydrocyanic acid. Because both ions react with water, the final pH depends on the relative strength of the acidic hydrolysis of NH4+ and the basic hydrolysis of CN-. This is why NH4CN is not solved the same way as a strong acid, strong base, or a salt such as NaCl.
The key idea is simple: if the base strength of CN- outweighs the acid strength of NH4+, the solution will be basic. If the acid strength of NH4+ were greater, the solution would be acidic. In practice, cyanide is a stronger base than ammonium is an acid, so the solution ends up above pH 7. For standard values at 25 degrees Celsius, a 0.01 M solution of ammonium cyanide typically has a pH close to 9.23.
Step 1: Write the ions produced by NH4CN in water
When ammonium cyanide dissolves, it separates almost completely into its ions:
Each ion then interacts with water:
- NH4+ + H2O ⇌ NH3 + H3O+
- CN- + H2O ⇌ HCN + OH-
The ammonium ion increases hydronium concentration and lowers pH. The cyanide ion increases hydroxide concentration and raises pH. The resulting pH is determined by which effect is stronger.
Step 2: Identify the needed equilibrium constants
To evaluate the competition, use the base dissociation constant of ammonia and the acid dissociation constant of hydrocyanic acid. Common textbook values at 25 degrees Celsius are:
| Species | Constant | Typical value | Interpretation |
|---|---|---|---|
| NH3 | Kb | 1.8 x 10^-5 | Ammonia is a weak base |
| HCN | Ka | 6.2 x 10^-10 | Hydrocyanic acid is a very weak acid |
| NH4+ | Ka = Kw / Kb of NH3 | 5.56 x 10^-10 | Conjugate acid strength of ammonia |
| CN- | Kb = Kw / Ka of HCN | 1.61 x 10^-5 | Conjugate base strength of HCN |
Notice something important: the Kb of CN- is much larger than the Ka of NH4+. That already tells you the solution should be basic.
Step 3: Use the weak acid and weak base salt formula
For a salt formed from a weak acid and a weak base, the pH can often be estimated using the very convenient relationship:
For ammonium cyanide, the parent weak base is NH3 and the parent weak acid is HCN, so:
Now evaluate the ratio:
Take the base-10 logarithm:
Multiply by 0.5:
Add that to 7:
Final answer: the pH of a 0.01 molar solution of NH4CN is approximately 9.23 when standard 25 degrees Celsius constants are used.
Why the concentration of 0.01 M does not dominate this particular shortcut
Students often expect the concentration to appear directly in the final formula. For salts like NH4CN, the elegant approximation above arises because both ions are present at the same starting concentration. In the simplified derivation, the equal concentrations cancel out. That means the pH depends primarily on the relative acid and base strengths, not the formal concentration, as long as the solution is dilute enough and the approximation remains valid.
That said, the 0.01 M concentration still matters in a practical sense. It confirms that the solution is reasonably dilute, which supports use of the common hydrolysis approximation. At very high concentrations, ionic strength effects and activity corrections can shift the measured pH slightly away from the ideal textbook answer.
How to think about NH4CN chemically
Ammonium cyanide is a good example of why acid-base chemistry is about equilibrium, not just labels. The cation NH4+ is acidic, but only weakly. The anion CN- is basic, and also weak in an absolute sense, but stronger than NH4+ as a competing hydrolyzing ion under these conditions. Because cyanide produces hydroxide more effectively than ammonium produces hydronium, the overall solution becomes basic.
Another useful way to see this is by comparing the hydrolysis constants directly:
- Ka for NH4+ = 5.56 x 10^-10
- Kb for CN- = 1.61 x 10^-5
The difference spans roughly five orders of magnitude. That is a strong indication that base formation dominates, even though both ions are weakly reactive.
Comparison with other 0.01 M salts
It helps to compare NH4CN with salts that contain only one hydrolyzing ion. The table below shows how the pH changes depending on whether the salt contributes an acidic ion, a basic ion, or both.
| 0.01 M salt | Hydrolyzing ion(s) | Dominant behavior | Approximate pH at 25 degrees Celsius |
|---|---|---|---|
| NH4Cl | NH4+ only | Weakly acidic | 5.63 |
| NaCN | CN- only | Weakly basic | 11.10 |
| NH4CN | NH4+ and CN- | Basic because CN- dominates | 9.23 |
These values are useful checkpoints. NH4Cl is acidic because chloride does not significantly hydrolyze, leaving ammonium to control pH. NaCN is much more basic because sodium does not hydrolyze, so cyanide fully dictates the equilibrium. NH4CN falls in between, but still on the basic side.
Common mistakes when calculating the pH of NH4CN
- Treating NH4CN as a neutral salt. It is not neutral, because both ions hydrolyze.
- Using only NH4+ or only CN-. You must compare both ion effects, not just one.
- Confusing Ka and Kb values. The formula uses Kb of NH3 and Ka of HCN, or equivalently Kb of CN- and Ka of NH4+.
- Assuming concentration always changes the answer strongly. For this weak acid and weak base salt approximation, equal initial concentrations cancel in the shortcut.
- Forgetting temperature assumptions. Most textbook values assume 25 degrees Celsius, where Kw = 1.0 x 10^-14.
Shortcut versus full equilibrium treatment
The shortcut formula is usually sufficient for instructional problems and standard chemistry homework. A fuller treatment would write mass balance, charge balance, and all equilibrium expressions, then solve the system numerically. That approach is more rigorous, especially when concentrations are high or when activity effects are considered. However, for a 0.01 M aqueous NH4CN problem at standard conditions, the approximate pH of 9.23 is accepted in most general chemistry settings.
If you want to verify the result from another perspective, convert the parent constants into the conjugate ion constants:
- Ka of NH4+ = 1.0 x 10^-14 / 1.8 x 10^-5 = 5.56 x 10^-10
- Kb of CN- = 1.0 x 10^-14 / 6.2 x 10^-10 = 1.61 x 10^-5
Because the basic hydrolysis constant is so much larger, the equilibrium shifts toward OH- production more strongly than toward H3O+ production.
How this relates to pKa and pKb values
Many students find logarithmic constants easier to compare:
- pKb of NH3 ≈ 4.74
- pKa of HCN ≈ 9.21
Using the alternate relation for weak acid and weak base salts:
To avoid confusion, many instructors prefer the constant-ratio formula directly in K values. It is less likely to produce sign errors.
Practical interpretation of the answer
A pH of 9.23 means the solution is moderately basic, not strongly caustic like a concentrated sodium hydroxide solution. It contains more hydroxide than pure water, but the pH remains far below 14 because both the acid and base components are weak and only partially hydrolyze. In a lab context, this matters for indicators, reaction compatibility, and safety planning.
For example, phenolphthalein would tend to show a pink color near this pH region, while methyl orange would not be suitable for fine discrimination here. The answer also tells you the cyanide ion remains a significant base in water, which is chemically and safety relevant.
Authoritative references and further reading
If you want to deepen your understanding of acid-base equilibria, weak electrolytes, and cyanide chemistry, these sources are useful starting points:
- U.S. Environmental Protection Agency: Cyanide overview
- NIST Chemistry WebBook
- Purdue University: Conjugate acid-base overview
Final takeaway
To calculate the pH of a 0.01 molar solution of NH4CN, treat the salt as the product of a weak acid and a weak base. Compare the base strength of ammonia through its Kb to the acid strength of hydrocyanic acid through its Ka. Using standard values of Kb for NH3 = 1.8 x 10^-5 and Ka for HCN = 6.2 x 10^-10 gives:
This means a 0.01 M ammonium cyanide solution is basic, and the reason is that CN- is a significantly stronger base than NH4+ is an acid.