Calculate the pH of 8.50 x 10-5 M HCN
This premium calculator solves the pH of dilute hydrocyanic acid solutions using weak acid equilibrium. It includes an exact calculation that accounts for water autoionization, a fast approximation, and a visual concentration chart for HCN, H+, and CN–.
HCN pH Calculator
Default inputs represent the problem: calculate the pH of 8.50 x 10^-5 M HCN.
Ready to calculate
Enter or keep the default values and click Calculate pH.
How to calculate the pH of 8.50 x 10-5 M HCN
To calculate the pH of 8.50 x 10^-5 M HCN, you need to recognize that hydrocyanic acid is a weak acid. That means it does not ionize completely in water. Instead of assuming that the hydrogen ion concentration equals the initial acid concentration, as you would for a strong acid, you must use an equilibrium expression based on the acid dissociation constant, Ka. For HCN at 25 C, a commonly used value is Ka = 6.2 x 10^-10, which corresponds to a pKa near 9.21.
Step 1: Write the balanced ionization reaction
The first step is to write the equilibrium reaction for hydrocyanic acid in water:
Because water is the solvent, it is not included in the equilibrium expression. The acid dissociation expression is:
Since HCN is weak, the hydrogen ion concentration formed at equilibrium is much smaller than the initial acid concentration in most routine classroom examples. That is why the weak acid approximation often works well.
Step 2: Set up an ICE table
An ICE table tracks Initial, Change, and Equilibrium concentrations:
- Initial [HCN] = 8.50 x 10^-5 M
- Initial [H+] from the acid is approximately 0
- Initial [CN–] = 0
If x dissociates, then:
- [HCN] at equilibrium = 8.50 x 10^-5 – x
- [H+] at equilibrium = x
- [CN–] at equilibrium = x
Substitute these into the equilibrium expression:
Step 3: Use the weak acid approximation
Because Ka is very small, x is tiny compared with 8.50 x 10^-5. So the denominator can be approximated as 8.50 x 10^-5:
This gives the acid generated hydrogen ion concentration:
Now convert that to pH:
So the standard textbook answer is:
Why this problem is a little more subtle than it looks
This concentration is dilute enough that the natural hydrogen ion concentration of pure water, 1.0 x 10^-7 M at 25 C, is no longer completely negligible. The H+ generated by HCN is only a little larger than the pure water baseline. That means a more exact treatment should include water autoionization. When you do that, the exact pH comes out slightly lower than the value predicted by a weak acid approximation alone, but the result still sits very close to 6.64.
In practical problem solving, teachers and textbooks often accept the weak acid approximation because it highlights the main concept: HCN is weak, so use equilibrium rather than strong acid dissociation. However, in analytical chemistry or software modeling, the exact numerical solution is usually preferred.
Exact treatment using charge balance and Kw
For greater accuracy, you can combine the weak acid equilibrium with charge balance and the water ion product. At 25 C, Kw = 1.0 x 10^-14. The exact solution can be obtained numerically, which is what the calculator above does by default.
This exact approach is especially helpful for:
- Very dilute weak acid solutions
- Very weak acids where acid ionization is comparable to water ionization
- High precision laboratory work
- Software tools, simulators, and engineering calculations
For the concentration in this problem, the exact answer remains in the neighborhood of pH 6.64, confirming the weak acid logic while improving rigor.
How strong is HCN compared with other weak acids?
HCN is a very weak acid. Its pKa near 9.2 means it is much less dissociated in water than acids like HF or acetic acid. This explains why even at 8.50 x 10^-5 M, the solution is only mildly acidic. The table below compares common weak acids using representative 25 C values.
| Acid | Formula | Approximate Ka at 25 C | Approximate pKa | Relative acidity vs HCN |
|---|---|---|---|---|
| Hydrocyanic acid | HCN | 6.2 x 10^-10 | 9.21 | Baseline |
| Acetic acid | CH3COOH | 1.8 x 10^-5 | 4.76 | About 29,000 times larger Ka |
| Hypochlorous acid | HOCl | 3.0 x 10^-8 | 7.52 | About 48 times larger Ka |
| Hydrofluoric acid | HF | 6.8 x 10^-4 | 3.17 | About 1.1 million times larger Ka |
This comparison helps explain why HCN solutions often have pH values that may surprise students. Even though cyanide chemistry is medically and environmentally important, the acid itself is weak from an acid base perspective.
Numerical comparison at different HCN concentrations
The next table shows how dilute HCN solutions behave at 25 C using the common weak acid estimate pH ≈ -log(√(KaC)). These values illustrate the logarithmic nature of pH and why concentration changes do not shift pH linearly.
| Initial [HCN] | Estimated [H+] | Estimated pH | Percent ionization |
|---|---|---|---|
| 1.0 x 10^-2 M | 2.49 x 10^-6 M | 5.60 | 0.0249% |
| 1.0 x 10^-3 M | 7.87 x 10^-7 M | 6.10 | 0.0787% |
| 8.50 x 10^-5 M | 2.30 x 10^-7 M | 6.64 | 0.270% |
| 1.0 x 10^-5 M | 7.87 x 10^-8 M | 7.10 before water correction | 0.787% |
The last row is especially informative. If you rely only on the approximation, the pH can drift toward or above neutral, which signals that the water contribution matters and the exact method should be used.
Common mistakes students make
- Assuming HCN is a strong acid and setting [H+] = 8.50 x 10^-5 M directly. That would give a pH near 4.07, which is far too acidic.
- Forgetting to square root after multiplying Ka by concentration.
- Using the wrong exponent sign for concentration or Ka.
- Ignoring that 10^-7 M hydrogen ion from water can matter in very dilute solutions.
- Mixing pKa and Ka without converting properly.
A useful reality check is this: if your answer suggests that dilute HCN is as acidic as a moderate strong acid solution, something went wrong.
Why HCN matters beyond the math
Hydrocyanic acid and cyanide compounds matter in toxicology, industrial safety, and environmental regulation. Their acid base chemistry affects volatility, speciation, and transport in water. The protonated form, HCN, is especially significant because it is molecular and can partition differently than CN– under various pH conditions. That makes pH calculations more than just classroom exercises. They connect directly to air exposure risk, wastewater treatment, and hazardous materials handling.
For authoritative background, you can review resources from the Agency for Toxic Substances and Disease Registry, the U.S. Environmental Protection Agency, and the National Institutes of Health PubChem database.
Best method for exam problems
If your chemistry class asks for the pH of 8.50 x 10^-5 M HCN and no additional instructions are given, the accepted path is usually:
- Write the HCN equilibrium reaction.
- Use Ka = [H+][CN–] / [HCN].
- Apply the weak acid approximation x = √(KaC).
- Compute [H+] and then pH.
- Report pH ≈ 6.64.
If the instructor emphasizes precision at low concentration, mention that water autoionization contributes nontrivially and justify using an exact solver. Doing this shows deeper understanding and can earn partial credit even if the teacher intended the simpler approach.
Final answer
Using Ka = 6.2 x 10^-10 for hydrocyanic acid and an initial concentration of 8.50 x 10^-5 M, the weak acid equilibrium calculation gives:
That is the standard answer to the question, calculate the pH of 8.50 x 10^-5 M HCN. The calculator above also shows the exact value with water autoionization included, which is ideal for dilute solution accuracy.