Calculate the pH of a 0.082 M Solution of NaCN
Use this premium chemistry calculator to determine the pH, pOH, hydroxide concentration, and cyanide hydrolysis behavior for an aqueous sodium cyanide solution. The tool applies weak base equilibrium principles using the conjugate acid of cyanide, hydrogen cyanide, to estimate the final basic pH accurately.
NaCN pH Calculator
Expert Guide: How to Calculate the pH of a 0.082 M Solution of NaCN
To calculate the pH of a 0.082 M solution of sodium cyanide, you need to recognize what type of compound NaCN is when dissolved in water. Sodium cyanide is an ionic salt made from sodium hydroxide, which is a strong base, and hydrogen cyanide, which is a weak acid. Because sodium comes from a strong base, the Na+ ion does not significantly affect pH. The important species is the cyanide ion, CN–, which acts as a weak base by reacting with water to produce hydroxide ions. That hydroxide makes the solution basic, so the pH will be greater than 7.
This type of calculation appears often in general chemistry, AP Chemistry, college equilibrium courses, and lab practicals. Students frequently make one of two mistakes: they either treat NaCN like a neutral salt because it is ionic, or they incorrectly use the concentration directly as if CN– were a strong base like OH–. Neither approach is correct. Instead, NaCN must be handled as a weak base equilibrium problem, where the basicity of cyanide is derived from the acid dissociation constant of HCN.
Step 1: Write the dissociation and hydrolysis reactions
First, sodium cyanide dissociates completely in water:
Next, the cyanide ion undergoes hydrolysis:
This reaction shows why the solution becomes basic. Cyanide removes a proton from water, generating hydroxide. Since hydroxide concentration rises, the pH rises as well.
Step 2: Convert the acid constant of HCN into a base constant for CN-
The conjugate acid of cyanide is hydrogen cyanide, HCN. At 25 degrees C, a commonly used value for the acid dissociation constant of HCN is approximately 4.9 × 10-10. To find the base dissociation constant of cyanide, use the relationship:
With Kw = 1.0 × 10-14 and Ka = 4.9 × 10-10:
This tells you cyanide is a weak base, but not an extremely weak one. It hydrolyzes enough to produce a measurable amount of hydroxide, especially at concentrations such as 0.082 M.
Step 3: Set up the ICE table
Now use an ICE table for the equilibrium:
Initial: 0.082 0 0
Change: -x +x +x
Equilibrium: 0.082 – x x x
The equilibrium expression is:
Substitute Kb = 2.04 × 10-5:
Step 4: Solve for hydroxide concentration
In many classroom settings, you can use the weak base approximation because x is small compared with 0.082. That gives:
So the hydroxide concentration is about 1.29 × 10-3 M. Because this is less than 5 percent of the initial concentration, the approximation is reasonable. A quadratic solution gives a nearly identical answer and is what the calculator above uses internally for improved accuracy.
Step 5: Calculate pOH and pH
Now calculate pOH:
Then use:
The pH of a 0.082 M NaCN solution is therefore approximately 11.11 at 25 degrees C when using Ka(HCN) = 4.9 × 10-10.
Why the solution is basic
Understanding the qualitative chemistry matters as much as getting the right number. Sodium cyanide is not acidic because it does not donate protons. It is not neutral because CN– is the conjugate base of a weak acid. The weaker the acid, the stronger its conjugate base tends to be. Since HCN is weak, CN– has enough basic strength to pull protons from water and generate hydroxide. That basic hydrolysis drives the pH above 7.
- If the anion comes from a strong acid, it is usually pH neutral.
- If the anion comes from a weak acid, it usually makes the solution basic.
- If the cation comes from a weak base, it can make the solution acidic.
- Na+ is neutral, so all pH behavior comes from CN–.
Comparison table: common weak base salts in water
| Salt | Active basic ion | Conjugate acid | Typical acid constant of conjugate acid | General pH behavior |
|---|---|---|---|---|
| NaCN | CN– | HCN | 4.9 × 10-10 | Clearly basic |
| CH3COONa | CH3COO– | Acetic acid | 1.8 × 10-5 | Mildly basic |
| NaF | F– | HF | 6.8 × 10-4 | Slightly basic |
The comparison is useful because it shows why cyanide gives a more basic solution than acetate or fluoride at the same molarity. HCN is much weaker than acetic acid or HF, so CN– is a stronger conjugate base than acetate or fluoride.
Approximation check and percent hydrolysis
When using the approximation x << C, you should check whether it is justified. For the NaCN example:
Because 1.57 percent is well under 5 percent, the approximation is valid. In other words, only a small fraction of the cyanide ions hydrolyze. Most remain as CN–, but enough react to produce a distinctly basic pH.
Exact versus approximate calculation
For a more rigorous result, solve the quadratic form of the equilibrium expression:
Then compute:
This produces almost the same hydroxide concentration as the square root approximation for 0.082 M NaCN. In practical classroom work, both methods lead to a pH near 11.11, although the exact value may vary slightly depending on which Ka for HCN your textbook or professor uses.
Data table: expected pH of NaCN solutions at 25 degrees C
| NaCN concentration (M) | Calculated [OH-] (M) | Approximate pOH | Approximate pH |
|---|---|---|---|
| 0.010 | 4.52 × 10-4 | 3.34 | 10.66 |
| 0.050 | 1.01 × 10-3 | 3.00 | 11.00 |
| 0.082 | 1.28 × 10-3 | 2.89 | 11.11 |
| 0.100 | 1.42 × 10-3 | 2.85 | 11.15 |
| 0.500 | 3.18 × 10-3 | 2.50 | 11.50 |
This table highlights an important trend: as NaCN concentration increases, the solution becomes more basic, but pH does not rise linearly with concentration because the logarithmic pH scale compresses changes in hydroxide concentration.
Common mistakes students make
- Treating NaCN as a strong base. Only strong bases like NaOH dissociate to release hydroxide directly. NaCN does not contain OH–; it generates OH– only through hydrolysis.
- Using Ka instead of Kb. Since CN– is acting as a base, you need Kb, which must be calculated from the Ka of HCN.
- Ignoring the conjugate pair relationship. Remember that KaKb = Kw for conjugate acid-base pairs at the same temperature.
- Confusing pOH and pH. You find [OH–] first, then pOH, then convert to pH.
- Forgetting temperature assumptions. The common relation pH + pOH = 14.00 applies at 25 degrees C using Kw = 1.0 × 10-14.
Authoritative references for equilibrium constants and water chemistry
For deeper verification and formal reference material, consult these authoritative resources:
- U.S. Environmental Protection Agency cyanide resources
- NIST Chemistry WebBook
- Chemistry educational materials hosted by university partners
Final answer summary
To calculate the pH of a 0.082 M solution of NaCN, treat cyanide as a weak base. Use the Ka of HCN to calculate Kb for CN–, set up the hydrolysis equilibrium, solve for hydroxide concentration, then determine pOH and pH. With Ka(HCN) = 4.9 × 10-10 and Kw = 1.0 × 10-14, the pH comes out to approximately 11.11 at 25 degrees C. That result confirms sodium cyanide forms a distinctly basic aqueous solution.