Calculate the pH of a 2.23 m Solution of KCN
Interactive weak-base hydrolysis calculator for potassium cyanide, with exact and approximation methods, step-by-step output, and a live chart.
KCN pH Calculator
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Default setup uses 2.23 m KCN, Ka(HCN) = 6.2 × 10-10, and Kw = 1.0 × 10-14.
Expert Guide: How to Calculate the pH of a 2.23 m Solution of KCN
Potassium cyanide, KCN, is a salt that dissociates completely in water into K+ and CN–. The potassium ion is a spectator ion because it comes from the strong base KOH and has essentially no effect on pH. The cyanide ion, however, is the conjugate base of the weak acid hydrocyanic acid, HCN. That single fact controls the chemistry of the solution: CN– reacts with water to produce OH–, making the solution basic.
If your goal is to calculate the pH of a 2.23 m solution of KCN, the core idea is that you are solving a weak base equilibrium problem. In many classroom and exam settings, the notation m means molality, but for equilibrium calculations it is common to approximate the working concentration numerically using the entered value when no density is provided. This calculator follows that standard chemistry practice and lets you use either an exact quadratic solution or the familiar square-root approximation.
1. Start with the dissociation and hydrolysis reactions
KCN is a strong electrolyte, so it dissociates essentially completely:
The pH comes from the hydrolysis of cyanide:
This reaction shows why the solution is basic. Every time CN– accepts a proton from water, hydroxide ion is generated. More hydroxide means lower pOH and therefore a higher pH.
2. Convert Ka of HCN into Kb of CN–
Because cyanide is the conjugate base of HCN, its base dissociation constant is related to the acid dissociation constant by:
Using standard 25 degrees C values:
- Ka(HCN) ≈ 6.2 × 10-10
- Kw = 1.0 × 10-14
So:
This tells you CN– is a weak base, but not an extremely weak one. In a concentrated solution such as 2.23 m, it produces a measurable hydroxide concentration.
3. Set up the ICE table
For the hydrolysis equilibrium
you can use an ICE table. Taking the initial cyanide concentration as 2.23:
- Initial: [CN–] = 2.23, [HCN] = 0, [OH–] = 0
- Change: [CN–] = -x, [HCN] = +x, [OH–] = +x
- Equilibrium: [CN–] = 2.23 – x, [HCN] = x, [OH–] = x
Substitute into the base equilibrium expression:
4. Solve by approximation
If x is much smaller than 2.23, then 2.23 – x ≈ 2.23. That gives:
Now calculate pOH:
Then calculate pH:
That is the standard answer most instructors expect when asked to calculate the pH of a 2.23 m solution of KCN under introductory equilibrium assumptions.
5. Solve exactly with the quadratic equation
The exact solution uses:
where C = 2.23 and Kb = 1.61 × 10-5. Solving gives an x value that is almost identical to the approximation. The exact pH is still about 11.78 to two decimal places. This confirms that the small-x approximation is fully justified here.
6. Why the approximation works so well
In weak base and weak acid problems, a quick check is to compare x to the initial concentration. Here, x ≈ 0.006 while the starting concentration is 2.23. That means the change is only about 0.27% of the initial cyanide concentration, well below the common 5% rule. Since the equilibrium shift is tiny relative to the starting amount, replacing 2.23 – x with 2.23 is safe.
| Quantity | Value | Interpretation |
|---|---|---|
| Ka of HCN | 6.2 × 10-10 | HCN is a weak acid |
| Kb of CN– | 1.61 × 10-5 | CN– is a weak base |
| Calculated [OH–] | 5.99 × 10-3 | Hydroxide formed by hydrolysis |
| pOH | 2.22 | Moderately basic |
| pH | 11.78 | Strongly basic relative to neutral water |
7. Molality versus molarity: why wording matters
The problem statement uses 2.23 m, which denotes molality. Strictly speaking, molality is moles of solute per kilogram of solvent, while molarity is moles per liter of solution. Equilibrium constants are commonly written in terms of concentrations or activities, and in rigorous physical chemistry, ionic strength and activity coefficients matter, especially at high concentration. However, in general chemistry and many online textbook settings, instructors often expect you to use the given numerical value directly in the equilibrium setup unless density or activity data are provided.
That is why this calculator clearly labels the concentration basis assumption. If you were doing high-precision work, you would need density, activity coefficients, and perhaps a nonideal solution model. For ordinary educational chemistry, using 2.23 as the working concentration is acceptable and leads to the conventional answer.
8. Comparison data: how KCN concentration affects pH
The table below uses Ka(HCN) = 6.2 × 10-10 and Kw = 1.0 × 10-14, with the standard weak-base approximation. It gives realistic benchmark values for how pH changes with concentration.
| KCN concentration | Kb of CN– | Estimated [OH–] | Estimated pH |
|---|---|---|---|
| 0.010 | 1.61 × 10-5 | 4.02 × 10-4 | 10.60 |
| 0.100 | 1.61 × 10-5 | 1.27 × 10-3 | 11.10 |
| 1.00 | 1.61 × 10-5 | 4.01 × 10-3 | 11.60 |
| 2.23 | 1.61 × 10-5 | 5.99 × 10-3 | 11.78 |
9. Common mistakes students make
- Using Ka directly instead of converting to Kb. Since CN– is a base, you need Kb, not Ka.
- Treating KCN as acidic. The cyanide ion is the conjugate base of a weak acid, so the solution is basic.
- Forgetting that K+ is a spectator ion. Potassium does not control the pH here.
- Confusing pOH and pH. Once you calculate [OH–], you find pOH first, then convert to pH.
- Ignoring the approximation check. It is good practice to verify that x is small compared with the initial concentration.
10. Safety and chemical context
KCN is not just an academic salt. It is an extremely hazardous cyanide compound. In any real laboratory, industrial, or environmental context, cyanide chemistry must be handled under strict safety controls because cyanide can form highly toxic hydrogen cyanide gas in acidic conditions. For reliable chemical and toxicological information, review authoritative resources such as the NIH PubChem entry for potassium cyanide, the U.S. Environmental Protection Agency cyanide resources, and the educational chemistry materials used by university-level instructors.
11. Authoritative chemistry references you can trust
- NIH PubChem: Hydrogen cyanide data
- EPA: Cyanide environmental and safety information
- Michigan State University: acid-base equilibrium reference
12. Final answer
Using Ka(HCN) = 6.2 × 10-10 at 25 degrees C, the pH of a 2.23 m solution of KCN is:
pH ≈ 11.78
This result comes from cyanide acting as a weak base in water. The exact quadratic method and the standard weak-base approximation agree to two decimal places, so 11.78 is a robust answer for textbook and most instructional purposes.