Calculate The Ph Of A 0.100 M Kcn Solution.

Use this premium chemistry calculator to determine the pH, pOH, hydroxide concentration, cyanide hydrolysis, and related equilibrium values for potassium cyanide in water. The tool uses the weak-base hydrolysis of cyanide, exact quadratic solving, and a responsive chart for instant visualization.

KCN pH Calculator

How to calculate the pH of a 0.100 m KCN solution

Potassium cyanide, KCN, is a salt that dissociates almost completely in water into potassium ions, K⁺, and cyanide ions, CN^–. The potassium ion is essentially a spectator ion for acid-base chemistry because it comes from the strong base KOH. The cyanide ion, however, is the conjugate base of hydrocyanic acid, HCN, which is a weak acid. Because CN^– is a conjugate base of a weak acid, it reacts with water to generate hydroxide ions. That makes a KCN solution basic, often strongly basic compared with neutral water.

When the question asks you to calculate the pH of a 0.100 m KCN solution, the chemistry is based on a base hydrolysis equilibrium. In many classroom problems, a 0.100 m solution is treated approximately like a 0.100 M dilute aqueous solution unless density data are provided. This calculator follows that standard educational convention, while still letting you adjust constants if your course, lab manual, or textbook uses a slightly different value for the acid dissociation constant of HCN.

Step 1: Write the dissociation and hydrolysis reactions

The first reaction is the complete dissolution of potassium cyanide:

• KCN(aq) → K⁺(aq) + CN^–(aq)

The acid-base chemistry comes from cyanide hydrolyzing in water:

• CN^–(aq) + H₂O(l) ⇌ HCN(aq) + OH^–(aq)

This equilibrium explains why the solution becomes basic. Each mole of cyanide that reacts with water forms one mole of hydroxide ion.

Step 2: Convert the acid constant of HCN into a base constant for CN^–

Most textbooks provide the acid dissociation constant, K_a, for hydrocyanic acid rather than the base dissociation constant, K_b, for cyanide. The relationship at 25 degrees Celsius is:

• K_a × K_b = K_w

Using a common reference value, K_a(HCN) = 6.2 × 10^-10 and K_w = 1.0 × 10^-14, you get:

• K_b = K_w / K_a
• K_b = (1.0 × 10^-14) / (6.2 × 10^-10)
• K_b ≈ 1.61 × 10^-5

Step 3: Set up an ICE table

For the hydrolysis reaction:

• CN^– + H₂O ⇌ HCN + OH^–

If the initial KCN concentration is 0.100, then initially:

• [CN^–]_initial = 0.100
• [HCN]_initial = 0
• [OH^–]_initial = 0

Let x be the amount of CN^– that hydrolyzes. At equilibrium:

• [CN^–] = 0.100 – x
• [HCN] = x
• [OH^–] = x

The equilibrium expression is:

• K_b = [HCN][OH^–] / [CN^–] = x² / (0.100 – x)

Step 4: Solve for x

There are two common approaches. The first is the weak-base approximation, which assumes x is much smaller than 0.100. Then:

• K_b ≈ x² / 0.100
• x ≈ √(K_b × 0.100)

Substituting the values:

• x ≈ √(1.61 × 10^-5 × 0.100)
• x ≈ √(1.61 × 10^-6)
• x ≈ 1.27 × 10^-3

That means:

• [OH^–] ≈ 1.27 × 10^-3 M

The exact solution comes from the quadratic equation:

• x² + K_bx – K_bC = 0

where C is the initial concentration. Solving this gives nearly the same answer for a 0.100 solution because the approximation is very good in this concentration range.

Step 5: Calculate pOH and pH

Once you know hydroxide concentration, calculate pOH:

• pOH = -log[OH^–]

Using 1.27 × 10^-3:

• pOH ≈ 2.90

Then use:

• pH = 14.00 – pOH

So the pH is:

• pH ≈ 11.10

This is the expected answer for a 0.100 m KCN solution under standard classroom assumptions at 25 degrees Celsius.

Bottom line: For a 0.100 m KCN solution, the pH is approximately 11.10 when you use K_a(HCN) = 6.2 × 10^-10 and K_w = 1.0 × 10^-14.

Why KCN solutions are basic

Students often memorize that salts of strong bases and weak acids produce basic solutions, but it helps to understand why. KCN contains K⁺, which does not significantly affect pH, and CN^–, which is the conjugate base of the weak acid HCN. Since HCN is weak, its conjugate base has enough basic strength to remove a proton from water:

1. Cyanide accepts a proton from water.
2. Hydrocyanic acid forms.
3. Hydroxide ion is released.
4. The hydroxide raises the pH above 7.

The larger the cyanide concentration, the more hydroxide can form, so pH rises with concentration. However, the increase is not perfectly linear because equilibrium chemistry follows logarithmic relationships.

Reference constants and comparison data

Quantity	Typical value at 25 degrees Celsius	Meaning for the KCN problem
Kw	1.0 × 10^-14	Used to convert Ka of HCN to Kb of CN^–
Ka of HCN	6.2 × 10^-10	Shows HCN is a weak acid
Kb of CN^–	1.61 × 10^-5	Indicates cyanide is a weak base
Calculated [OH^–] for 0.100 KCN	1.26 × 10^-3 to 1.27 × 10^-3	Depends slightly on exact versus approximate solving
Calculated pH	About 11.10	Expected classroom answer

Approximate versus exact calculation

In weak acid and weak base problems, instructors often ask whether the small-x approximation is valid. Here, it is. The estimated x is about 1.27 × 10^-3, while the initial concentration is 0.100. The percentage change is:

• (1.27 × 10^-3 / 0.100) × 100 ≈ 1.27%

Since this is well below the common 5% rule, the approximation is acceptable. The calculator on this page can show both methods, which is useful for homework checking and test preparation.

Method	[OH^–]	pOH	pH	Comment
Weak-base approximation	1.269 × 10^-3	2.896	11.104	Fast and valid here
Exact quadratic solution	1.261 × 10^-3	2.899	11.101	More rigorous

Common mistakes when solving the pH of KCN

• Using K_a directly as if cyanide were an acid. Cyanide is a base in water, so you need K_b.
• Forgetting that K_b = K_w / K_a. This is one of the most common setup errors.
• Confusing pOH with pH. You calculate hydroxide first, so pOH comes before pH.
• Treating K⁺ as reactive. Potassium does not significantly affect the acid-base equilibrium.
• Ignoring the stated concentration basis. In strict physical chemistry, molality and molarity are not identical, but in many dilute educational problems they are treated as nearly equivalent unless density is given.

How concentration changes the pH

If you lower the KCN concentration, the pH drops, though it stays above 7 because cyanide still hydrolyzes to form hydroxide. If you raise the concentration, pH increases. This trend follows from the approximate relationship:

• [OH^–] ≈ √(K_bC)

Because pH depends logarithmically on hydroxide concentration, doubling concentration does not double pH. Instead, the pH rises modestly. That is why plotting concentration against pH is so useful for intuition: you see a smooth rise rather than a dramatic straight-line increase.

Safety note about cyanide chemistry

Cyanide compounds are highly toxic. This page is intended solely for chemistry education, stoichiometry practice, and equilibrium calculation. Never handle cyanide salts without formal training, proper institutional approval, and laboratory safety controls. Hydrocyanic acid and cyanide salts present serious acute hazards. For safety and toxicological guidance, consult official sources such as the CDC, NIH, EPA, and university environmental health and safety offices.

Authoritative resources for acid-base constants and cyanide chemistry

The following resources are useful if you want to verify constants, review equilibrium theory, or read official safety and environmental information:

• U.S. Environmental Protection Agency on cyanide
• National Center for Biotechnology Information toxicology reference for cyanide
• University-hosted chemistry course materials and equilibrium reviews

Worked summary for the exact question

1. Start with 0.100 m KCN and treat it as a dilute aqueous cyanide concentration.
2. Use the reaction CN^– + H₂O ⇌ HCN + OH^–.
3. Find K_b from K_w / K_a.
4. With K_a(HCN) = 6.2 × 10^-10, obtain K_b ≈ 1.61 × 10^-5.
5. Set up K_b = x² / (0.100 – x).
6. Solve for x ≈ 1.26 × 10^-3 to 1.27 × 10^-3.
7. Then pOH ≈ 2.90.
8. Finally, pH ≈ 11.10.

If your instructor uses a slightly different K_a for HCN, your final pH may differ by a few hundredths of a unit. That is normal. The method remains the same: identify cyanide as a weak base, derive K_b, solve the equilibrium, calculate pOH, and convert to pH.

Educational note: This calculator is designed for learning equilibrium chemistry and gives results based on user-entered constants. For advanced analytical or industrial work, activity coefficients, ionic strength, and exact molality-to-molarity conversion may be required.