Calculate the pH of a 0.150 M HCN Solution
Use this interactive weak acid calculator to find the equilibrium hydrogen ion concentration, pH, percent ionization, and the remaining HCN concentration for a hydrocyanic acid solution.
HCN pH Calculator
HCN ⇌ H+ + CN-Ka = [H+][CN-] / [HCN]
Click Calculate pH to solve for the pH of the hydrocyanic acid solution and visualize the equilibrium composition.
Equilibrium Composition Chart
This chart compares the equilibrium concentrations of undissociated HCN, hydrogen ions, and cyanide ions after the acid partially ionizes in water.
How to Calculate the pH of a 0.150 M HCN Solution
To calculate the pH of a 0.150 M HCN solution, you treat hydrocyanic acid as a weak acid rather than a strong acid. That distinction matters because weak acids do not fully dissociate in water. Instead, only a small portion of the original HCN molecules donate protons to water, producing hydronium ions and cyanide ions at equilibrium. Since pH depends on the hydrogen ion concentration, the central task is finding the equilibrium value of [H+].
Hydrocyanic acid is written as HCN, and its dissociation in water can be expressed as:
HCN ⇌ H+ + CN–
The acid dissociation constant, Ka, measures how strongly the acid ionizes. For HCN at 25 C, a commonly used value is approximately 6.2 × 10-10. This is a very small Ka, which immediately tells you HCN is a weak acid. In practical terms, that means the equilibrium hydrogen ion concentration will be much smaller than the initial acid concentration of 0.150 M.
Step 1: Write the Ka expression
For the dissociation reaction of HCN, the equilibrium expression is:
Ka = [H+][CN–] / [HCN]
Suppose the initial concentration of HCN is 0.150 M and the initial concentrations of H+ and CN– from the acid are both 0. If x mol/L of HCN dissociates, then at equilibrium:
- [HCN] = 0.150 – x
- [H+] = x
- [CN–] = x
Substituting those values into the Ka expression gives:
6.2 × 10-10 = x2 / (0.150 – x)
Step 2: Solve for x
Because HCN is weak, x is extremely small compared with 0.150. In many chemistry classes, this lets you use the standard weak acid approximation:
0.150 – x ≈ 0.150
Then the equation simplifies to:
6.2 × 10-10 = x2 / 0.150
Multiply both sides by 0.150:
x2 = 9.30 × 10-11
Take the square root:
x = 9.64 × 10-6 M
Since x represents [H+], the hydrogen ion concentration is approximately 9.64 × 10-6 M.
Step 3: Convert [H+] to pH
Now apply the pH definition:
pH = -log[H+]
Substitute the value of [H+]:
pH = -log(9.64 × 10-6) ≈ 5.016
Why HCN Has a Relatively High pH for an Acid
Students are often surprised that a 0.150 M acid solution has a pH around 5 instead of 1 or 2. The reason is that concentration alone does not determine pH. Acid strength is just as important. A strong acid such as HCl dissociates almost completely, so a 0.150 M HCl solution would produce nearly 0.150 M H+ and have a pH near 0.82. HCN behaves very differently because only a tiny fraction of dissolved molecules ionize.
For this specific HCN solution, the percent ionization is:
(9.64 × 10-6 / 0.150) × 100 ≈ 0.00643%
That means over 99.99% of the HCN remains undissociated at equilibrium. This is exactly what you expect from a weak acid with a very small Ka.
Exact solution versus approximation
The weak acid approximation is useful, but it is always good chemistry practice to understand the exact treatment. Using the quadratic form of
Ka = x2 / (C – x)
you can rewrite the expression as:
x2 + Kax – KaC = 0
For C = 0.150 M and Ka = 6.2 × 10-10, the positive root gives x ≈ 9.6415 × 10-6 M, which is essentially the same as the approximation. The difference is so small because x is tiny relative to 0.150.
| Method | [H+] (M) | Calculated pH | Difference from exact |
|---|---|---|---|
| Exact quadratic solution | 9.6415 × 10-6 | 5.0159 | 0% |
| Weak acid approximation | 9.6437 × 10-6 | 5.0158 | Less than 0.03% |
ICE Table Setup for 0.150 M HCN
An ICE table is the cleanest way to organize weak acid problems.
| Species | Initial (M) | Change (M) | Equilibrium (M) |
|---|---|---|---|
| HCN | 0.150 | -x | 0.150 – x |
| H+ | 0 | +x | x |
| CN– | 0 | +x | x |
Once the ICE table is written, the equilibrium constant expression follows directly. This is one reason chemistry instructors emphasize ICE tables for acid-base equilibrium. They reduce mistakes, especially sign errors or confusion about which species increase and which decrease.
Common Mistakes When Solving This Problem
- Treating HCN like a strong acid. If you assume full dissociation, you would get pH = -log(0.150) ≈ 0.824, which is completely incorrect for HCN.
- Using the wrong Ka. Different textbooks may round the Ka slightly differently, such as 4.9 × 10-10 or 6.2 × 10-10. Your pH may differ slightly depending on the source value provided by your course.
- Forgetting that x equals [H+]. In a simple monoprotic weak acid problem, the amount dissociated becomes both the hydrogen ion concentration and the conjugate base concentration.
- Skipping the pH step. Solving for x gives the equilibrium hydrogen ion concentration, not the pH itself.
- Using the approximation without checking reasonableness. Although it works beautifully here, in some problems x may not be negligible relative to the initial concentration.
How HCN Compares with Other Weak Acids
HCN is weaker than common acids such as acetic acid and hydrofluoric acid. A smaller Ka means less dissociation and therefore a higher pH when concentrations are comparable. The following table compares several familiar weak acids at 25 C.
| Acid | Formula | Ka at 25 C | pKa | Relative strength vs HCN |
|---|---|---|---|---|
| Hydrocyanic acid | HCN | 6.2 × 10-10 | 9.21 | Baseline |
| Acetic acid | CH3COOH | 1.8 × 10-5 | 4.76 | About 29,000 times larger Ka |
| Hydrofluoric acid | HF | 6.8 × 10-4 | 3.17 | Over 1,000,000 times larger Ka |
| Carbonic acid, first dissociation | H2CO3 | 4.3 × 10-7 | 6.37 | About 690 times larger Ka |
This comparison helps explain why HCN solutions are often only mildly acidic despite moderate formal concentration. Its ionization is extremely limited, so the concentration of free hydrogen ions remains low.
Effect of Concentration on the pH of HCN
For weak acids, pH changes with concentration, but not as drastically as for strong acids. Because [H+] is approximately proportional to the square root of KaC, raising the concentration by a factor of 100 lowers the pH by about 1 unit rather than 2 units. The next table shows how concentration affects the pH of HCN using the same Ka value.
| Initial HCN concentration (M) | Approximate [H+] (M) | Approximate pH | Percent ionization |
|---|---|---|---|
| 0.001 | 7.87 × 10-7 | 6.10 | 0.0787% |
| 0.010 | 2.49 × 10-6 | 5.60 | 0.0249% |
| 0.150 | 9.64 × 10-6 | 5.02 | 0.00643% |
| 1.00 | 2.49 × 10-5 | 4.60 | 0.00249% |
A key trend appears here: as the initial acid concentration increases, the percent ionization decreases. This is a general pattern for weak acids and weak bases. It follows from Le Chatelier’s principle and the mathematical structure of the equilibrium expression.
Why the Result Matters in Chemistry
Knowing how to calculate the pH of a 0.150 M HCN solution is not just a textbook exercise. It reinforces several core ideas in general chemistry:
- The difference between acid strength and acid concentration
- The use of equilibrium constants to predict solution composition
- The interpretation of pH on a logarithmic scale
- The reason weak acids often require approximations or quadratic solutions
- The relationship between Ka, pKa, and ionization percent
These same methods apply to many equilibrium problems involving weak acids, weak bases, buffers, salt hydrolysis, and biological acid-base systems. Once you can confidently solve HCN, you can use the same strategy for countless similar problems.
Quick Problem Solving Checklist
- Write the balanced acid dissociation equation.
- Set up an ICE table using the initial concentration.
- Insert equilibrium concentrations into the Ka expression.
- Solve for x using either the approximation or the quadratic formula.
- Interpret x as [H+].
- Calculate pH using pH = -log[H+].
- Optionally calculate percent ionization to judge whether the approximation was valid.
Final Takeaway
If you are asked to calculate the pH of a 0.150 M HCN solution, the most defensible answer under standard textbook conditions is pH ≈ 5.02, assuming Ka = 6.2 × 10-10 at 25 C. The reason the pH is relatively high is that HCN is a weak acid and ionizes only very slightly in water. The equilibrium hydrogen ion concentration is only about 9.64 × 10-6 M, and the percent ionization is roughly 0.00643%.