Calculate the pH of a 0.020 M Sodium Cyanide Solution
Use this interactive weak-base hydrolysis calculator to determine the pH, pOH, hydroxide concentration, cyanide ion equilibrium, and percent hydrolysis for aqueous sodium cyanide. The default values are preloaded for a 0.020 M NaCN solution at 25 C.
NaCN pH Calculator
Results
Click Calculate pH to solve the equilibrium for a sodium cyanide solution.
Reaction Model
Salt dissociation:
NaCN -> Na+ + CN-
Base hydrolysis:
CN- + H2O ⇌ HCN + OH-
Relationship between constants:
Kb = Kw / Ka
Equilibrium expression:
Kb = [HCN][OH-] / [CN-]
How to Calculate the pH of a 0.020 M Sodium Cyanide Solution
To calculate the pH of a 0.020 M sodium cyanide solution, you treat sodium cyanide as a soluble ionic salt that dissociates essentially completely in water. That first step is straightforward: NaCN separates into sodium ions and cyanide ions. The sodium ion is a spectator ion for acid-base chemistry because it comes from the strong base sodium hydroxide. The cyanide ion, however, is the conjugate base of hydrocyanic acid, HCN, which is a weak acid. That means cyanide reacts with water to form hydroxide ions, making the solution basic.
The key hydrolysis reaction is:
CN- + H2O ⇌ HCN + OH-
Once you identify that reaction, the entire problem becomes a weak-base equilibrium calculation. Since cyanide is the conjugate base of HCN, you usually start with the acid dissociation constant of HCN and convert it to a base dissociation constant for CN-. At 25 C, a common textbook value for the acid dissociation constant of HCN is about 4.9 × 10-10. Using the water ion product, 1.0 × 10-14, you can calculate the cyanide base constant:
Kb = Kw / Ka = (1.0 × 10^-14) / (4.9 × 10^-10) ≈ 2.04 × 10^-5
That value tells you cyanide is a weak base, but not an extremely weak one. In a 0.020 M solution, it hydrolyzes enough to produce a measurable amount of hydroxide. If you let x represent the amount of hydroxide formed at equilibrium, then the ICE setup is:
- Initial: [CN-] = 0.020, [HCN] = 0, [OH-] = 0
- Change: [CN-] = -x, [HCN] = +x, [OH-] = +x
- Equilibrium: [CN-] = 0.020 – x, [HCN] = x, [OH-] = x
Substitute those values into the equilibrium expression:
Kb = x^2 / (0.020 – x)
For a quick estimate, many chemistry students use the weak-base approximation and assume x is small compared with 0.020. That gives:
x ≈ √(Kb × C) = √((2.04 × 10^-5)(0.020)) ≈ 6.39 × 10^-4 M
Because x corresponds to hydroxide concentration, you then calculate pOH:
pOH = -log(6.39 × 10^-4) ≈ 3.19
And therefore:
pH = 14.00 – 3.19 ≈ 10.81
If you solve the quadratic equation instead of using the approximation, the result is almost the same and slightly more accurate. Using the exact equation:
x = (-Kb + √(Kb^2 + 4KbC)) / 2
For C = 0.020 M and Kb ≈ 2.04 × 10-5, the exact hydroxide concentration is about 6.28 × 10-4 M. That gives a pOH near 3.20 and a pH near 10.80. So the standard answer for the pH of a 0.020 M sodium cyanide solution is approximately 10.8 at 25 C.
Why Sodium Cyanide Produces a Basic Solution
This point is important because many acid-base problems become easy once you classify the salt correctly. Sodium cyanide is formed conceptually from sodium hydroxide, a strong base, and hydrocyanic acid, a weak acid. Salts of a strong base and weak acid generally produce solutions with pH values above 7. The sodium ion does not significantly affect pH, but the cyanide ion does. It pulls a proton from water, producing OH-. As hydroxide concentration rises, the solution becomes basic.
Students sometimes ask whether they should use the concentration of sodium cyanide directly as the hydroxide concentration. The answer is no. Unlike sodium hydroxide, sodium cyanide does not release OH- directly upon dissociation. Instead, it creates OH- indirectly through equilibrium hydrolysis. That is why the concentration of hydroxide must be solved with Kb rather than assumed equal to 0.020 M.
Step-by-Step Method for Any NaCN Concentration
- Write the dissociation of NaCN into Na+ and CN-.
- Recognize CN- as the conjugate base of HCN.
- Write the hydrolysis reaction: CN- + H2O ⇌ HCN + OH-.
- Convert Ka of HCN to Kb of CN- using Kb = Kw / Ka.
- Set up an ICE table with initial cyanide concentration equal to the salt concentration.
- Use either the weak-base approximation or solve the exact quadratic equation.
- Find [OH-], then calculate pOH and pH.
That seven-step process works not only for cyanide but also for many salts containing the conjugate bases of weak acids, such as sodium acetate, sodium fluoride, or sodium nitrite. The specific pH differs because each conjugate base has its own Kb value, but the structure of the calculation is the same.
Exact vs Approximate Calculation
For 0.020 M NaCN, the approximation is good because the extent of hydrolysis is only a few percent of the starting concentration. In acid-base equilibrium work, a common rule is that the approximation is acceptable when x is less than 5 percent of the initial concentration. Here, x is around 6.3 × 10-4 M, which is roughly 3.1 percent of 0.020 M. That means the shortcut is reasonable. However, exact solutions are preferable in digital calculators, educational tools, and lab reports because they avoid approximation error and are just as easy for software to evaluate.
| Quantity | Symbol | Value at 25 C | Role in the calculation |
|---|---|---|---|
| Initial NaCN concentration | C | 0.020 M | Starting cyanide concentration after complete salt dissociation |
| Hydrocyanic acid dissociation constant | Ka | 4.9 × 10-10 | Used to derive Kb for CN- |
| Water ion product | Kw | 1.0 × 10-14 | Connects acid and base strengths |
| Cyanide base dissociation constant | Kb | 2.04 × 10-5 | Defines hydrolysis strength of CN- |
| Exact hydroxide concentration | [OH-] | 6.28 × 10-4 M | Determines pOH and pH |
| Final pH | pH | 10.80 | Target result |
Comparison with Other Weak-Base Salt Solutions
One useful way to understand the result is to compare sodium cyanide with other salts of weak acids. A stronger conjugate base gives a higher pH at the same formal concentration. Cyanide is noticeably basic, though not as strongly basic as salts that directly contain hydroxide.
| Salt solution at 0.020 M | Conjugate base | Approximate Kb | Approximate pH |
|---|---|---|---|
| Sodium cyanide | CN- | 2.04 × 10-5 | 10.80 |
| Sodium acetate | CH3COO- | 5.6 × 10-10 | 8.52 |
| Sodium fluoride | F- | 1.47 × 10-11 | 7.73 |
| Sodium formate | HCOO- | 5.6 × 10-11 | 8.01 |
This comparison helps explain why NaCN produces a distinctly basic solution. Hydrocyanic acid is much weaker than acetic acid or hydrofluoric acid, so its conjugate base, CN-, is correspondingly stronger than acetate or fluoride. As a result, NaCN solutions often sit around pH 10 to 11 for moderate concentrations.
Common Mistakes to Avoid
- Treating NaCN like a strong base. It is a salt, not sodium hydroxide. The pH must be found through hydrolysis equilibrium.
- Using Ka directly instead of Kb. Cyanide is the base in solution, so you need Kb or must convert from Ka.
- Forgetting that Na+ is a spectator ion. Sodium does not control the pH here.
- Assuming pH is exactly 14 minus negative log of 0.020. The 0.020 M is the initial cyanide concentration, not the hydroxide concentration.
- Ignoring temperature dependence. Ka and Kw can shift with temperature, so the exact pH may change slightly outside 25 C.
How Accurate Is the 10.80 pH Value?
The answer is highly reliable for standard general chemistry assumptions, but remember that real solutions may differ slightly depending on the chosen reference value for Ka(HCN), ionic strength, temperature, and activity corrections. Introductory and analytical chemistry problems usually assume ideal dilute behavior, 25 C, and Kw = 1.0 × 10-14. Under those conditions, 10.8 is the correct practical answer. If an instructor provides a different Ka value, your final pH might shift by a few hundredths.
Safety and Chemical Context
Sodium cyanide is not just an equilibrium example. It is also an extremely hazardous substance and must be handled under strict safety controls in professional environments. Acidifying cyanide solutions can generate hydrogen cyanide gas, which is highly toxic. That real-world behavior is directly connected to the acid-base chemistry used in this calculation: cyanide and hydrocyanic acid exist in equilibrium, and lower pH shifts more of the cyanide toward HCN.
For authoritative reference material related to cyanide chemistry, toxicology, and chemical properties, consult sources such as the U.S. Environmental Protection Agency cyanide resources, the NIST Chemistry WebBook entry for hydrogen cyanide, and the ATSDR toxic substances fact sheet on cyanide.
Bottom Line
If you are asked to calculate the pH of a 0.020 M sodium cyanide solution, the most important idea is that the cyanide ion is a weak base. Convert Ka of HCN to Kb of CN-, solve for hydroxide concentration using an ICE table, and then convert from pOH to pH. The exact calculation gives a pH of about 10.80, which is the value you should report for a standard 25 C chemistry problem unless your instructor specifies different constants.
Use the calculator above if you want to test other concentrations, compare exact and approximate methods, or explore how changes in Ka affect the final pH. That makes it useful for homework checks, exam review, and chemistry instruction focused on salt hydrolysis and conjugate acid-base relationships.