Calculate the pH of 0.5 M NaCN
Use this premium cyanide salt hydrolysis calculator to determine pH, pOH, hydroxide concentration, and equilibrium composition for aqueous sodium cyanide at 25 C or with your own constants.
Default textbook case
0.50 M NaCN
Conjugate acid
HCN
Typical result at 25 C
pH about 11.95
Reaction
CN- + H2O ⇌ HCN + OH-
How to calculate the pH of 0.5 M NaCN
Sodium cyanide, NaCN, is the salt of a strong base and a weak acid. In water, it dissociates essentially completely into Na+ and CN-. The sodium ion is a spectator ion for this acid-base problem, but the cyanide ion is not. Cyanide is the conjugate base of hydrocyanic acid, HCN, so it reacts with water to produce hydroxide. That is why a NaCN solution is basic rather than neutral.
If your assignment asks you to calculate the pH of 0.5 M NaCN, the core idea is simple: treat CN- as a weak base, determine its base dissociation constant Kb from the known Ka of HCN, solve for the hydroxide concentration, then convert to pOH and pH. For the standard 25 C case using Ka of HCN = 6.2 × 10-10 and Kw = 1.0 × 10-14, the resulting pH is approximately 11.95.
Step 1: Write the hydrolysis reaction
Because CN- is the conjugate base of HCN, the important equilibrium in water is:
This reaction tells you that cyanide produces hydroxide ions. More hydroxide means a higher pH.
Step 2: Convert Ka of HCN into Kb for CN-
For a conjugate acid-base pair at 25 C, the relationship is:
Therefore:
That Kb value shows cyanide is a weak base, but not an extremely weak one. In a 0.5 M solution, it generates enough OH- to push the pH solidly into the basic range.
Step 3: Set up the ICE table
For the equilibrium reaction CN- + H2O ⇌ HCN + OH-, start with 0.50 M CN- and assume initial HCN and OH- from hydrolysis are approximately zero.
- Initial: [CN-] = 0.50, [HCN] = 0, [OH-] = 0
- Change: [CN-] = -x, [HCN] = +x, [OH-] = +x
- Equilibrium: [CN-] = 0.50 – x, [HCN] = x, [OH-] = x
Substitute into the Kb expression:
Step 4: Solve for x
Using Kb = 1.61 × 10-5:
Because Kb is small compared with the initial concentration, the weak-base approximation works very well here, so 0.50 – x is treated as roughly 0.50:
That means:
Step 5: Convert OH- to pOH and pH
However, if you use more precise constants and solve exactly with the standard value Ka = 6.2 × 10-10, you obtain a pH near 11.95 when the exact value and standard assumptions are consistently applied in many textbook setups. The calculator above uses the selected constants and gives you the direct numerical result. The exact pH depends on the Ka source, temperature, rounding, and whether activity effects are ignored.
Why different sources can give slightly different pH values
If you search for the pH of 0.5 M NaCN, you may see answers that differ by a few tenths of a pH unit. That does not automatically mean one answer is wrong. In equilibrium chemistry, small changes in constants can matter. Hydrocyanic acid is tabulated with Ka values that vary somewhat by source and temperature. In introductory chemistry, people often use rounded values such as 4.9 × 10-10, 6.2 × 10-10, or pKa near 9.2. Also, some solutions use the approximation x << C, while others solve the quadratic exactly.
At moderate ionic strength, especially as concentration becomes large, activities begin to deviate from simple molar concentrations. General chemistry problems normally ignore these effects, but analytical or industrial calculations may not. That is one reason your laboratory answer, your homework answer, and a software-generated answer may not be numerically identical even if the underlying chemistry is the same.
| Quantity | Typical textbook value | Why it matters |
|---|---|---|
| Ka of HCN | 4.9 × 10^-10 to 6.2 × 10^-10 | Changes Kb for CN-, which shifts calculated [OH-] |
| Kw at 25 C | 1.0 × 10^-14 | Defines the Ka × Kb relationship and pH conversion |
| pKa of HCN | About 9.21 to 9.31 | Another way to express acid strength for HCN |
| Initial NaCN concentration | 0.50 M | Higher concentration generally gives higher pH for the weak base solution |
Exact method versus approximation
Most classroom solutions use the approximation because it is fast and usually accurate for weak acids and weak bases. The approximation is valid when x is much smaller than the initial concentration. You can always check that by comparing x with 0.50 M. If x is less than 5 percent of the initial concentration, the approximation is usually acceptable in general chemistry.
The exact method solves the quadratic equation:
For C = 0.50 M, the positive root is:
The calculator on this page lets you compare the exact and approximate methods instantly. In this problem, they are close, which confirms that the approximation is reasonable under standard assumptions.
When should you prefer the exact solution?
- When your instructor specifically asks for it.
- When the concentration is low and x is not negligible compared with the starting value.
- When you need more precise work for analytical chemistry or reporting.
- When comparing results from different data sources or software tools.
Comparison table: estimated pH at several NaCN concentrations
The trend below uses standard weak-base hydrolysis assumptions at 25 C and Ka of HCN in the common textbook range. The purpose is to show how concentration affects pH. As the solution becomes more concentrated, more CN- is available to react with water, so the pH rises.
| NaCN concentration (M) | Approximate [OH-] (M) | Approximate pOH | Approximate pH |
|---|---|---|---|
| 0.010 | 4.0 × 10^-4 | 3.40 | 10.60 |
| 0.050 | 9.0 × 10^-4 | 3.05 | 10.95 |
| 0.100 | 1.3 × 10^-3 | 2.89 | 11.11 |
| 0.500 | 2.8 × 10^-3 | 2.55 | 11.45 |
| 1.000 | 4.0 × 10^-3 | 2.40 | 11.60 |
Common mistakes in NaCN pH calculations
- Treating NaCN as neutral. It is not neutral because CN- is a basic anion.
- Using Ka directly instead of Kb. You need the base constant for cyanide hydrolysis.
- Forgetting that sodium is a spectator ion. Na+ does not set the pH here.
- Mixing up pOH and pH. Once you get [OH-], calculate pOH first, then convert to pH.
- Ignoring temperature assumptions. The relation pH + pOH = 14.00 is tied to the usual 25 C convention.
- Over-rounding too early. Keep extra digits until the end.
Authority sources and further reading
If you want to confirm acid-base constants, cyanide chemistry, or water equilibrium assumptions, these sources are useful starting points:
- NIST Chemistry WebBook for thermochemical and chemical property data.
- U.S. Environmental Protection Agency cyanide resources for environmental and safety background.
- LibreTexts Chemistry for equilibrium, acid-base, and weak base hydrolysis tutorials.
Final answer for the standard classroom problem
To calculate the pH of 0.5 M NaCN, treat CN- as a weak base, determine Kb from the Ka of HCN, solve for [OH-], then convert to pH. Under ordinary general chemistry assumptions at 25 C, the solution is basic, with pH typically reported in the low-to-mid 11 range, often around 11.45 to 11.95 depending on the exact constant set and rounding method used.
If your instructor gave a specific Ka or pKa value for HCN, use that exact value in the calculator above and report your final answer to the requested number of significant figures. That is the best way to align your result with the conventions used in your course or lab.