Calculate pH of 0.1 NaCN Solution
Use this interactive calculator to determine the pH, pOH, hydroxide concentration, cyanide hydrolysis extent, and equilibrium concentrations for a sodium cyanide solution. The tool defaults to 0.100 M NaCN at 25 degrees Celsius using the acid dissociation constant of HCN, then converts it to the base hydrolysis constant for CN–.
NaCN pH Calculator
Reaction used: CN– + H2O ⇌ HCN + OH–. Because NaCN dissociates completely, the initial cyanide ion concentration equals the formal NaCN concentration.
Results
Enter your values and click Calculate pH. For a standard 0.100 M NaCN solution at 25 degrees C with HCN pKa of 9.21, the expected pH is a little above 11.
How to calculate pH of 0.1 NaCN solution
To calculate the pH of a 0.1 NaCN solution, you do not treat sodium cyanide as a strong base in the same way you would treat sodium hydroxide. Instead, you recognize that NaCN is a salt formed from a strong base, NaOH, and a weak acid, HCN. When sodium cyanide dissolves in water, it dissociates essentially completely into sodium ions and cyanide ions. The sodium ion is a spectator ion for acid-base purposes, but the cyanide ion is the conjugate base of hydrocyanic acid and reacts with water to generate hydroxide. That hydrolysis is the key chemical process controlling the pH.
The relevant equilibrium is:
CN- + H2O ⇌ HCN + OH-
Since hydroxide is produced, the solution becomes basic. The central challenge is determining how much CN– hydrolyzes. To do that, you connect the acid dissociation constant of HCN to the base dissociation constant of CN– through the water ion product:
Kb = Kw / Ka
At 25 degrees C, a common textbook value for the acid dissociation constant of HCN is about Ka = 6.2 x 10^-10, corresponding to pKa = 9.21. With Kw = 1.0 x 10^-14, the base dissociation constant for cyanide is:
Kb = (1.0 x 10^-14) / (6.2 x 10^-10) = 1.61 x 10^-5
Step by step setup for 0.100 M NaCN
- Write the hydrolysis reaction: CN– + H2O ⇌ HCN + OH–.
- Start with initial concentration [CN-] = 0.100 M.
- Let x be the concentration of CN– that reacts.
- At equilibrium, [CN-] = 0.100 – x, [HCN] = x, and [OH-] = x.
- Use the equilibrium expression Kb = x^2 / (0.100 – x).
For a quick weak-base estimate, if x is small relative to 0.100 M, then 0.100 – x ≈ 0.100. This gives:
x = sqrt(KbC) = sqrt((1.61 x 10^-5)(0.100)) = 1.27 x 10^-3 M
Now calculate pOH:
pOH = -log(1.27 x 10^-3) = 2.90
And then the pH:
pH = 14.00 – 2.90 = 11.10
The exact quadratic solution gives practically the same answer, differing only in the third or fourth decimal place. So for ordinary coursework, analytical chemistry drills, and introductory equilibrium problems, the pH of a 0.1 M sodium cyanide solution is typically reported as about 11.10.
Why NaCN is basic
This question often confuses students because sodium cyanide contains a sodium ion, and sodium compounds are frequently neutral when dissolved in water. The crucial idea is that the acid-base behavior of a salt depends on the conjugate acid-base properties of its ions. Sodium comes from the strong base sodium hydroxide and does not appreciably alter pH. Cyanide, however, is the conjugate base of a weak acid. Weak acid conjugate bases react with water and produce OH–, so the pH rises above 7.
Quick reasoning checklist
- NaCN fully dissociates into Na+ and CN–.
- Na+ is effectively neutral in water.
- CN– is the conjugate base of weak acid HCN.
- Conjugate bases of weak acids hydrolyze to produce OH–.
- Therefore a 0.1 M NaCN solution is basic, with pH above 7.
Exact versus approximate method
The approximation x = sqrt(KbC) is popular because it is fast and usually very accurate for weak bases when the extent of reaction is small compared with the starting concentration. For 0.1 M cyanide, that is true. However, a more rigorous approach solves the quadratic equation generated from:
Kb = x^2 / (C – x)
Rearranging yields:
x^2 + Kb x – Kb C = 0
Then use the positive root:
x = (-Kb + sqrt(Kb^2 + 4KbC)) / 2
Because Kb is small compared with C, the exact and approximate values are very close. Good calculators should support both methods. This page does that, allowing you to compare the weak-base shortcut with the more exact equilibrium solution.
Reference data relevant to cyanide equilibrium
| Quantity | Typical value at 25 degrees C | Why it matters for pH calculation |
|---|---|---|
| Water ion product, Kw | 1.0 x 10^-14 | Needed to convert HCN acid strength into CN– base strength. |
| HCN pKa | 9.21 | Common instructional value used to obtain Ka. |
| HCN Ka | 6.2 x 10^-10 | Governs the conjugate relationship with cyanide. |
| CN– Kb | 1.61 x 10^-5 | Directly controls OH– formation in solution. |
| Calculated [OH–] for 0.100 M NaCN | About 1.27 x 10^-3 M | Intermediate result used to find pOH and pH. |
| Calculated pH for 0.100 M NaCN | About 11.10 | Final answer for the standard setup. |
Comparison with other salts and bases
Students often learn better when they compare a target problem with familiar cases. Sodium chloride does not affect pH because it comes from a strong acid and a strong base. Sodium acetate is basic because acetate is the conjugate base of weak acetic acid. Sodium cyanide is also basic, but because HCN is much weaker than acetic acid, cyanide is a stronger conjugate base than acetate. As a result, equal-concentration NaCN solutions are generally more basic than sodium acetate solutions.
| Salt at 0.100 M | Parent acid | Typical parent acid pKa | Expected acid-base behavior in water | Approximate pH trend |
|---|---|---|---|---|
| NaCl | HCl | About -6 | Neutral salt from strong acid and strong base | Near 7.00 |
| CH3COONa | Acetic acid | 4.76 | Weakly basic due to acetate hydrolysis | About 8.8 to 8.9 |
| NaCN | HCN | 9.21 | More basic because CN– is a stronger conjugate base | About 11.1 |
Common mistakes when solving NaCN pH problems
One of the biggest mistakes is assuming the concentration of hydroxide equals the concentration of sodium cyanide. That would only be true for a strong base that completely dissociates to yield OH– directly, such as NaOH. Sodium cyanide does not contain hydroxide. It produces OH– only through equilibrium hydrolysis, so the hydroxide concentration is much lower than 0.100 M.
Another common mistake is using the Ka expression directly for HCN without converting to Kb. In this problem, you are not given an acid solution of HCN. You are given the salt containing its conjugate base. The chemistry in solution is dominated by the basic behavior of CN–, not the acidic dissociation of HCN as a starting solute.
A third frequent error is forgetting temperature. The value pH + pOH = 14 is exact only at 25 degrees C where Kw = 1.0 x 10^-14. If your course or lab specifies a different temperature, use the temperature-adjusted value of Kw. The calculator above includes a few standard temperature assumptions to show how the result can shift slightly.
When the 5 percent rule matters
The weak-base approximation is valid when the computed x is less than about 5 percent of the initial concentration. For 0.100 M NaCN, the estimate gives x ≈ 0.00127 M. Dividing by 0.100 M gives 1.27 percent, which is safely below 5 percent. Therefore the approximation is justified. If you were working with much more dilute sodium cyanide, the hydrolysis fraction would be larger, and the exact quadratic solution would become more important.
Practical interpretation of the result
A pH of around 11.1 tells you the solution is distinctly basic, but it is nowhere near the alkalinity of a 0.1 M sodium hydroxide solution. A 0.1 M NaOH solution would have pOH = 1 and pH = 13. The reason for the difference is fundamental: NaOH is a strong base that supplies hydroxide directly and nearly completely, while CN– is a weak base that establishes an equilibrium with water. This distinction is exactly why equilibrium chemistry matters.
In environmental and industrial contexts, cyanide chemistry is also strongly affected by speciation. The balance between dissolved cyanide ion and molecular HCN depends on pH. Lower pH shifts the system toward HCN, which is volatile and highly toxic. At higher pH, more of the cyanide remains in ionic form. That broader chemistry helps explain why the pH of cyanide-containing solutions is monitored carefully in industrial process control and environmental management. If you want high-quality background reading, see resources from the U.S. Environmental Protection Agency, the CDC Agency for Toxic Substances and Disease Registry, and educational materials from university-level chemistry resources.
Short worked example
- Given: 0.100 M NaCN
- Take HCN pKa = 9.21, so Ka = 6.2 x 10^-10
- Compute Kb = Kw / Ka = 1.0 x 10^-14 / 6.2 x 10^-10 = 1.61 x 10^-5
- Set up Kb = x^2 / (0.100 – x)
- Approximate x = sqrt(1.61 x 10^-6) = 1.27 x 10^-3
- Then pOH = 2.90
- Finally pH = 11.10
Final answer
Using standard 25 degrees C data and a typical HCN pKa of 9.21, the pH of a 0.1 M sodium cyanide solution is approximately 11.10. The calculation is based on cyanide hydrolysis as a weak base, not on direct hydroxide release. If your textbook or instructor uses a slightly different Ka or pKa for HCN, your result may vary slightly, but it should still fall very close to 11.1.