Calculate the pH of a 0.025 NaCN Solution
Use this premium calculator to find the pH, pOH, hydroxide concentration, and cyanide hydrolysis behavior for sodium cyanide in water. Ideal for chemistry students, lab users, and anyone reviewing weak-base salt calculations.
NaCN pH Calculator
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How to calculate the pH of a 0.025 NaCN solution
To calculate the pH of a 0.025 NaCN solution, you need to recognize what sodium cyanide does in water. NaCN is a soluble ionic compound, so it dissociates essentially completely into Na+ and CN–. The sodium ion is a spectator ion in acid-base chemistry, but the cyanide ion is the conjugate base of the weak acid HCN. That means CN– reacts with water to generate hydroxide ions, making the solution basic.
The key reaction is:
CN– + H2O ⇌ HCN + OH–
Since hydroxide is produced, the pH will be greater than 7. The full strategy is simple: convert the acid dissociation constant of HCN into the base dissociation constant of CN–, solve for the hydroxide concentration, then calculate pOH and finally pH.
Step 1: Write the initial concentration
A 0.025 M NaCN solution gives an initial cyanide concentration of 0.025 M because sodium cyanide dissociates completely in water:
NaCN → Na+ + CN–
Therefore:
- Initial [CN–] = 0.025 M
- Initial [OH–] from hydrolysis = approximately 0
- Initial [HCN] = 0
Step 2: Convert Ka of HCN to Kb of CN–
The acid dissociation constant of hydrocyanic acid, HCN, at 25 degrees C is commonly taken as about 4.9 × 10-10. Since cyanide is its conjugate base, we use the relationship:
Kb = Kw / Ka
Kb = (1.0 × 10-14) / (4.9 × 10-10) = 2.04 × 10-5
This tells us cyanide is a weak base, but it is strong enough to produce a clearly basic solution at moderate concentration.
Step 3: Set up the equilibrium expression
For the reaction CN– + H2O ⇌ HCN + OH–, let x be the amount of CN– that reacts.
- [CN–] at equilibrium = 0.025 – x
- [HCN] at equilibrium = x
- [OH–] at equilibrium = x
Then:
Kb = x2 / (0.025 – x)
Substituting Kb = 2.04 × 10-5 gives:
2.04 × 10-5 = x2 / (0.025 – x)
Step 4: Solve for hydroxide concentration
In many classroom settings, because Kb is relatively small compared with the starting concentration, the approximation 0.025 – x ≈ 0.025 works very well. That gives:
x = √(Kb × C) = √((2.04 × 10-5) × 0.025)
x = √(5.10 × 10-7) ≈ 7.14 × 10-4 M
So the hydroxide concentration is approximately:
- [OH–] ≈ 7.14 × 10-4 M
If you solve the equation exactly with the quadratic formula, the result changes only slightly, which confirms that the approximation is valid here.
Step 5: Calculate pOH and pH
Once hydroxide concentration is known, compute pOH:
pOH = -log[OH–]
pOH = -log(7.14 × 10-4) ≈ 3.15
Then use:
pH = 14.00 – pOH = 14.00 – 3.15 = 10.85
Therefore, the pH of a 0.025 M NaCN solution at 25 degrees C is approximately 10.85.
Final answer for 0.025 NaCN
Under standard assumptions at 25 degrees C, using Ka(HCN) = 4.9 × 10-10 and Kw = 1.0 × 10-14, the calculated value is:
- [OH–] ≈ 7.14 × 10-4 M
- pOH ≈ 3.15
- pH ≈ 10.85
Why NaCN forms a basic solution
Students often memorize that “a salt of a weak acid and a strong base gives a basic solution,” but it helps to know why. Sodium cyanide comes from:
- NaOH, a strong base
- HCN, a weak acid
The sodium ion has negligible acid-base effect in water, but the cyanide ion still has a strong tendency to accept a proton from water because its conjugate acid, HCN, is weak. That proton transfer produces OH–. The weaker the parent acid, the stronger its conjugate base. Since HCN is weak, CN– is basic enough to raise the pH substantially above neutral.
Approximate method vs exact method
In weak acid and weak base equilibrium problems, it is common to test whether the approximation is acceptable. For 0.025 M NaCN, the hydrolyzed amount x is much smaller than 0.025 M, so the square root method works nicely. However, exact calculations are useful in software, advanced chemistry, or exam checking because they remove approximation error.
| Method | Formula Used | Computed [OH-] | Computed pH | Comment |
|---|---|---|---|---|
| Approximation | x = √(Kb × C) | 7.14 × 10-4 M | 10.85 | Excellent for this concentration and Kb value |
| Exact quadratic | x2 + Kb x – KbC = 0 | 7.04 × 10-4 M | 10.85 | More rigorous and used by this calculator |
Useful equilibrium data for cyanide calculations
The numbers you choose matter. At ordinary room temperature, many textbooks and data references list HCN as a weak acid with Ka around 10-10, often near 4.9 × 10-10 to 6.2 × 10-10 depending on source and rounding. That means the pKa is roughly in the low 9s. Even small differences in Ka can shift the final pH slightly, though not enough to change the overall conclusion that NaCN solutions are basic.
| Quantity | Typical Value at 25 degrees C | Role in Calculation | Practical Effect |
|---|---|---|---|
| Kw of water | 1.0 × 10-14 | Converts Ka to Kb | Sets the pH and pOH relationship |
| Ka of HCN | 4.9 × 10-10 | Measures acid strength of HCN | Lower Ka means stronger conjugate base CN– |
| Kb of CN– | 2.04 × 10-5 | Controls OH– formation | Determines how basic NaCN solution becomes |
| pKa of HCN | About 9.31 | Alternative way to express HCN acidity | Confirms HCN is weak and CN– is basic |
Common mistakes when solving NaCN pH problems
- Treating NaCN like a neutral salt. It is not neutral because CN– hydrolyzes in water.
- Using Ka directly instead of converting to Kb. The reacting species in solution is CN–, not HCN.
- Forgetting that Na+ is a spectator ion. Sodium does not change pH appreciably.
- Mixing up pH and pOH. First solve for [OH–], then pOH, then pH.
- Ignoring temperature dependence. Kw changes with temperature, so pH values can shift if the solution is not at 25 degrees C.
When the 5 percent rule is valid
The approximation method assumes x is small relative to the initial concentration. A standard check is the 5 percent rule:
(x / C) × 100%
For this system:
- x ≈ 7.14 × 10-4 M
- C = 0.025 M
- Percent ionization ≈ (7.14 × 10-4 / 0.025) × 100 ≈ 2.86%
Since 2.86 percent is below 5 percent, the approximation is acceptable. This is why hand calculations and exact calculations agree closely for 0.025 M NaCN.
Real-world safety and chemical context
Sodium cyanide is a highly hazardous chemical. While this page focuses only on equilibrium chemistry, real laboratory handling requires strict safety controls. Cyanide salts can release hydrogen cyanide under acidic conditions, and hydrogen cyanide is extremely toxic. Never use online pH calculations as a substitute for approved safety protocols, institutional guidance, or regulatory handling requirements.
For authoritative background and safety information, consult official sources such as:
- CDC NIOSH
- PubChem, National Library of Medicine
- Chemistry LibreTexts
- U.S. Environmental Protection Agency
- NIST Chemistry WebBook
Summary of the chemistry
To calculate the pH of a 0.025 NaCN solution, start by identifying CN– as a weak base. Use the Ka of HCN to find Kb of cyanide. Then solve the hydrolysis equilibrium for [OH–], calculate pOH, and subtract from 14. With standard data at 25 degrees C, the resulting pH is about 10.85. This value makes sense chemically because cyanide is the conjugate base of a weak acid and therefore raises the hydroxide concentration in water.
Quick recap
- NaCN fully dissociates into Na+ and CN–
- CN– reacts with water to produce OH–
- Kb = Kw / Ka = 2.04 × 10-5
- [OH–] is about 7.1 × 10-4 M
- pOH is about 3.15
- pH is about 10.85