Calculate the pH of a 20 M Solution of KCN
Use this interactive chemistry calculator to estimate the pH, pOH, hydroxide concentration, and hydrolysis behavior of potassium cyanide in water. The default setup is a 20.0 M KCN solution at 25 degrees Celsius using the acid dissociation constant of HCN.
KCN pH Calculator
Ready to calculate. Click the button to solve for the pH of a 20 M solution of KCN.
How to calculate the pH of a 20 M solution of KCN
To calculate the pH of a 20 M solution of KCN, you treat potassium cyanide as a soluble ionic salt that dissociates almost completely in water into potassium ions and cyanide ions. The potassium ion, K+, is essentially neutral in acid-base chemistry because it comes from the strong base KOH. The cyanide ion, CN–, is the important species because it is the conjugate base of hydrocyanic acid, HCN, which is a weak acid. That means CN– reacts with water to form some hydroxide, OH–, and that is why the resulting solution is strongly basic.
The key hydrolysis equilibrium is:
CN– + H2O ⇌ HCN + OH–
Once you identify that equilibrium, the problem becomes a weak base calculation. Since KCN is fully dissociated at the start, the initial cyanide concentration is effectively the same as the formal salt concentration. In this case, a 20 M solution of KCN gives an initial cyanide concentration of approximately 20 M. Then you calculate the base dissociation constant of cyanide, Kb, from the acid dissociation constant of HCN.
Step 1: Convert Ka of HCN into Kb of CN-
The standard relationship is:
Kb = Kw / Ka
Using common 25 degrees Celsius values:
- Kw = 1.0 × 10-14
- Ka(HCN) = 6.2 × 10-10
Then:
Kb = (1.0 × 10-14) / (6.2 × 10-10) = 1.61 × 10-5
This tells you cyanide is a weak base, but because the concentration is so large at 20 M, the amount of hydroxide formed still becomes substantial.
Step 2: Set up the ICE table
For the reaction CN– + H2O ⇌ HCN + OH–, the initial, change, and equilibrium concentrations are:
- Initial: [CN–] = 20.0, [HCN] = 0, [OH–] = 0
- Change: [CN–] = -x, [HCN] = +x, [OH–] = +x
- Equilibrium: [CN–] = 20.0 – x, [HCN] = x, [OH–] = x
Insert those values into the equilibrium expression for Kb:
Kb = x2 / (20.0 – x)
Step 3: Solve for hydroxide concentration
You can solve this exactly with the quadratic equation or approximately using the common weak base shortcut. The approximation is:
x ≈ √(KbC)
Substituting values:
x ≈ √[(1.61 × 10-5)(20.0)]
x ≈ √(3.22 × 10-4) ≈ 1.79 × 10-2 M
So the hydroxide concentration is approximately:
[OH–] ≈ 0.0179 M
The exact quadratic gives nearly the same value because x is very small relative to 20.0 M. That means the weak base approximation is acceptable here.
Step 4: Calculate pOH and pH
Now convert hydroxide concentration into pOH:
pOH = -log[OH–] = -log(0.0179) ≈ 1.75
Then find pH:
pH = 14.00 – 1.75 = 12.25
Final answer: the pH of a 20 M solution of KCN is approximately 12.25 under standard textbook assumptions at 25 degrees Celsius.
Why KCN makes a basic solution
Students often ask why a salt can have a pH above 7. The answer depends on the acid and base from which the salt is derived. KCN comes from KOH, a strong base, and HCN, a weak acid. The cation from a strong base is neutral, while the anion from a weak acid is basic. In water, the cyanide ion removes a proton from water, producing HCN and OH–. That extra hydroxide drives the pH upward.
This pattern is common in acid-base chemistry:
- Strong acid + strong base salts are usually neutral.
- Strong acid + weak base salts are acidic.
- Weak acid + strong base salts are basic.
KCN falls clearly into the third category, so a basic pH is expected even before doing the math.
Comparison table: KCN concentration vs calculated pH
The following values use Ka(HCN) = 6.2 × 10-10 and Kw = 1.0 × 10-14 at 25 degrees Celsius. These figures are useful for showing how concentration affects the final pH.
| KCN concentration (M) | Estimated [OH-] (M) | pOH | pH |
|---|---|---|---|
| 0.001 | 1.27 × 10-4 | 3.90 | 10.10 |
| 0.01 | 4.01 × 10-4 | 3.40 | 10.60 |
| 0.10 | 1.27 × 10-3 | 2.90 | 11.10 |
| 1.0 | 4.01 × 10-3 | 2.40 | 11.60 |
| 5.0 | 8.97 × 10-3 | 2.05 | 11.95 |
| 10.0 | 1.27 × 10-2 | 1.90 | 12.10 |
| 20.0 | 1.79 × 10-2 | 1.75 | 12.25 |
Key equilibrium data used in the calculation
When solving weak acid and weak base problems, the numerical constants matter. The exact pH may vary slightly by textbook because different sources round Ka differently or assume slightly different temperatures.
| Parameter | Typical 25 degrees Celsius value | Why it matters |
|---|---|---|
| Ka of HCN | 6.2 × 10-10 | Determines how weak the parent acid is |
| pKa of HCN | About 9.21 | Log scale form of acid strength |
| Kw of water | 1.0 × 10-14 | Used to convert Ka into Kb |
| Kb of CN– | 1.61 × 10-5 | Directly used in the hydrolysis calculation |
Approximation vs exact solution
In many chemistry classes, students are taught to use the shortcut x = √(KbC) for weak bases. That method works because the amount of cyanide that reacts is tiny compared with the original 20 M concentration. In this problem, x is about 0.018 M, which is less than 0.1 percent of the starting concentration. So subtracting x from 20.0 changes the denominator by a negligible amount, and the approximation is excellent.
Still, the exact quadratic method is preferred in software calculators because it avoids unnecessary rounding and remains reliable even if the concentration is much smaller or if a different weak base is entered. This page includes both methods so you can compare them directly.
Important real-world caveat for a 20 M KCN solution
Although the equilibrium math is straightforward, a truly ideal 20 M aqueous KCN solution is not a simple laboratory condition. At very high concentrations, solutions stop behaving ideally. Activity effects, ion pairing, changes in density, and deviations from standard thermodynamic assumptions can all influence the real measured pH. Introductory chemistry problems usually ignore those factors and assume ideal dilute-solution style equations even at concentrations that are physically extreme. For classroom work, that is acceptable unless your instructor specifically asks for activity corrections.
So the best way to state the answer is this: under standard general chemistry assumptions, the pH is about 12.25. In advanced analytical or physical chemistry, the experimental value could differ because ionic strength is enormous at 20 M.
Common mistakes when solving KCN pH problems
- Using Ka directly instead of converting to Kb.
- Treating KCN as a neutral salt like KCl.
- Forgetting that CN– is the conjugate base of a weak acid.
- Calculating pH directly from x before converting x into pOH.
- Ignoring significant figures or rounding too early.
Fast exam strategy
If this appears on a quiz or exam, a quick strategy is:
- Write the hydrolysis reaction for CN–.
- Calculate Kb from Kw/Ka.
- Use x ≈ √(KbC) if the approximation is justified.
- Find pOH from [OH–].
- Convert pOH to pH.
For 20 M KCN, this gives a final pH near 12.25 very quickly.
Authoritative references for cyanide chemistry and safety
If you want deeper background, these high-authority resources are useful:
- U.S. Environmental Protection Agency: Cyanide
- Agency for Toxic Substances and Disease Registry: Cyanide Toxicity Factsheet
- NIST Chemistry WebBook
Final takeaway
To calculate the pH of a 20 M solution of KCN, treat cyanide as a weak base in water. Use the acid dissociation constant of HCN to find the base dissociation constant of CN–, solve for the hydroxide concentration, then convert to pOH and pH. With Ka(HCN) = 6.2 × 10-10 and Kw = 1.0 × 10-14, the result is a strongly basic solution with a textbook pH of about 12.25. That is the value most instructors and educational calculators will expect.