Calculate the pH of a 0.1 M NaCN Solution
Use this premium cyanide hydrolysis calculator to compute pH, pOH, hydroxide concentration, and percent hydrolysis for sodium cyanide solutions. The calculator uses the weak base behavior of CN- in water and can solve either by exact quadratic treatment or by the common approximation.
NaCN Solution pH Calculator
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Enter your values and click Calculate pH. For a standard 0.1 M NaCN solution at 25 C, the pH is expected to be strongly basic.
How to calculate the pH of a 0.1 M NaCN solution
To calculate the pH of a 0.1 M sodium cyanide solution, you need to recognize the chemistry of the ions produced when NaCN dissolves in water. Sodium cyanide is a soluble ionic compound, so it dissociates essentially completely into sodium ions and cyanide ions:
NaCN → Na+ + CN-
The sodium ion is a spectator ion in acid-base chemistry because it comes from the strong base sodium hydroxide. The cyanide ion, however, is the conjugate base of hydrocyanic acid, HCN, which is a weak acid. Because CN- is the conjugate base of a weak acid, it reacts with water to generate hydroxide ions:
CN- + H2O ⇌ HCN + OH-
This hydrolysis reaction is the key reason a sodium cyanide solution is basic. The pH is therefore found by determining how much OH- is produced at equilibrium, converting that to pOH, and then using the relation pH = 14.00 – pOH at 25 C.
Step 1: Identify the concentration of the weak base
Because NaCN dissociates fully, a 0.1 M NaCN solution gives an initial cyanide concentration of about 0.1 M. In an equilibrium setup, the starting concentrations can be written as:
- [CN-] initial = 0.100 M
- [HCN] initial = 0 M
- [OH-] initial = 0 M from hydrolysis, ignoring water autoionization at the start
Step 2: Convert Ka for HCN into Kb for CN-
The most common tabulated value for hydrocyanic acid at 25 C is Ka ≈ 6.2 × 10^-10. Since cyanide is the conjugate base of HCN, the base dissociation constant is found from:
Kb = Kw / Ka
At 25 C, Kw = 1.0 × 10^-14. Therefore:
Kb = (1.0 × 10^-14) / (6.2 × 10^-10) ≈ 1.61 × 10^-5
This value shows that cyanide is a weak base, but it is strong enough to produce a meaningful hydroxide concentration in a 0.1 M solution.
Step 3: Set up the equilibrium expression
Let x be the amount of CN- that reacts with water. Then at equilibrium:
- [CN-] = 0.100 – x
- [HCN] = x
- [OH-] = x
The equilibrium expression is:
Kb = [HCN][OH-] / [CN-] = x² / (0.100 – x)
Substitute the Kb value:
1.61 × 10^-5 = x² / (0.100 – x)
Step 4: Solve for x
There are two standard approaches. The first is the weak base approximation, which assumes x is small relative to 0.100. The second is the exact quadratic solution. For this case, both methods give nearly the same answer.
- Approximation method: If x is small, then 0.100 – x ≈ 0.100. This gives x² = (1.61 × 10^-5)(0.100), so x ≈ 1.27 × 10^-3 M.
- Exact method: Solve x² + (1.61 × 10^-5)x – 1.61 × 10^-6 = 0. The positive root is approximately x ≈ 1.26 × 10^-3 M.
Since x equals the hydroxide concentration produced by hydrolysis, [OH-] ≈ 1.26 × 10^-3 M.
Step 5: Convert hydroxide concentration to pOH and pH
Now compute pOH:
pOH = -log[OH-] = -log(1.26 × 10^-3) ≈ 2.90
At 25 C, pH and pOH add to 14.00:
pH = 14.00 – 2.90 = 11.10
So the pH of a 0.1 M NaCN solution is approximately 11.10 at 25 C.
Why NaCN is basic in water
This result is easier to understand when you compare NaCN with salts from other acid-base combinations. Salts derived from a strong base and a weak acid generally produce basic solutions. Sodium cyanide fits that pattern exactly:
- Na+ comes from the strong base NaOH and does not affect pH significantly.
- CN- comes from the weak acid HCN and therefore acts as a base in water.
The cyanide ion removes a proton from water, forming HCN and OH-. As OH- accumulates, the solution becomes strongly alkaline. This is why even a moderately concentrated sodium cyanide solution has a pH well above 7.
Worked example in full detail
Suppose your instructor asks, “Calculate the pH of a 0.1 M NaCN solution.” A complete exam-quality solution would look like this:
- Write dissociation and hydrolysis reactions:
- NaCN → Na+ + CN-
- CN- + H2O ⇌ HCN + OH-
- Use the acid dissociation constant for HCN:
- Ka(HCN) = 6.2 × 10^-10
- Kb(CN-) = Kw / Ka = 1.0 × 10^-14 / 6.2 × 10^-10 = 1.61 × 10^-5
- Set up the ICE table:
- Initial: [CN-] = 0.100, [HCN] = 0, [OH-] = 0
- Change: -x, +x, +x
- Equilibrium: 0.100 – x, x, x
- Write Kb expression:
- Kb = x² / (0.100 – x)
- Solve for x:
- x ≈ 1.26 × 10^-3 M
- Find pOH and pH:
- pOH = -log(1.26 × 10^-3) ≈ 2.90
- pH = 14.00 – 2.90 = 11.10
If you are writing this for a classroom setting, it is good practice to state that the approximation is valid because x is only about 1.3 percent of the starting concentration, which is comfortably below the common 5 percent rule.
Comparison table: acid-base constants relevant to the calculation
The constants below are commonly used in general chemistry and analytical chemistry discussions of cyanide hydrolysis.
| Quantity | Typical value at 25 C | Why it matters |
|---|---|---|
| Ka of HCN | 6.2 × 10^-10 | Determines how weak hydrocyanic acid is |
| pKa of HCN | 9.21 | Shows HCN is a weak acid and CN- is its conjugate base |
| Kw of water | 1.0 × 10^-14 | Used to convert Ka into Kb |
| Kb of CN- | 1.61 × 10^-5 | Directly controls OH- formation in solution |
How concentration changes the pH of sodium cyanide
The pH of sodium cyanide depends strongly on concentration. More cyanide in solution means more base available for hydrolysis, although because the ion is weakly basic, the pH increase does not scale linearly. The table below uses Ka(HCN) = 6.2 × 10^-10 at 25 C and gives approximate equilibrium values calculated from the same hydrolysis model used by the calculator above.
| NaCN concentration (M) | Approximate [OH-] (M) | Approximate pOH | Approximate pH |
|---|---|---|---|
| 0.001 | 1.19 × 10^-4 | 3.92 | 10.08 |
| 0.010 | 3.94 × 10^-4 | 3.40 | 10.60 |
| 0.100 | 1.26 × 10^-3 | 2.90 | 11.10 |
| 1.000 | 4.00 × 10^-3 | 2.40 | 11.60 |
Exact method versus approximation
Students often ask whether the square root shortcut is acceptable. In many classroom cases, yes. The approximation comes from assuming that x is small compared with the initial concentration of cyanide. For 0.1 M NaCN, that assumption works well because the hydrolyzed fraction is low. Still, the exact method is more rigorous and is preferred when:
- The concentration is very low
- The weak acid constant has uncertainty
- You need better precision
- You are preparing analytical chemistry calculations or software tools
In this problem, the exact and approximate methods differ only slightly, so the final pH remains about 11.1 either way.
Temperature effects on the answer
At introductory level, this problem is usually solved at 25 C because standard values for Ka and Kw are tabulated there. However, water’s ion product changes with temperature, and the apparent acid-base behavior can shift slightly. That is why this calculator includes a temperature selector. If you are working in process chemistry, plating chemistry, or environmental analysis, using a temperature-aware model can be a useful improvement over the simplest textbook approach.
In practice, the exact answer also depends on ionic strength, activity coefficients, and the reference constant set used in your source. For educational and routine calculation purposes, though, using Ka(HCN) ≈ 6.2 × 10^-10 at 25 C is standard and produces the accepted result.
Common mistakes when calculating the pH of NaCN
- Treating NaCN as neutral: It is not neutral because CN- is the conjugate base of a weak acid.
- Using Ka directly without converting to Kb: The species in solution is CN-, so the hydrolysis equilibrium is a base equilibrium.
- Forgetting complete dissociation: NaCN is a soluble ionic salt, so the initial [CN-] is the formal concentration of the salt.
- Mixing up pH and pOH: Find [OH-] first, then calculate pOH, and finally convert to pH.
- Ignoring significant figures: Most textbook inputs justify a pH around 11.10, not an excessively long decimal.
Practical interpretation of the result
A pH near 11.1 means the solution is distinctly basic. That matters in real systems because cyanide speciation is pH dependent. At higher pH, the deprotonated cyanide form CN- is favored over HCN. This distinction is chemically and toxicologically important, since hydrogen cyanide is volatile and highly hazardous. In laboratory and industrial settings, pH control is therefore a major safety and process consideration whenever cyanide-containing solutions are present.
Authoritative references for further reading
For readers who want verified scientific and safety information, these authoritative sources are useful:
- NIST Chemistry WebBook: Hydrogen cyanide data
- CDC: Facts about cyanide
- U.S. EPA: Cyanide information resources
Final answer
If you are asked simply to calculate the pH of a 0.1 M NaCN solution at 25 C, the accepted chemistry answer is:
pH ≈ 11.10
This comes from treating CN- as a weak base, using Kb = Kw / Ka, solving the hydrolysis equilibrium, and converting the resulting hydroxide concentration into pH. If your instructor uses a slightly different Ka value for HCN, your result may vary by a few hundredths of a pH unit, but it should remain very close to 11.1.