Calculate the pH of the Following Solutions: 0.050 M NaCN
Use this interactive chemistry calculator to determine the pH, pOH, hydroxide concentration, cyanide hydrolysis, and equilibrium values for a sodium cyanide solution.
How to Calculate the pH of 0.050 M NaCN
To calculate the pH of a 0.050 M sodium cyanide (NaCN) solution, you need to recognize what kind of salt NaCN is. Sodium cyanide is formed from a strong base, sodium hydroxide (NaOH), and a weak acid, hydrocyanic acid (HCN). Because the sodium ion is neutral in water while the cyanide ion is the conjugate base of a weak acid, the solution becomes basic when dissolved in water.
The key chemical idea is that the cyanide ion reacts with water in a hydrolysis equilibrium:
CN– + H2O ⇌ HCN + OH–
This reaction produces hydroxide ions, which raise the pH above 7. In other words, NaCN does not behave like a neutral salt such as NaCl. Instead, it acts as a salt of a weak acid, so the anion drives the acid-base behavior of the solution.
Step-by-Step Solution for 0.050 M NaCN
1. Identify the Basic Species
When NaCN dissolves in water, it dissociates essentially completely:
NaCN → Na+ + CN–
The sodium ion, Na+, is a spectator ion for acid-base purposes. The cyanide ion, CN–, is the species that matters because it is the conjugate base of HCN.
2. Use the Relationship Between Ka and Kb
Since HCN is a weak acid, the cyanide ion has a base dissociation constant given by:
Kb = Kw / Ka
At 25 °C, the ion-product constant of water is:
Kw = 1.0 × 10-14
A widely used value for the acid dissociation constant of HCN is about:
Ka ≈ 6.2 × 10-10
This corresponds to a pKa of about 9.21. Therefore:
Kb = (1.0 × 10-14) / (6.2 × 10-10) ≈ 1.61 × 10-5
3. Set Up the ICE Table
Let the initial concentration of cyanide be 0.050 M. If x mol/L of cyanide reacts with water, then:
- Initial [CN–] = 0.050 M
- Change in [CN–] = -x
- Change in [HCN] = +x
- Change in [OH–] = +x
So at equilibrium:
- [CN–] = 0.050 – x
- [HCN] = x
- [OH–] = x
Insert these values into the Kb expression:
Kb = x2 / (0.050 – x)
4. Solve for x
Because Kb is relatively small, the common approximation is that x is much smaller than 0.050. That gives:
1.61 × 10-5 = x2 / 0.050
x2 = 8.05 × 10-7
x ≈ 8.97 × 10-4 M
Since x represents the hydroxide concentration generated by hydrolysis:
[OH–] ≈ 8.97 × 10-4 M
5. Convert to pOH and pH
Next calculate pOH:
pOH = -log[OH–] = -log(8.97 × 10-4) ≈ 3.05
Finally:
pH = 14.00 – 3.05 = 10.95
Why NaCN Is Basic in Water
Many students first learn that salts formed from acids and bases can be acidic, neutral, or basic depending on the parent acid and base. Sodium cyanide is an excellent example of a basic salt. The sodium cation comes from a strong base and does not react appreciably with water. The cyanide anion comes from a weak acid and therefore has a noticeable tendency to accept a proton from water, generating hydroxide.
This is why the pH is not simply guessed from the concentration alone. You must account for chemical equilibrium. A 0.050 M NaCN solution contains a moderate concentration of a weak base, and although CN– does not hydrolyze completely, it hydrolyzes enough to push the pH significantly above neutrality.
Approximation vs Quadratic Method
For a weak base problem like this, the shortcut approach usually works well when x is less than about 5% of the initial concentration. In this case, x is around 0.000897 M while the initial concentration is 0.050 M, so the percent ionization is:
(0.000897 / 0.050) × 100 ≈ 1.79%
Since 1.79% is below 5%, the approximation is valid. That means the simplified equation gives a reliable result. The quadratic method is more exact and will give a nearly identical answer here. In practice, both methods support the conclusion that the pH is approximately 10.95.
| Parameter | Value for 0.050 M NaCN | Meaning |
|---|---|---|
| Initial [CN–] | 0.050 M | Concentration supplied by complete NaCN dissociation |
| Ka of HCN | 6.2 × 10-10 | Weak acid strength of hydrocyanic acid |
| Kb of CN– | 1.61 × 10-5 | Basicity of cyanide in water |
| [OH–] | 8.97 × 10-4 M | Hydroxide produced by hydrolysis |
| pOH | 3.05 | Negative log of hydroxide concentration |
| pH | 10.95 | Final basicity of the solution |
Comparison With Other Common Salt Solutions
It helps to compare NaCN with other salts that students often encounter in general chemistry. Not every salt of sodium is neutral. The crucial factor is whether the accompanying anion is the conjugate base of a strong acid or a weak acid.
| Salt | Parent Acid | Typical Acid Strength | Expected Solution Behavior |
|---|---|---|---|
| NaCl | HCl | Strong acid | Approximately neutral, pH near 7 |
| NaF | HF | Weak acid, Ka ≈ 6.8 × 10-4 | Basic, but less basic than NaCN at equal concentration |
| NaCN | HCN | Very weak acid, Ka ≈ 6.2 × 10-10 | Noticeably basic, pH around 10.95 at 0.050 M |
| NH4Cl | Conjugate acid NH4+ | Weak acid behavior | Acidic solution, pH below 7 |
Common Mistakes When Solving This Problem
- Treating NaCN as a neutral salt. This is the biggest error. Because CN– is the conjugate base of a weak acid, the solution is basic.
- Using Ka directly instead of converting to Kb. For cyanide hydrolysis, you must calculate Kb from HCN data.
- Confusing pOH with pH. After finding hydroxide concentration, calculate pOH first and then convert to pH.
- Ignoring the 5% rule. In many weak acid-base problems, the approximation is allowed, but you should still verify that it is reasonable.
- Forgetting units and equilibrium interpretation. The x value is a concentration in mol/L, not just a pure number.
Detailed Conceptual Explanation
The pH of a salt solution is one of the clearest examples of conjugate acid-base logic. If the anion is the conjugate base of a weak acid, it will remove a proton from water. The weaker the original acid, the stronger its conjugate base tends to be. HCN is a weak acid with a small Ka, so CN– is basic enough to create a measurable amount of hydroxide in solution.
This behavior is rooted in equilibrium thermodynamics. The system adjusts so that some cyanide ions become protonated to HCN while generating OH–. Although only a small fraction reacts, that fraction is still large enough to produce a pH close to 11. This is much more basic than neutral water, where [OH–] is only 1.0 × 10-7 M at 25 °C.
Another useful observation is that weak base hydrolysis often yields a pH that depends on both concentration and base strength. If the NaCN concentration were lower, the pH would decrease somewhat, though it would remain basic. If the concentration were higher, more hydroxide would be generated and the pH would rise. The calculator above lets you explore this effect instantly by changing the input concentration.
Practical Relevance of Cyanide Solution pH
In academic chemistry, this problem illustrates hydrolysis and equilibrium. In industrial and environmental chemistry, pH control around cyanide-containing systems is especially important. Cyanide speciation depends strongly on pH because lower pH shifts the equilibrium toward molecular HCN, which is far more volatile and dangerous than the ionic CN– form. That is one reason pH calculations involving cyanide are not merely textbook exercises.
For laboratory safety and technical reference material, authoritative organizations provide detailed information on cyanide chemistry, toxicology, and handling. If you want to deepen your understanding, review resources from:
- CDC NIOSH cyanide guidance
- NIH PubChem entry for hydrogen cyanide
- Chemistry LibreTexts educational reference
Quick Summary Formula Path
- Write the hydrolysis reaction for CN–.
- Find Kb from Kw / Ka.
- Set up an ICE table with initial concentration 0.050 M.
- Solve for x = [OH–].
- Compute pOH = -log[OH–].
- Compute pH = 14 – pOH.
Following these steps leads to the final result of pH ≈ 10.95 for a 0.050 M sodium cyanide solution at 25 °C using standard acid-base data for HCN.
Final Takeaway
If you are asked to calculate the pH of the following solution, 0.050 M NaCN, the correct approach is to treat cyanide as a weak base. Use the Ka of HCN to derive Kb, solve the hydrolysis equilibrium, and convert the resulting hydroxide concentration to pH. The answer is clearly basic, not neutral and not acidic. Under standard conditions, the calculated pH is approximately 10.95.