Calculate the pH of 0.15 M NaCN Solution
Use this interactive calculator to determine the pH, pOH, hydroxide concentration, and cyanide hydrolysis behavior for a sodium cyanide solution. The tool uses weak-base equilibrium chemistry, treating CN– as the conjugate base of HCN.
NaCN pH Calculator
Results
Enter values and click Calculate pH to see the equilibrium solution.
How to Calculate the pH of 0.15 M NaCN Solution
To calculate the pH of a 0.15 M NaCN solution, you need to recognize what sodium cyanide does in water. NaCN is a soluble ionic compound that dissociates almost completely into Na+ and CN–. The sodium ion is a spectator ion for acid-base chemistry, but the cyanide ion is important because it is the conjugate base of the weak acid HCN, hydrocyanic acid. That means CN– reacts with water to generate hydroxide ions:
CN– + H2O ⇌ HCN + OH–
Because hydroxide is produced, the solution is basic. The entire pH problem is therefore a weak-base equilibrium calculation. If the concentration of NaCN is 0.15 M, then the initial concentration of CN– is also 0.15 M, assuming complete dissociation of the salt.
Step 1: Convert Ka of HCN into Kb of CN–
Most reference data lists the acid dissociation constant of HCN rather than the base dissociation constant of CN–. The relation is:
Kb = Kw / Ka
At 25 degrees C, a commonly used value is:
- Ka(HCN) = 6.2 × 10-10
- Kw = 1.0 × 10-14
So:
Kb = (1.0 × 10-14) / (6.2 × 10-10) = 1.61 × 10-5
Step 2: Set up the equilibrium expression
Let x be the amount of CN– that reacts with water. Then the ICE setup is:
- Initial: [CN–] = 0.15, [HCN] = 0, [OH–] = 0
- Change: [CN–] = -x, [HCN] = +x, [OH–] = +x
- Equilibrium: [CN–] = 0.15 – x, [HCN] = x, [OH–] = x
The equilibrium expression becomes:
Kb = x2 / (0.15 – x)
Step 3: Solve for hydroxide concentration
If you use the standard weak-base approximation, where x is small compared with 0.15, then:
x ≈ √(Kb × C)
Substituting values:
x ≈ √((1.61 × 10-5) × 0.15) = √(2.415 × 10-6) ≈ 1.55 × 10-3 M
So the hydroxide concentration is approximately 0.00155 M.
Step 4: Convert OH– to pOH and pH
Once you know hydroxide concentration, calculate pOH:
pOH = -log[OH–]
pOH = -log(1.55 × 10-3) ≈ 2.81
Then:
pH = 14.00 – 2.81 = 11.19
This is the expected pH for a 0.15 M sodium cyanide solution at 25 degrees C using standard data.
Why NaCN Makes Water Basic
Students often wonder why a salt can produce a basic solution. The key is the identity of the ions. Sodium cyanide comes from a strong base, NaOH, and a weak acid, HCN. The cation from a strong base is usually pH-neutral in water, but the anion from a weak acid can act as a base by accepting a proton from water. In this case, CN– grabs H+ from water and leaves behind OH–, raising the pH.
This is a classic example of salt hydrolysis. Similar behavior is observed for salts such as sodium acetate, sodium fluoride, and sodium carbonate, though the exact pH depends on the strength of the conjugate base and the concentration of the solution.
Approximation vs Exact Quadratic Method
For many weak acid and weak base calculations, the shortcut x = √(KC) is used. It is fast and usually accurate when the percentage ionization is small, commonly under 5 percent. In the case of 0.15 M NaCN, the approximation works very well because the calculated x is much smaller than the initial cyanide concentration. However, if concentration becomes very low or equilibrium constants become relatively larger, the exact quadratic method is better.
| Parameter | Approximate Method | Exact Quadratic Method | Difference |
|---|---|---|---|
| [OH–] for 0.15 M NaCN | 1.554 × 10-3 M | 1.546 × 10-3 M | 0.008 × 10-3 M |
| pOH | 2.808 | 2.811 | 0.003 |
| pH | 11.192 | 11.189 | 0.003 |
| Percent hydrolysis | 1.04% | 1.03% | 0.01% |
The table shows why introductory chemistry courses often accept the shortcut. The error is tiny here. Still, for professional accuracy, especially in software tools and technical reports, the exact solution is the better default.
Comparison of pH at Different NaCN Concentrations
Concentration matters. Since cyanide is a weak base, higher concentrations generate more hydroxide and therefore higher pH values. The relationship is not linear on the pH scale because pH is logarithmic. The following table shows calculated values at 25 degrees C using Ka(HCN) = 6.2 × 10-10 and the weak-base approximation.
| NaCN Concentration (M) | Kb of CN– | Estimated [OH–] (M) | pOH | pH |
|---|---|---|---|---|
| 0.010 | 1.61 × 10-5 | 4.02 × 10-4 | 3.396 | 10.604 |
| 0.050 | 1.61 × 10-5 | 8.97 × 10-4 | 3.047 | 10.953 |
| 0.100 | 1.61 × 10-5 | 1.27 × 10-3 | 2.896 | 11.104 |
| 0.150 | 1.61 × 10-5 | 1.55 × 10-3 | 2.808 | 11.192 |
| 0.200 | 1.61 × 10-5 | 1.80 × 10-3 | 2.745 | 11.255 |
Common Mistakes When Solving This Problem
- Treating NaCN as a strong base. Sodium cyanide is not itself a strong Arrhenius base like NaOH. It forms a basic solution because CN– hydrolyzes.
- Using Ka directly in the ICE table. The reacting species in water is CN–, so the equilibrium constant in the hydrolysis expression is Kb, not Ka.
- Forgetting complete dissociation of the salt. A 0.15 M NaCN solution provides about 0.15 M CN– initially.
- Mixing up pH and pOH. Since the calculation first gives hydroxide concentration, you find pOH before converting to pH.
- Ignoring temperature dependence of Kw. If the temperature differs substantially from 25 degrees C, Kw changes, and so can the final pH.
Detailed Chemical Interpretation
The hydrolysis of cyanide reveals a broader acid-base principle: the weaker the parent acid, the stronger its conjugate base. HCN is a weak acid, so CN– has noticeable basicity. However, it is still much weaker than hydroxide. That is why the pH of 0.15 M NaCN is around 11.19 rather than near 13 or 14. Only a small percentage of cyanide actually hydrolyzes, but that small percentage is enough to produce a distinctly basic solution.
For 0.15 M NaCN, the exact hydroxide concentration is roughly 1.546 × 10-3 M. Compared with the starting 0.15 M cyanide concentration, this corresponds to hydrolysis of just about 1 percent. This low fractional reaction is exactly why the square-root approximation works so well.
Safety and Practical Context
Sodium cyanide is extremely hazardous and should never be handled casually. Cyanide chemistry is discussed widely in analytical chemistry, metallurgy, toxicology, and environmental chemistry because cyanide compounds can interfere with cellular respiration and pose serious poisoning risks. In any real laboratory or industrial context, proper safety training, ventilation, personal protective equipment, and regulated waste handling are essential.
If you are studying this problem for class, focus on the equilibrium concept rather than practical preparation. In real use cases, sodium cyanide solutions are tightly controlled substances. For chemistry reference and safety data, consult official institutional resources rather than informal web summaries.
Authoritative References
- PubChem, U.S. National Institutes of Health: Sodium Cyanide
- Chemistry LibreTexts educational resource
- U.S. Environmental Protection Agency: Cyanide information
Quick Summary
- NaCN dissociates completely to Na+ and CN–.
- CN– is the conjugate base of weak acid HCN.
- Use Kb = Kw / Ka to convert acid data into base data.
- For 0.15 M NaCN with Ka(HCN) = 6.2 × 10-10, Kb ≈ 1.61 × 10-5.
- Solving the equilibrium gives [OH–] ≈ 1.55 × 10-3 M.
- pOH ≈ 2.81 and pH ≈ 11.19.
Data in the worked example use standard 25 degrees C equilibrium values commonly adopted in general chemistry instruction. Minor variations in Ka reference values can shift the final pH by a few hundredths of a pH unit.