Calculate the pH of a 0.025 M HCN Solution
Use this premium weak-acid calculator to determine the pH, hydrogen ion concentration, percent ionization, and equilibrium behavior of hydrocyanic acid at 25 degrees Celsius. The default setup is preloaded for a 0.025 M HCN solution.
How to calculate the pH of a 0.025 M HCN solution
To calculate the pH of a 0.025 M HCN solution, you treat hydrogen cyanide as a weak acid and use its acid dissociation constant rather than assuming complete ionization. This is the key idea that separates weak-acid calculations from strong-acid calculations. HCN does not fully break apart in water. Instead, only a very small fraction of the dissolved molecules donate protons to water, producing hydronium ions and cyanide ions at equilibrium.
The equilibrium reaction is:
HCN + H2O ⇌ H3O+ + CN–
Because HCN is weak, the concentration of H3O+ at equilibrium is much smaller than the original 0.025 M concentration of the acid. The relationship between the equilibrium concentrations is summarized by the Ka expression:
Ka = [H3O+][CN–] / [HCN]
For hydrogen cyanide at 25 degrees Celsius, a commonly used value is Ka = 6.2 × 10-10. If the initial concentration is 0.025 M, an ICE table gives the following setup:
- Initial: [HCN] = 0.025, [H3O+] = 0, [CN–] = 0
- Change: [HCN] = -x, [H3O+] = +x, [CN–] = +x
- Equilibrium: [HCN] = 0.025 – x, [H3O+] = x, [CN–] = x
Substituting into the Ka expression gives:
6.2 × 10-10 = x2 / (0.025 – x)
Since x is tiny compared with 0.025, many chemistry courses first use the weak-acid approximation:
6.2 × 10-10 ≈ x2 / 0.025
Solving for x:
x = √(KaC) = √[(6.2 × 10-10)(0.025)] ≈ 3.94 × 10-6 M
That x value is the equilibrium hydronium concentration, so:
pH = -log[H3O+] = -log(3.94 × 10-6) ≈ 5.40
Using the exact quadratic method leads to essentially the same result, which confirms that the approximation is valid here. Therefore, the pH of a 0.025 M HCN solution is about 5.40.
Why HCN does not behave like a strong acid
One of the most common mistakes in acid-base chemistry is to see an acid concentration and assume that the hydrogen ion concentration is equal to that concentration. That is only true for strong monoprotic acids such as HCl, HBr, or HNO3. Hydrogen cyanide is very different. Its Ka is very small, which tells you the equilibrium strongly favors undissociated HCN rather than ions.
A small Ka means a weak tendency to donate a proton. In practical terms, most HCN molecules remain intact in solution. As a result, the pH stays much higher than the pH of a strong acid with the same analytical concentration. If 0.025 M were a strong acid, the pH would be about 1.60. For HCN, the actual pH is about 5.40, a major difference caused by weak ionization.
| Acid | Ka at about 25 degrees Celsius | pKa | Relative strength vs HCN |
|---|---|---|---|
| Hydrogen cyanide, HCN | 6.2 × 10-10 | 9.21 | Reference weak acid |
| Hydrofluoric acid, HF | 6.8 × 10-4 | 3.17 | About 1.1 million times larger Ka than HCN |
| Acetic acid, CH3COOH | 1.8 × 10-5 | 4.76 | About 29,000 times larger Ka than HCN |
| Formic acid, HCOOH | 1.8 × 10-4 | 3.75 | About 290,000 times larger Ka than HCN |
This comparison makes it easier to understand why HCN solutions are only mildly acidic despite containing an acid. The lower the Ka, the less ionization occurs and the lower the hydronium concentration becomes.
Step by step method using an ICE table
1. Write the equilibrium reaction
Start with the dissociation of HCN in water:
HCN + H2O ⇌ H3O+ + CN–
2. Set up initial concentrations
For a freshly prepared 0.025 M solution of HCN, assume that no significant hydronium or cyanide from the acid is present initially:
- [HCN] = 0.025
- [H3O+] = 0
- [CN–] = 0
3. Define the change
If x mol/L dissociates, then:
- HCN decreases by x
- H3O+ increases by x
- CN– increases by x
4. Write equilibrium concentrations
- [HCN] = 0.025 – x
- [H3O+] = x
- [CN–] = x
5. Substitute into Ka
6.2 × 10-10 = x2 / (0.025 – x)
6. Solve for x
You can solve this exactly with the quadratic formula, or approximately with x ≈ √(KaC). For this concentration, both methods give essentially the same hydronium concentration of about 3.94 × 10-6 M.
7. Convert to pH
pH = -log(3.94 × 10-6) ≈ 5.40
When the approximation works and when it does not
The shortcut x ≈ √(KaC) is one of the most useful tools in weak-acid chemistry, but it should not be applied blindly. It depends on x being small enough that subtracting it from the initial concentration has little effect. A common classroom check is the 5% rule: if x is less than 5% of the original acid concentration, the approximation is acceptable.
For 0.025 M HCN, the percent ionization is:
(3.94 × 10-6 / 0.025) × 100 ≈ 0.0157%
That is far below 5%, so the approximation is excellent. In fact, the exact and approximate pH values are indistinguishable for most practical reporting. This is why many chemistry instructors are comfortable teaching the square-root method first for HCN.
| Initial HCN concentration (M) | Exact [H3O+] (M) | Exact pH | Percent ionization |
|---|---|---|---|
| 0.100 | 7.87 × 10-6 | 5.104 | 0.0079% |
| 0.050 | 5.57 × 10-6 | 5.254 | 0.0111% |
| 0.025 | 3.94 × 10-6 | 5.405 | 0.0157% |
| 0.010 | 2.49 × 10-6 | 5.604 | 0.0249% |
| 0.005 | 1.76 × 10-6 | 5.754 | 0.0352% |
This trend also shows a useful principle: as a weak acid solution becomes more dilute, the pH rises, but the percent ionization increases. Even though the solution becomes less acidic overall, a larger fraction of the acid molecules dissociate.
Common mistakes students make on this problem
- Treating HCN as a strong acid. If you set [H3O+] equal to 0.025 M directly, you would get a completely wrong pH.
- Using pKa incorrectly. If a source gives pKa instead of Ka, convert it with Ka = 10-pKa.
- Forgetting the logarithm sign. pH is negative log, not just log.
- Ignoring significant figures. Since Ka values vary slightly by source, your final pH may differ in the second or third decimal place.
- Skipping the equilibrium setup. An ICE table makes the logic clear and reduces errors.
Conceptual meaning of the final answer
A pH of about 5.40 means the solution is acidic, but only mildly so. It is much more acidic than pure water, yet far less acidic than a similarly concentrated strong acid solution. This reflects the molecular behavior of HCN in water: weak proton donation, limited ion production, and an equilibrium that lies strongly to the left.
From a practical chemistry perspective, this is a classic weak-acid equilibrium problem. It teaches how thermodynamic constants like Ka connect directly to measurable properties such as pH. It also shows why concentration alone never tells the full story. Two acids with the same formal molarity can produce vastly different pH values depending on their strength.
Exact formula for a weak monoprotic acid
If you want the exact result without approximation, solve the quadratic expression derived from the Ka equation:
x = [-Ka + √(Ka2 + 4KaC)] / 2
Where:
- x = [H3O+] at equilibrium
- Ka = acid dissociation constant
- C = initial acid concentration
For HCN with C = 0.025 and Ka = 6.2 × 10-10, the formula returns x ≈ 3.94 × 10-6 M, which gives pH ≈ 5.405. The calculator above performs that exact computation automatically when you choose the quadratic method.
Safety and chemical context
Although this page focuses on equilibrium calculations, it is worth noting that hydrogen cyanide and cyanide chemistry are hazardous topics in laboratory and industrial settings. Real handling procedures require formal training, engineering controls, and institution-specific safety protocols. Never use pH calculations as a substitute for chemical safety guidance.
Authoritative references
Final takeaway
If you are asked to calculate the pH of a 0.025 M HCN solution, the correct chemistry approach is to recognize HCN as a weak acid, write its Ka expression, solve for the equilibrium hydronium concentration, and then convert that value to pH. Using Ka = 6.2 × 10-10, the resulting pH is approximately 5.40. This value is consistent with both the exact quadratic solution and the weak-acid approximation because the fraction ionized is extremely small.
Use the calculator above if you want to test nearby concentrations, compare exact and approximate methods, or visualize how pH changes as HCN concentration varies. That is especially helpful for homework checking, exam review, and quick laboratory prep calculations.