Calculate The Ph Of A 0.1 M Kcn Solution

Use this interactive chemistry calculator to find pH, pOH, Kb, hydroxide concentration, and equilibrium concentrations for aqueous potassium cyanide.

How to calculate the pH of a 0.1 M KCN solution

To calculate the pH of a 0.1 M potassium cyanide (KCN) solution, you need to recognize that KCN is a salt made from a strong base and a weak acid. Potassium ion, K⁺, is the conjugate acid of the strong base KOH and does not significantly affect pH in water. The cyanide ion, CN⁻, is the conjugate base of hydrocyanic acid, HCN, which is a weak acid. That means CN⁻ reacts with water, generating hydroxide ions and making the solution basic.

The key hydrolysis reaction is:

CN⁻ + H₂O ⇌ HCN + OH⁻

Because hydroxide ions are produced, the pH of a KCN solution is greater than 7. For the common textbook case of 0.1 M KCN at 25 C, the pH is approximately 11.10 when using a typical value of Ka(HCN) = 6.2 × 10⁻¹⁰.

Why KCN makes water basic

Many students first look at KCN and think of it only as an ionic compound. That is true, but pH behavior depends on what the ions do after dissolution. In water, KCN dissociates essentially completely:

KCN → K⁺ + CN⁻

The potassium ion is a spectator ion for acid-base purposes in dilute aqueous solution. The cyanide ion, however, is basic because it can accept a proton from water. When that happens, some water molecules are converted into hydroxide ions. Even though the hydrolysis is not complete, enough OH⁻ forms to make the solution distinctly alkaline.

Step-by-step chemistry setup

1. Write the dissolution of KCN: KCN → K⁺ + CN⁻.
2. Identify CN⁻ as the conjugate base of HCN.
3. Write the base hydrolysis equilibrium: CN⁻ + H₂O ⇌ HCN + OH⁻.
4. Convert Ka of HCN into Kb of CN⁻ using Kb = Kw / Ka.
5. Use an ICE table to solve for the hydroxide concentration.
6. Calculate pOH = -log[OH⁻].
7. Calculate pH = 14.00 – pOH at 25 C.

Compute Kb for CN⁻

At 25 C, water has:

Kw = 1.0 × 10⁻¹⁴

Given a representative acid dissociation constant for HCN:

Ka(HCN) = 6.2 × 10⁻¹⁰

Then:

Kb(CN⁻) = Kw / Ka = (1.0 × 10⁻¹⁴) / (6.2 × 10⁻¹⁰) = 1.61 × 10⁻⁵

This value tells us cyanide is a weak base, but not an extremely weak one. In a 0.1 M solution, it generates enough hydroxide to push the pH above 11.

ICE table for 0.1 M KCN

Use the hydrolysis reaction:

CN⁻ + H₂O ⇌ HCN + OH⁻

Initial concentrations:

• [CN⁻] = 0.100 M
• [HCN] = 0
• [OH⁻] = 0, ignoring the tiny contribution from pure water

Let x be the amount of CN⁻ that reacts:

• [CN⁻] at equilibrium = 0.100 – x
• [HCN] at equilibrium = x
• [OH⁻] at equilibrium = x

Now write the equilibrium expression:

Kb = [HCN][OH⁻] / [CN⁻] = x² / (0.100 – x)

Substitute the numbers:

1.61 × 10⁻⁵ = x² / (0.100 – x)

For a fast approximation, because x is much smaller than 0.100, use:

x² / 0.100 ≈ 1.61 × 10⁻⁵

x² ≈ 1.61 × 10⁻⁶

x ≈ 1.27 × 10⁻³ M

So the hydroxide concentration is approximately:

[OH⁻] ≈ 1.27 × 10⁻³ M

Then:

pOH = -log(1.27 × 10⁻³) ≈ 2.90

pH = 14.00 – 2.90 = 11.10

Using the exact quadratic equation gives essentially the same result, approximately pH = 11.10.

Final answer

The pH of a 0.1 M KCN solution at 25 C is typically reported as:

pH ≈ 11.10

Common mistakes when solving this problem

• Treating KCN as neutral: it is not neutral because CN⁻ hydrolyzes to form OH⁻.
• Using Ka directly instead of Kb: you must first convert Ka(HCN) into Kb(CN⁻).
• Using pH = -log[CN⁻]: concentration alone is not the pH. You must calculate the hydroxide generated by hydrolysis.
• Forgetting the conjugate relationship: CN⁻ is the base and HCN is its conjugate acid.
• Ignoring temperature assumptions: Kw changes with temperature, so highly precise answers depend on the specified temperature.

Approximation versus exact solution

In many introductory chemistry courses, the approximation method is accepted when the percent ionization is small. For 0.1 M KCN, the hydrolysis extent is about 1.26 percent, so the square-root approximation is excellent. However, an exact quadratic solution is more rigorous and becomes more useful at lower concentrations or when the equilibrium shift is not negligible.

Parameter	Value used	Meaning
KCN concentration	0.100 M	Initial cyanide ion concentration after complete dissolution
Ka of HCN	6.2 × 10⁻¹⁰	Weak-acid strength of hydrocyanic acid
Kw at 25 C	1.0 × 10⁻¹⁴	Autoionization constant of water
Kb of CN⁻	1.61 × 10⁻⁵	Base strength of cyanide ion
[OH⁻]	1.26 to 1.27 × 10⁻³ M	Hydroxide produced by hydrolysis
pOH	About 2.90	Negative log of hydroxide concentration
pH	About 11.10	Final alkalinity of the solution

How pH changes with KCN concentration

One of the most useful ways to understand this system is to see how pH changes as concentration changes. Because KCN is a weak-base salt, the pH does not increase linearly with concentration. Instead, [OH⁻] follows the equilibrium relation, so pH rises more gradually than a direct one-to-one concentration relationship would suggest.

KCN concentration (M)	Approximate [OH⁻] (M)	Approximate pOH	Approximate pH at 25 C
0.001	1.27 × 10⁻⁴	3.90	10.10
0.010	4.01 × 10⁻⁴	3.40	10.60
0.100	1.27 × 10⁻³	2.90	11.10
0.500	2.84 × 10⁻³	2.55	11.45
1.000	4.01 × 10⁻³	2.40	11.60

These values are based on the standard weak-base approximation using the same HCN acidity constant. They show that increasing KCN concentration certainly raises pH, but not as dramatically as one might expect from a strong base.

Interpreting the chemistry beyond the arithmetic

The reason this problem appears frequently in analytical chemistry, general chemistry, and environmental chemistry is that it combines several major concepts in one compact example: salt hydrolysis, conjugate acid-base pairs, equilibrium constants, and logarithmic pH scales. It also demonstrates that not every soluble ionic compound is neutral in water. Salts derived from weak acids or weak bases often alter pH significantly.

In the case of KCN, the basicity comes entirely from the cyanide ion. If you compare KCN with a salt like KCl, the difference becomes clear. Chloride is the conjugate base of the strong acid HCl and is effectively pH-neutral in water, whereas cyanide is the conjugate base of weak HCN and is appreciably basic.

Quick comparison with other potassium salts

• KCl: approximately neutral in water
• KNO₃: approximately neutral in water
• KCN: basic in water because CN⁻ hydrolyzes
• KCH₃COO: also basic, because acetate is the conjugate base of a weak acid

When to use the 5 percent rule

Students are often taught to check whether the approximation is valid by comparing x with the initial concentration. For 0.1 M KCN, the exact hydroxide concentration is around 0.00126 M. That is only about 1.26 percent of the initial cyanide concentration, so replacing 0.100 – x with 0.100 is acceptable. If the percent change were larger than about 5 percent, the approximation would become less reliable and the exact quadratic solution would be preferred.

Practical notes and safety context

Although this page focuses on acid-base equilibrium math, potassium cyanide is an extremely hazardous substance. Any real-world handling must follow strict institutional, industrial, and regulatory safety protocols. In educational settings, KCN examples are usually treated as paper calculations rather than laboratory exercises. The pH calculation itself is standard chemistry, but the compound involved demands serious respect.

Authoritative references for deeper study

If you want to verify constants, review cyanide chemistry, or study aqueous equilibrium in more depth, these sources are helpful:

• NIH PubChem: Hydrogen Cyanide
• NIST Chemistry WebBook: Hydrogen Cyanide
• University-hosted instructional reference on acid-base properties of salts

Bottom line

To calculate the pH of a 0.1 M KCN solution, treat cyanide as a weak base, convert the acid constant of HCN into the base constant of CN⁻, solve the hydrolysis equilibrium, and then convert hydroxide concentration into pOH and pH. With standard values at 25 C, the result is about pH 11.10. That makes the solution clearly basic, which is exactly what you should expect from a salt containing the conjugate base of a weak acid.