Calculate the pH of 0.10 M NaCN
Use this interactive sodium cyanide calculator to determine hydroxide concentration, pOH, and final pH for aqueous NaCN solutions at 25°C. The calculator supports both the common square-root approximation and the exact quadratic solution.
Calculation Results
Visual Breakdown
Expert Guide: How to Calculate the pH of 0.10 M NaCN
Calculating the pH of a 0.10 M sodium cyanide solution is a classic weak-base hydrolysis problem from general chemistry. The key idea is that NaCN is not itself an acid or a base in the Brønsted sense after dissociation. Instead, the sodium ion, Na+, is effectively neutral in water, while the cyanide ion, CN–, is the conjugate base of hydrocyanic acid, HCN. Because HCN is a weak acid, its conjugate base is appreciably basic. As a result, when sodium cyanide dissolves in water, the solution becomes basic and its pH rises above 7.
Step 1: Recognize the chemistry behind NaCN in water
Sodium cyanide is a strong electrolyte, so it dissociates essentially completely:
The sodium ion does not significantly affect pH. The cyanide ion does. It reacts with water according to the hydrolysis equilibrium:
This equilibrium produces hydroxide, OH–, which is why the solution is basic. Therefore, to calculate pH, we first find the base dissociation constant of cyanide, then determine the hydroxide concentration.
Step 2: Convert Ka of HCN into Kb of CN-
The relationship between a weak acid and its conjugate base at 25°C is:
For hydrocyanic acid, a commonly used value is:
So the base constant for cyanide is:
This number shows CN– is a weak base, but not an extremely weak one. In a 0.10 M solution, enough cyanide hydrolyzes to produce a measurable OH– concentration.
Step 3: Set up the ICE table
For the equilibrium CN– + H2O ⇌ HCN + OH–, begin with the formal concentration of cyanide coming from the dissolved sodium cyanide:
- Initial [CN–] = 0.10 M
- Initial [HCN] = 0
- Initial [OH–] ≈ 0 for setup purposes
If x is the amount of CN– that reacts, then at equilibrium:
- [CN–] = 0.10 – x
- [HCN] = x
- [OH–] = x
Substitute into the equilibrium expression:
Step 4: Solve for x, the hydroxide concentration
Because Kb is much smaller than the starting concentration, the common classroom approximation is to assume x is small relative to 0.10. That simplifies the denominator:
So the hydroxide concentration is approximately:
If you solve the quadratic exactly, you get nearly the same answer:
Using C = 0.10 M and Kb = 1.61 × 10-5, the exact value is still about 1.26 × 10-3 M. The approximation works very well because x is only about 1.3% of the initial concentration, which is comfortably below the usual 5% guideline.
Step 5: Convert hydroxide concentration to pOH and pH
Once [OH–] is known, calculate pOH:
Then use the standard room-temperature relationship:
Final answer: the pH of 0.10 M NaCN at 25°C is approximately 11.10.
Why the solution is basic instead of neutral
Students often memorize that salts can be neutral, acidic, or basic depending on the acid and base from which they are derived. NaCN is formed from NaOH, a strong base, and HCN, a weak acid. Salts of a strong base and weak acid generally produce basic solutions because the anion reacts with water to generate hydroxide. That pattern lets you quickly predict the direction of pH change even before doing any math.
Compare that to NaCl, which comes from NaOH and HCl, both strong species in water chemistry. Neither Na+ nor Cl– hydrolyzes significantly, so a sodium chloride solution remains close to neutral. Cyanide is different because it is the conjugate base of a weak acid, so it accepts protons from water and forms OH–.
Comparison table: how NaCN concentration affects pH
The pH depends on concentration because hydroxide generation depends on the amount of cyanide present. The values below use Ka(HCN) = 6.2 × 10-10 at 25°C and the standard pKw of 14.00.
| NaCN concentration (M) | Kb of CN- | Approx. [OH-] (M) | pOH | pH |
|---|---|---|---|---|
| 0.0010 | 1.61 × 10-5 | 1.27 × 10-4 | 3.90 | 10.10 |
| 0.010 | 1.61 × 10-5 | 4.01 × 10-4 | 3.40 | 10.60 |
| 0.10 | 1.61 × 10-5 | 1.27 × 10-3 | 2.90 | 11.10 |
| 1.00 | 1.61 × 10-5 | 4.01 × 10-3 | 2.40 | 11.60 |
This trend shows that each tenfold increase in NaCN concentration raises pH, but not by a full unit, because the dependence is approximately square-root based for weak-base hydrolysis.
Comparison table: acid-base data behind the calculation
The pH result depends strongly on the acid strength of HCN and the autoionization of water. These values are standard reference data used in general chemistry instruction and environmental chemistry.
| Quantity | Typical value at 25°C | Why it matters |
|---|---|---|
| Kw for water | 1.0 × 10-14 | Links pH and pOH through pH + pOH = 14.00 |
| Ka for HCN | 6.2 × 10-10 | Used to compute Kb of cyanide |
| pKa for HCN | About 9.21 | Shows HCN is a weak acid, so CN– is a weak base |
| Kb for CN– | 1.61 × 10-5 | Directly controls OH– production in NaCN solution |
When should you use the exact quadratic instead of the shortcut?
The square-root approximation is efficient and usually accurate when x is much smaller than the initial concentration C. A common test is the 5% rule:
- Calculate x using the approximation.
- Divide x by the starting concentration.
- If the percentage is below 5%, the approximation is acceptable.
For 0.10 M NaCN, x ≈ 1.27 × 10-3 M, so x/C ≈ 1.27%. That is well within the safe range. Still, the exact method is useful when concentrations are low, equilibrium constants are larger, or you want a more rigorous answer for lab reporting.
Common mistakes students make
- Using the Ka of HCN directly instead of converting it to Kb for CN–.
- Treating NaCN as a strong base like NaOH. It is not. Only the cyanide ion hydrolyzes weakly.
- Forgetting that you calculate pOH first, then convert to pH.
- Assuming every salt solution is neutral. Salt hydrolysis depends on the parent acid and base.
- Ignoring temperature. The standard pH + pOH = 14.00 relation strictly applies at 25°C.
Safety and reference context
Cyanide chemistry is not just an academic topic. It matters in toxicology, environmental monitoring, and industrial process control. If you want supporting reference material on cyanide properties and public health considerations, review authoritative sources such as the Agency for Toxic Substances and Disease Registry cyanide fact sheet, the National Center for Biotechnology Information toxicology overview, and the NIST Chemistry WebBook entry for hydrogen cyanide. These sources do not replace your equilibrium calculation, but they provide real-world context for why cyanide speciation and pH matter.
In environmental systems, cyanide behavior is strongly affected by pH because protonation changes the balance between CN– and HCN. At lower pH, more cyanide exists as HCN, which is more volatile and toxicologically important. At higher pH, cyanide remains more in the ionic CN– form. That is one reason acid-base chemistry around cyanide is emphasized in analytical and safety literature.
Bottom line
To calculate the pH of 0.10 M NaCN, treat cyanide as a weak base, compute Kb from the Ka of HCN, solve for [OH–], determine pOH, and then convert to pH. Using Ka(HCN) = 6.2 × 10-10 at 25°C gives Kb(CN–) = 1.61 × 10-5, [OH–] ≈ 1.27 × 10-3 M, pOH ≈ 2.90, and pH ≈ 11.10.
If you are solving homework, preparing a lab report, or checking a water chemistry calculation, that is the standard chemistry answer expected under normal room-temperature assumptions.