Calculate The Ph Of A 0.1 M Sodium Cyanide Solution

This premium calculator determines the pH, pOH, hydroxide concentration, and cyanide hydrolysis behavior for aqueous sodium cyanide. It uses the weak-base equilibrium of CN^–, the conjugate base of hydrocyanic acid, and solves the equilibrium expression with a quadratic approach for robust accuracy.

Sodium Cyanide pH Calculator

Use the default values for a standard 0.1 M NaCN solution at 25°C, or adjust the assumptions for comparison.

Chemistry model used: NaCN dissociates completely to Na⁺ and CN^–. The cyanide ion hydrolyzes water according to CN^– + H₂O ⇌ HCN + OH^–.

Core relationships
K_b = K_w / K_a
K_b = x² / (C – x)
x = [OH^–]
pOH = -log₁₀[OH^–], pH = 14 – pOH

How to calculate the pH of a 0.1 M sodium cyanide solution

To calculate the pH of a 0.1 M sodium cyanide solution, you begin by recognizing that sodium cyanide, NaCN, is a salt composed of a strong-base cation and a weak-acid anion. Sodium ion, Na⁺, comes from sodium hydroxide and is effectively neutral in water. Cyanide ion, CN^–, is the conjugate base of hydrocyanic acid, HCN, which is a weak acid. That means the cyanide ion reacts with water and produces hydroxide ions, making the solution basic.

The hydrolysis reaction is:

CN^– + H₂O ⇌ HCN + OH^–

Because hydroxide is formed, the pH rises above 7. For a standard textbook problem, the key values used are the initial cyanide concentration, usually 0.100 M, and the acid dissociation constant for HCN. A commonly cited value for HCN at 25°C is K_a = 6.2 × 10^-10. Since cyanide acts as a base, you convert that to K_b using water’s ion-product constant:

K_b = K_w / K_a = 1.0 × 10^-14 / 6.2 × 10^-10 = 1.61 × 10^-5

Now write the base equilibrium table. If the initial cyanide concentration is 0.100 M and x is the amount that reacts:

• Initial: [CN^–] = 0.100, [HCN] = 0, [OH^–] = 0
• Change: [CN^–] = -x, [HCN] = +x, [OH^–] = +x
• Equilibrium: [CN^–] = 0.100 – x, [HCN] = x, [OH^–] = x

The equilibrium expression becomes:

K_b = x² / (0.100 – x)

Many chemistry classes use the weak-base approximation, assuming x is small compared with 0.100. Then:

x ≈ √(K_bC) = √[(1.61 × 10^-5)(0.100)] = 1.27 × 10^-3 M

That gives:

• [OH^–] ≈ 1.27 × 10^-3 M
• pOH = -log(1.27 × 10^-3) ≈ 2.90
• pH = 14.00 – 2.90 = 11.10

If you solve the quadratic exactly, you get essentially the same answer, which confirms the approximation is valid. So the pH of a 0.1 M sodium cyanide solution is approximately 11.1 at 25°C using standard constants.

Final practical answer: a 0.1 M NaCN solution has a pH of about 11.10 when calculated with Ka(HCN) = 6.2 × 10^-10 at 25°C.

Why sodium cyanide makes water basic

This problem becomes easier once you classify the salt correctly. Sodium cyanide is not acidic because the sodium ion does not significantly hydrolyze in water. It also is not neutral, because the cyanide ion is the conjugate base of a weak acid. Any anion derived from a weak acid can, in many cases, accept a proton from water and generate hydroxide. That is exactly what CN^– does. In acid-base chemistry language, sodium cyanide is a basic salt.

The strength of that basicity is not arbitrary. It is directly related to the weakness of hydrocyanic acid. The weaker the parent acid, the stronger its conjugate base. Since HCN is weak, CN^– has a measurable K_b, and this is why the pH shifts into the basic range instead of remaining close to neutral.

Quick classification checklist

• Na⁺: spectator ion, effectively neutral
• CN^–: weak base, hydrolyzes water
• Net effect: OH^– production and pH above 7

Step-by-step expert method

1. Write the dissolution of sodium cyanide: NaCN → Na⁺ + CN^–.
2. Identify CN^– as the conjugate base of HCN.
3. Write the hydrolysis equilibrium: CN^– + H₂O ⇌ HCN + OH^–.
4. Use the known Ka of HCN and convert it to Kb with Kb = Kw/Ka.
5. Set up an ICE table using the formal cyanide concentration.
6. Solve for x, where x equals the equilibrium hydroxide concentration.
7. Calculate pOH from -log[OH^–].
8. Convert to pH using pH = 14 – pOH at 25°C.

This method works not only for 0.1 M sodium cyanide but also for any cyanide salt concentration where ideal dilute-solution assumptions are acceptable. When concentration gets very high, ionic strength effects can shift the result slightly, but for standard educational and many practical calculations, the above procedure is the accepted approach.

Comparison table: exact and approximate pH values for NaCN solutions

The table below uses Ka(HCN) = 6.2 × 10^-10 and Kw = 1.0 × 10^-14 at 25°C. The exact values come from solving the equilibrium expression quadratically. The approximate values come from x ≈ √(K_bC).

NaCN concentration (M)	Kb for CN^–	Exact [OH^–] (M)	Exact pH	Approximate pH	Approximation error
0.001	1.61 × 10^-5	1.19 × 10^-4	10.08	10.10	0.02 pH units
0.010	1.61 × 10^-5	3.94 × 10^-4	10.60	10.60	<0.01 pH units
0.100	1.61 × 10^-5	1.26 × 10^-3	11.10	11.10	<0.01 pH units
1.000	1.61 × 10^-5	4.00 × 10^-3	11.60	11.60	<0.01 pH units

What assumptions are built into this calculation?

When chemists or students calculate the pH of a 0.1 M sodium cyanide solution, several assumptions are usually made. First, sodium cyanide is treated as fully dissociated in water. That is reasonable because it is an ionic sodium salt. Second, activity effects are neglected, so concentrations are treated as if they were ideal activities. Third, the calculation assumes 25°C unless otherwise stated, because the value of K_w and even the reported Ka of HCN are temperature dependent. Fourth, any side reactions, volatilization of HCN, oxidation, or complexation with metals are ignored.

These assumptions are standard for general chemistry and for many practical calculations involving dilute to moderately concentrated lab solutions. They are also why your answer may differ slightly from another source if that source uses a different Ka for HCN or includes activity corrections.

Most important source of variation

The biggest reason different websites or textbooks may show slightly different final pH values is that they use slightly different reported Ka or pKa values for HCN. A shift in pKa by even a few hundredths changes Kb a little, which slightly shifts [OH^–] and therefore pH. In practice, answers around 11.0 to 11.1 are often entirely consistent with the same chemistry.

Comparison table: sodium cyanide versus selected salts in water

Students often confuse sodium cyanide with salts that produce neutral or acidic solutions. The comparison below helps classify common examples at 25°C.

Salt	Ions in water	Acid-base behavior	Typical pH trend at 0.1 M	Reason
NaCl	Na^+, Cl^–	Neutral	About 7.0	Both ions are from strong parent species
NH4Cl	NH4^+, Cl^–	Acidic	About 5.1	NH4^+ is a weak acid
CH3COONa	Na^+, CH3COO^–	Basic	About 8.9	Acetate is the conjugate base of a weak acid
NaCN	Na^+, CN^–	Basic	About 11.1	Cyanide is a stronger weak base than acetate

Worked example using the exact quadratic solution

If you want the rigorous calculation instead of the approximation, start with:

K_b = x² / (0.100 – x)

Substitute K_b = 1.61 × 10^-5:

1.61 × 10^-5 = x² / (0.100 – x)

Rearrange to standard quadratic form:

x² + (1.61 × 10^-5)x – 1.61 × 10^-6 = 0

Applying the quadratic formula gives:

x = [-b + √(b² – 4ac)] / 2a

The physically meaningful positive root is approximately:

x = 1.26 × 10^-3 M

Then:

• pOH = -log(1.26 × 10^-3) ≈ 2.90
• pH = 14.00 – 2.90 = 11.10

Notice how close this is to the square-root estimate. Since x is only about 1.26% of the initial 0.100 M concentration, the small-x approximation is justified here.

Common mistakes when solving sodium cyanide pH problems

• Using Ka directly instead of Kb. Cyanide is acting as a base, so you must convert Ka(HCN) to Kb(CN^–).
• Assuming the solution is neutral. Sodium salts are not always neutral. The anion matters.
• Forgetting to calculate pOH first. The equilibrium gives [OH^–], so pOH usually comes before pH.
• Using the wrong parent acid. CN^– is conjugate to HCN, not to a strong acid.
• Ignoring units or log rules. Small arithmetic slips can change the pH by tenths of a unit.

Safety and real-world context

Sodium cyanide is an industrially important but highly hazardous substance. Although pH calculations are often presented in classroom settings, real sodium cyanide handling requires strict safety protocols because cyanide chemistry is tightly linked to acute toxicity and to the formation of hydrogen cyanide gas under acidic conditions. In practical environmental and industrial settings, pH control is not just an academic exercise. It is central to safe storage, process control, and waste treatment.

For example, cyanide-containing solutions are often kept strongly basic to minimize conversion of cyanide ion into volatile HCN. This is one reason understanding cyanide acid-base equilibria matters far beyond homework problems. The equilibrium relationship between CN^– and HCN directly affects exposure risk.

Authoritative references for cyanide chemistry and acid-base data

• U.S. Environmental Protection Agency: Cyanide
• CDC ATSDR Toxic Substances Portal: Cyanide Facts
• University chemistry educational resources for acid-base equilibria

Bottom line

If you are asked to calculate the pH of a 0.1 M sodium cyanide solution, the professional workflow is straightforward: identify CN^– as a weak base, compute K_b from the Ka of HCN, solve the hydrolysis equilibrium, and convert hydroxide concentration to pH. Using Ka(HCN) = 6.2 × 10^-10 at 25°C, the result is pH ≈ 11.10. That answer is chemically consistent, mathematically justified, and aligned with standard general chemistry practice.

Important safety note: Sodium cyanide is extremely dangerous. This page is for educational chemistry calculation purposes only and is not a substitute for laboratory training, process safety protocols, or regulatory guidance.