Calculate the pH of 0.050 M NaCN
Use this interactive sodium cyanide hydrolysis calculator to find hydroxide concentration, pOH, and pH from concentration and acid dissociation data for HCN. The default setup is preloaded for 0.050 M NaCN at 25 degrees Celsius.
How to calculate the pH of 0.050 M NaCN
Sodium cyanide, NaCN, is the salt of a strong base and a weak acid. When it dissolves in water, the sodium ion is essentially a spectator ion, but the cyanide ion reacts with water to produce hydroxide. That makes the solution basic. For the specific problem calculate the pH of 0.050 M NaCN, the chemistry is governed by the hydrolysis of CN–, which is the conjugate base of hydrocyanic acid, HCN.
The central reaction is:
To solve the problem, you first connect the acid dissociation constant of HCN to the base dissociation constant of CN–. At 25 degrees Celsius, water has Kw = 1.0 × 10-14. If the accepted value of Ka for HCN is 4.9 × 10-10, then:
Because NaCN dissociates completely, the initial cyanide concentration is 0.050 M. You can then write an ICE table for the hydrolysis reaction:
- Initial: [CN–] = 0.050, [HCN] = 0, [OH–] = 0
- Change: [CN–] = -x, [HCN] = +x, [OH–] = +x
- Equilibrium: [CN–] = 0.050 – x, [HCN] = x, [OH–] = x
The equilibrium expression is:
If you use the weak base approximation, you assume that x is small compared with 0.050, so the denominator stays close to 0.050:
That value is the hydroxide concentration. Then:
- pOH = -log(1.01 × 10-3) ≈ 3.00
- pH = 14.00 – 3.00 ≈ 11.00
So the pH of a 0.050 M sodium cyanide solution is approximately 11.00. The exact quadratic treatment gives nearly the same answer, which confirms that the approximation is valid in this concentration range.
Why NaCN solutions are basic
This problem often appears in general chemistry because it tests whether you can identify the acid-base behavior of a salt. Not all salts are neutral in water. A salt formed from a strong acid and a strong base, such as NaCl, is typically neutral. A salt formed from a weak acid and a strong base, such as NaCN, produces a basic solution because the anion acts as a proton acceptor. In this case, CN– removes a proton from water and generates OH–.
That is why the pH is above 7, even though sodium cyanide itself is not an Arrhenius base like NaOH. The basicity comes from hydrolysis, not from direct release of OH– during dissolution.
Step by step expert method
If you want a reliable exam-ready approach, follow this sequence every time:
- Identify the ions produced when the salt dissolves.
- Determine which ion can react with water.
- Relate Ka and Kb through Kw.
- Set up an ICE table for the hydrolysis reaction.
- Solve for x using either the approximation or the quadratic formula.
- Convert x to pOH, then to pH.
For 0.050 M NaCN, the hydrolyzing ion is CN–. The value of x is small relative to the initial concentration, so the approximation is usually justified. You can quickly verify this by comparing x to 5 percent of the initial concentration. Here, 5 percent of 0.050 M is 0.0025 M, and the calculated x is about 0.0010 M, so the approximation passes the test.
Exact solution versus approximation
Many students learn the shortcut x = √(KbC), but it is important to understand when it works. The exact equation is:
Using the quadratic formula gives:
For this NaCN problem, the exact and approximate answers are extremely close. That is typical for moderately concentrated weak bases with small equilibrium constants. However, if the concentration were much lower, or if the equilibrium constant were larger, the exact treatment would become more important.
| Quantity | Value for 0.050 M NaCN | Meaning |
|---|---|---|
| Ka of HCN | 4.9 × 10-10 | Weak acid dissociation constant |
| Kb of CN– | 2.04 × 10-5 | Base strength of cyanide ion in water |
| [OH–] | 1.00 × 10-3 M | Hydroxide generated by hydrolysis |
| pOH | About 3.00 | Negative log of hydroxide concentration |
| pH | About 11.00 | Basic solution result |
Common mistakes when calculating the pH of 0.050 M NaCN
- Treating NaCN as neutral: This ignores cyanide hydrolysis and leads to a pH near 7, which is incorrect.
- Using Ka directly in the ICE table: Since CN– is acting as a base, you need Kb, not Ka.
- Forgetting to convert pOH to pH: Once you obtain hydroxide concentration, you usually get pOH first.
- Using the wrong parent acid: The conjugate acid of CN– is HCN.
- Ignoring the 5 percent check: The approximation should be validated when used.
How concentration changes the pH
The pH of sodium cyanide depends strongly on concentration. More cyanide means a greater capacity to hydrolyze and produce hydroxide. Because weak base systems follow a square root relationship in the common approximation, increasing concentration by a factor of 100 does not increase hydroxide concentration by a factor of 100, but by a factor of 10. This is why pH changes more gradually than concentration.
| NaCN concentration (M) | Approximate [OH–] (M) | Approximate pOH | Approximate pH |
|---|---|---|---|
| 0.001 | 1.43 × 10-4 | 3.84 | 10.16 |
| 0.010 | 4.52 × 10-4 | 3.34 | 10.66 |
| 0.050 | 1.01 × 10-3 | 3.00 | 11.00 |
| 0.100 | 1.43 × 10-3 | 2.84 | 11.16 |
This comparison table makes an important point: a 0.050 M NaCN solution is distinctly basic, but not nearly as basic as a 0.050 M strong base such as NaOH. A 0.050 M NaOH solution would have [OH–] = 0.050 M, pOH about 1.30, and pH about 12.70. In contrast, the same formal concentration of NaCN yields only about 0.001 M hydroxide because the hydrolysis equilibrium lies far from complete.
Comparison with other salts
Salt hydrolysis is easier to understand when compared across categories:
- NaCl: strong acid + strong base, usually neutral, pH about 7
- NH4Cl: strong acid + weak base, acidic solution
- NaF: strong base + weak acid, basic solution
- NaCN: strong base + weak acid, basic solution, often more basic than fluoride salts because CN– is the conjugate base of a weaker acid than HF
Because HCN is a very weak acid, its conjugate base is comparatively stronger than the conjugate base of many other weak acids. That is why cyanide solutions can reach pH values around 11 at moderate concentrations.
Real-world context and safety relevance
Cyanide chemistry is not just an academic topic. Cyanide compounds are used in mining, electroplating, and some industrial syntheses. Their acid-base behavior matters because acidic conditions can convert cyanide salts into hydrogen cyanide gas, which is extremely toxic. From a safety standpoint, understanding whether a cyanide solution is basic is important because pH control strongly affects the distribution between CN– and HCN.
At higher pH, more cyanide remains in the ionized CN– form. At lower pH, the equilibrium shifts toward HCN. Since HCN is volatile and highly hazardous, environmental and industrial guidelines often emphasize maintaining alkaline conditions when handling cyanide-containing solutions. For that reason, pH calculations are directly relevant to laboratory safety, waste treatment, and industrial controls.
Exam shortcut for this exact problem
If you encounter “calculate the pH of 0.050 M NaCN” on a quiz or exam, the fastest accurate route is:
- Write Kb = 1.0 × 10-14 / 4.9 × 10-10 = 2.04 × 10-5
- Use x = √(KbC) = √((2.04 × 10-5)(0.050))
- Find x ≈ 1.01 × 10-3 M
- Find pOH ≈ 3.00
- Report pH ≈ 11.00
That method is concise, defensible, and usually accepted when the approximation is valid. If your instructor requires an exact method, solve the quadratic. The result still rounds to essentially the same pH.
Authoritative references for cyanide and acid-base context
- U.S. Environmental Protection Agency: Cyanide overview
- CDC NIOSH: Cyanide information and safety context
- NIST Chemistry WebBook: Hydrogen cyanide data
Final answer
For a 0.050 M NaCN solution at 25 degrees Celsius, using Ka(HCN) = 4.9 × 10-10, the calculated hydroxide concentration is about 1.0 × 10-3 M. Therefore, the pOH is about 3.00 and the pH is about 11.00. This confirms that sodium cyanide forms a moderately basic aqueous solution because the cyanide ion hydrolyzes water to produce hydroxide.