Calculate The Ph Of A 0.100 M Kcn Solution

Use this interactive chemistry calculator to determine the pH, pOH, hydroxide concentration, cyanide hydrolysis extent, and weak-base equilibrium behavior for aqueous potassium cyanide. The tool uses standard weak-base equilibrium relations and visualizes where your solution falls on the pH scale.

KCN pH Calculator

Enter the concentration and acid dissociation information for HCN. For a standard textbook problem, keep the defaults at 0.100 M KCN and Ka = 6.2 × 10^-10 at 25 degrees Celsius.

Chemistry model: KCN dissociates completely to K⁺ and CN^–, then CN^– hydrolyzes in water: CN^– + H₂O ⇌ HCN + OH^–.

Results

How to calculate the pH of a 0.100 M KCN solution

To calculate the pH of a 0.100 M KCN solution, you do not treat potassium cyanide as an acidic salt. Instead, you recognize that it is the salt of a strong base and a weak acid. Potassium ion, K⁺, is essentially neutral in water because it comes from the strong base KOH. Cyanide ion, CN^–, is the conjugate base of hydrocyanic acid, HCN, which is a weak acid. That means the cyanide ion reacts with water to generate hydroxide ions, making the solution basic.

This is the central idea behind the problem: a solution of KCN has a pH greater than 7 because CN^– hydrolyzes. In standard general chemistry, this is classified as a weak-base equilibrium problem. When a textbook asks you to calculate the pH of a 0.100 M KCN solution, it is really asking you to find the equilibrium hydroxide concentration generated by the cyanide ion.

Step 1: Write the dissociation and hydrolysis reactions

Potassium cyanide dissociates essentially completely in water:

KCN(aq) → K+(aq) + CN-(aq)

The potassium ion does not significantly affect pH. The cyanide ion reacts with water as a weak base:

CN-(aq) + H2O(l) ⇌ HCN(aq) + OH-(aq)

Once this hydrolysis equation is written, the problem becomes much easier. The concentration of CN^– starts near 0.100 M, and as equilibrium is established, some CN^– is converted to HCN while OH^– is produced in equal amount.

Step 2: Find the base dissociation constant Kb for cyanide

Most data tables list the acid dissociation constant for HCN rather than the base dissociation constant for CN^–. So you convert using:

Kb = Kw / Ka

At 25 degrees Celsius, the ionic product of water is usually taken as K_w = 1.0 × 10^-14. A common textbook value for hydrocyanic acid is K_a = 6.2 × 10^-10. Substituting:

Kb = (1.0 × 10^-14) / (6.2 × 10^-10) Kb ≈ 1.61 × 10^-5

This tells us cyanide is a weak base, but strong enough to produce a distinctly basic solution at 0.100 M.

Step 3: Set up the ICE table

For the hydrolysis reaction CN^– + H₂O ⇌ HCN + OH^–, use an ICE table:

• Initial: [CN^–] = 0.100, [HCN] = 0, [OH^–] = 0
• Change: [CN^–] decreases by x, [HCN] increases by x, [OH^–] increases by x
• Equilibrium: [CN^–] = 0.100 – x, [HCN] = x, [OH^–] = x

Then place those equilibrium values into the K_b expression:

Kb = [HCN][OH-] / [CN-] 1.61 × 10^-5 = x^2 / (0.100 – x)

Step 4: Solve for x

Because K_b is much smaller than the starting concentration, many instructors use the weak-base approximation and assume x is small compared with 0.100. That simplifies the denominator:

1.61 × 10^-5 ≈ x^2 / 0.100 x^2 ≈ 1.61 × 10^-6 x ≈ 1.27 × 10^-3 M

Since x represents [OH^–], we get:

[OH-] ≈ 1.27 × 10^-3 M

The exact quadratic solution gives nearly the same answer, which confirms that the approximation is valid for this concentration range.

Step 5: Convert hydroxide concentration to pOH and pH

Now calculate pOH:

pOH = -log[OH-] pOH = -log(1.27 × 10^-3) pOH ≈ 2.90

Then use:

pH = 14.00 – pOH pH ≈ 14.00 – 2.90 pH ≈ 11.10

So the typical answer is:

pH of 0.100 M KCN ≈ 11.10

Final textbook-style answer: a 0.100 M KCN solution is basic, with pH usually reported around 11.1 at 25 degrees Celsius, depending on the exact K_a value used for HCN.

Why KCN is basic instead of neutral

Students often ask why a salt like KCN does not simply have a neutral pH. The answer comes from the acid-base strengths of the parent compounds. Potassium hydroxide is a strong base, so K⁺ does not hydrolyze appreciably. Hydrocyanic acid is weak, so its conjugate base CN^– has measurable basicity. That basicity shifts the equilibrium with water toward hydroxide production. In contrast, salts like KCl are neutral because both ions come from strong parents and do not appreciably alter [H⁺] or [OH^–].

Quick conceptual rule for salt pH

• Strong acid + strong base salt: usually neutral
• Strong acid + weak base salt: acidic
• Weak acid + strong base salt: basic
• Weak acid + weak base salt: depends on relative K_a and K_b

KCN clearly belongs in the weak-acid plus strong-base category, so a basic pH is expected before you even start the math.

Exact versus approximate calculation

For many classroom problems, the approximation x << C works beautifully. But in a premium calculator or a more rigorous setting, it is better to solve the equilibrium exactly. Starting with:

Kb = x^2 / (C – x)

Rearrange into a quadratic:

x^2 + Kb x – Kb C = 0

The physically meaningful root is:

x = (-Kb + √(Kb^2 + 4KbC)) / 2

For 0.100 M KCN and K_b ≈ 1.61 × 10^-5, x differs only slightly from the approximate answer. Still, exact calculation is helpful when concentrations are lower or when the equilibrium constant is larger relative to the starting concentration.

Comparison data for HCN and cyanide equilibrium

The exact numerical answer can vary slightly depending on which literature value for HCN acidity is used. Different textbooks and data compilations round K_a differently, which causes a small shift in the computed pH.

Assumed HCN Ka at 25 degrees Celsius	Calculated CN- Kb	Approximate [OH-] in 0.100 M KCN	Estimated pH
4.9 × 10^-10	2.04 × 10^-5	1.43 × 10^-3 M	11.16
6.2 × 10^-10	1.61 × 10^-5	1.27 × 10^-3 M	11.10
6.6 × 10^-10	1.52 × 10^-5	1.23 × 10^-3 M	11.09

This table shows why you might see small answer differences in homework solutions, online calculators, or exam keys. The chemistry is the same; only the adopted equilibrium constant varies slightly.

How KCN compares with other common salts of weak acids

Putting the result in context can help you understand whether the final pH makes sense. Cyanide is a stronger conjugate base than acetate because HCN is a much weaker acid than acetic acid. Therefore, a 0.100 M KCN solution should be more basic than a 0.100 M sodium acetate solution.

Salt solution (0.100 M)	Conjugate acid	Approximate conjugate-acid Ka	Expected pH behavior	Typical pH range
KCl	HCl	Very large	Essentially neutral	About 7.0
CH3COONa	Acetic acid	1.8 × 10^-5	Mildly basic	About 8.8 to 8.9
KCN	HCN	About 10^-10	Distinctly basic	About 11.1

This kind of comparison is useful on tests. Even if you do not have time to work every detail, you can often estimate whether the final answer should be just above 7, moderately basic, or strongly basic.

Common mistakes when solving the pH of a KCN solution

1. Using K_a directly instead of converting to K_b. Since CN^– is acting as a base, you need K_b, not K_a.
2. Treating KCN as a strong base. Cyanide is a weak base, so [OH^–] is not simply equal to 0.100 M.
3. Ignoring hydrolysis completely. If you conclude pH = 7, you have missed the role of CN^–.
4. Confusing pOH and pH. Once you find [OH^–], calculate pOH first, then convert to pH.
5. Not checking the small-x approximation. A quick percent ionization check helps verify whether the shortcut is valid.

Percent hydrolysis check

For the standard values above, x ≈ 1.27 × 10^-3 M. Compared with the initial 0.100 M cyanide concentration, the fraction hydrolyzed is:

% hydrolysis = (x / 0.100) × 100 ≈ (1.27 × 10^-3 / 0.100) × 100 ≈ 1.27%

Because this is well below 5%, the approximation x << 0.100 is justified.

Does using 0.100 m instead of 0.100 M matter?

Strictly speaking, molality and molarity are not the same. Molality is moles of solute per kilogram of solvent, while molarity is moles of solute per liter of solution. In dilute aqueous solutions at room temperature, their numerical values are often close enough for introductory chemistry calculations. That is why many educational problems treat 0.100 m and 0.100 M nearly interchangeably unless high precision is required. This calculator notes that approximation explicitly.

Temperature and data-source effects

The exact pH depends on temperature because K_w changes with temperature, and equilibrium constants can also vary. In most general chemistry settings, unless a different temperature is specified, you should assume 25 degrees Celsius and use K_w = 1.0 × 10^-14. If your instructor gives a different K_a value for HCN or a different temperature, use those numbers rather than memorized defaults.

Authoritative references for cyanide chemistry and equilibrium data

If you want to verify constants or review cyanide chemistry from reliable sources, these references are useful starting points:

• NIST Chemistry WebBook for trusted chemical property data and reference material.
• U.S. Environmental Protection Agency cyanide resources for environmental and chemical context related to cyanide compounds.
• University of Wisconsin weak-base equilibrium tutorial for educational support on weak-base calculations.

Final takeaway

When you calculate the pH of a 0.100 M KCN solution, the key chemical insight is that cyanide is the conjugate base of the weak acid HCN. That makes the solution basic. The workflow is consistent and reliable: write the hydrolysis reaction, convert K_a of HCN into K_b of CN^–, build an ICE table, solve for [OH^–], and then convert from pOH to pH. Using a typical HCN acidity constant near 6.2 × 10^-10, the calculated pH is approximately 11.10 at 25 degrees Celsius.

That result is not just a number to memorize. It reflects an important acid-base principle: salts derived from weak acids and strong bases often create basic solutions because their anions hydrolyze in water. Once you understand that principle, problems involving acetate, fluoride, cyanide, nitrite, and similar ions become much more intuitive.