Calculate the pH of a 0.500 M HCN Solution
Use this premium weak-acid calculator to determine the hydrogen ion concentration, pH, pOH, and percent ionization for hydrocyanic acid. The calculator supports an exact quadratic solution and an approximation check, then visualizes the equilibrium composition with a responsive Chart.js graph.
HCN pH Calculator
Enter the concentration of HCN and its acid dissociation constant, then choose the calculation method. The default values correspond to a standard textbook problem for a 0.500 M HCN solution.
Click Calculate pH to solve for a 0.500 M HCN solution.
Expert Guide: How to Calculate the pH of a 0.500 M HCN Solution
Hydrocyanic acid, written as HCN, is a classic example of a weak acid. That means it does not ionize completely in water. When you are asked to calculate the pH of a 0.500 M HCN solution, the chemistry is not handled the same way as a strong acid such as HCl. Instead of assuming that the acid concentration equals the hydrogen ion concentration, you must use an equilibrium approach based on the acid dissociation constant, Ka.
This matters because the pH depends on how much HCN actually dissociates into H+ and CN−. HCN is a very weak acid, so only a small fraction of the original 0.500 M concentration becomes hydrogen ions. As a result, the pH is much higher than students often expect when they first see a relatively large molarity. A concentrated weak acid can still have a moderate pH because the acid remains mostly undissociated.
Step 1: Write the Equilibrium Reaction
The first step is to write the acid dissociation equation in water:
The equilibrium expression is:
For HCN at 25 degrees Celsius, many general chemistry references use a Ka value close to 6.2 × 10−10. Some sources list values in a nearby range because dissociation constants can vary slightly by reference, ionic strength assumptions, or rounding conventions. For standard homework and introductory chemistry work, 6.2 × 10−10 is a common and reliable value.
Step 2: Set Up the ICE Table
Because HCN is weak, you need an equilibrium setup. The most common method uses an ICE table, which stands for Initial, Change, and Equilibrium.
| Species | Initial (M) | Change (M) | Equilibrium (M) |
|---|---|---|---|
| HCN | 0.500 | -x | 0.500 – x |
| H+ | 0 | +x | x |
| CN− | 0 | +x | x |
Substitute those equilibrium concentrations into the Ka expression:
This becomes:
Step 3: Solve for x, the Hydrogen Ion Concentration
Since HCN is very weak, the amount dissociated is tiny compared with 0.500 M. That lets us make the standard weak-acid approximation:
Then the equation simplifies to:
That means:
Step 4: Convert Hydrogen Ion Concentration to pH
Use the definition of pH:
So the calculated pH of a 0.500 M HCN solution is:
If you solve the full quadratic equation instead of using the approximation, you get essentially the same answer because x is extremely small relative to 0.500 M. That is why the approximation is valid here.
Why the Approximation Works So Well
In weak-acid equilibrium problems, chemists often use the 5 percent rule. If the calculated x is less than 5 percent of the initial acid concentration, then subtracting x from the initial concentration barely changes the denominator and the approximation is acceptable.
For this case:
That is far less than 5 percent, so the approximation is excellent. In fact, it is not merely acceptable, it is nearly exact for practical classroom calculations.
Exact Solution Using the Quadratic Formula
If you want the mathematically exact solution, start from:
Rearrange:
Plugging in Ka = 6.2 × 10−10 gives:
Solving the quadratic gives x very close to 1.76 × 10−5 M, so the pH still comes out to about 4.75. This is a useful reminder that weak-acid approximations should be checked, but for very small Ka values and substantial initial concentrations, they generally perform very well.
Comparison With Strong Acids and Other Weak Acids
Students sometimes assume that a 0.500 M acid should always be strongly acidic, perhaps with a pH near 0.3 if they are thinking of HCl. HCN behaves very differently. Because it is weak, most of the molecules stay as HCN rather than producing free hydrogen ions. The result is a pH more than four units higher than a strong acid of the same molarity.
| Acid | Typical Ka or Behavior | Initial Concentration (M) | Approximate [H+] (M) | Approximate pH |
|---|---|---|---|---|
| HCl | Strong acid, essentially complete dissociation | 0.500 | 0.500 | 0.30 |
| HCN | Ka ≈ 6.2 × 10−10 | 0.500 | 1.76 × 10−5 | 4.75 |
| Acetic acid | Ka ≈ 1.8 × 10−5 | 0.500 | 3.0 × 10−3 | 2.52 |
The contrast is striking. A 0.500 M HCl solution is strongly acidic because every mole of HCl contributes roughly one mole of H+. A 0.500 M HCN solution contributes only a tiny amount of H+ because the equilibrium lies overwhelmingly to the left.
Interpreting pKa and Acid Strength
Another useful way to understand this problem is through pKa, where pKa = -log(Ka). For HCN:
A larger pKa means a weaker acid. HCN has a significantly larger pKa than acids like acetic acid, so it dissociates much less in water. This explains why its pH remains relatively high even at a substantial concentration of 0.500 M.
| Weak Acid | Typical Ka | Typical pKa | Relative Strength vs HCN |
|---|---|---|---|
| Hydrocyanic acid, HCN | 6.2 × 10−10 | 9.21 | Baseline reference |
| Hypochlorous acid, HOCl | 3.0 × 10−8 | 7.52 | Stronger than HCN |
| Acetic acid, CH3COOH | 1.8 × 10−5 | 4.74 | Much stronger than HCN |
Common Mistakes When Solving This Problem
- Treating HCN as a strong acid. This is the biggest mistake. If you set [H+] equal to 0.500 M, you get a pH of 0.30, which is completely wrong for HCN.
- Using the wrong Ka value. Be sure you are using a Ka for HCN, not another weak acid.
- Forgetting that x represents [H+]. In the ICE table, the increase in H+ is x, which is what you need to convert to pH.
- Not checking the approximation. Although the approximation works extremely well here, you should still understand why it is valid.
- Mixing up pH and pOH. After finding pH, remember that pOH = 14.00 – pH at 25 degrees Celsius.
What the Result Means Chemically
A pH of about 4.75 tells you the solution is acidic, but not strongly acidic. Despite the 0.500 M concentration, the actual hydrogen ion concentration is only around 1.76 × 10−5 M. The rest remains mostly undissociated HCN. This is a hallmark of weak acids: concentration alone does not determine acidity. Acid strength, expressed by Ka or pKa, is just as important.
You can also estimate the equilibrium concentrations after dissociation:
- [H+] ≈ 1.76 × 10−5 M
- [CN−] ≈ 1.76 × 10−5 M
- [HCN] ≈ 0.500 – 0.0000176 ≈ 0.499982 M
Notice how little the HCN concentration changes. This is further evidence that the acid dissociates only minimally.
Quick Solution Summary
- Write the dissociation: HCN ⇌ H+ + CN−
- Use Ka = [H+][CN−]/[HCN]
- Set up the ICE table with initial HCN = 0.500 M
- Solve 6.2 × 10−10 = x²/(0.500 – x)
- Approximate 0.500 – x as 0.500 because x is tiny
- Find x = 1.76 × 10−5 M
- Compute pH = -log(1.76 × 10−5) = 4.75
Safety and Reference Notes
Although this page focuses on academic acid-base calculations, hydrogen cyanide and cyanide chemistry are serious safety topics in real laboratory and industrial settings. If you are studying HCN beyond textbook equilibrium work, use only official safety and toxicology resources and institutional lab protocols.
Helpful authoritative references include: CDC and NIOSH cyanide resources, U.S. EPA cyanide compounds information, and university-level acid-base equilibrium instruction.
Final Answer
Using Ka = 6.2 × 10−10 for hydrocyanic acid, the pH of a 0.500 M HCN solution is approximately 4.75. The hydrogen ion concentration is about 1.76 × 10−5 M, and the percent ionization is only about 0.0035%. That very low ionization is exactly why HCN, despite its substantial molarity, does not produce the extremely low pH associated with strong acids.