Calculate the pH of 0.35 M HCN
Use this interactive calculator to find the pH of hydrocyanic acid solution from concentration and Ka. The default setup solves the common chemistry problem: what is the pH of 0.35 M HCN?
Enter molarity in mol/L.
Default Ka commonly used in general chemistry.
Results
Click Calculate pH to solve for the pH of 0.35 M HCN and view the equilibrium chart.
How to calculate the pH of 0.35 M HCN
To calculate the pH of 0.35 M HCN, you need to recognize that hydrocyanic acid is a weak acid. That single fact changes the entire method. Unlike a strong acid such as HCl, which is assumed to dissociate nearly completely in water, HCN only ionizes slightly. Because of that, the hydrogen ion concentration is not simply 0.35 M. Instead, you must use the acid dissociation constant, Ka, together with an equilibrium expression.
The dissociation reaction is:
HCN + H2O ⇌ H3O+ + CN-
In many chemistry classes, the Ka value for HCN at 25 C is taken as approximately 4.9 × 10^-10. Since this value is very small, HCN remains mostly in the undissociated form at equilibrium. That means the pH of a 0.35 M solution will be acidic, but not nearly as acidic as a strong acid at the same concentration.
Bottom line: for 0.35 M HCN using Ka = 4.9 × 10^-10, the equilibrium hydrogen ion concentration is about 1.31 × 10^-5 M, giving a pH of 4.88.
Step 1: Write the equilibrium expression
Start with the acid dissociation constant expression:
Ka = [H+][CN-] / [HCN]
If the initial concentration of HCN is 0.35 M and the amount that ionizes is x, then at equilibrium:
- [HCN] = 0.35 – x
- [H+] = x
- [CN-] = x
Substitute those values into the Ka expression:
4.9 × 10^-10 = x^2 / (0.35 – x)
Step 2: Solve for x
There are two standard ways to solve the equation:
- Use the weak acid approximation, where 0.35 – x is treated as about 0.35 if x is very small.
- Use the exact quadratic solution, which is mathematically more rigorous.
With the approximation:
x^2 / 0.35 = 4.9 × 10^-10
x^2 = 1.715 × 10^-10
x = √(1.715 × 10^-10) ≈ 1.31 × 10^-5
Since x represents the hydrogen ion concentration, [H+] ≈ 1.31 × 10^-5 M.
Step 3: Convert hydrogen ion concentration to pH
Use the pH definition:
pH = -log10[H+]
pH = -log10(1.31 × 10^-5)
pH ≈ 4.88
If you solve the problem using the exact quadratic equation, the answer is effectively the same to standard classroom precision because the acid is so weak and the ionization is such a tiny fraction of the original concentration.
Why HCN does not behave like a strong acid
Students often make the mistake of assuming that every acid concentration can be converted directly into hydrogen ion concentration. That is only valid for strong acids in introductory chemistry when complete dissociation is assumed. HCN is different because its Ka is very small. A Ka of 4.9 × 10^-10 means the equilibrium strongly favors the reactant side, so most of the dissolved HCN remains as HCN molecules instead of forming H+ and CN- ions.
This weak ionization leads to a pH that is far higher than what you would see for a strong acid at the same formal concentration. For example, a 0.35 M solution of HCl would have a pH close to 0.46 because it dissociates almost completely. By contrast, 0.35 M HCN has a pH around 4.88. That difference of more than four pH units corresponds to a dramatic change in hydrogen ion concentration.
ICE table method for 0.35 M HCN
The ICE table approach is one of the clearest ways to set up the problem correctly. ICE stands for Initial, Change, Equilibrium.
| Species | Initial (M) | Change (M) | Equilibrium (M) |
|---|---|---|---|
| HCN | 0.35 | -x | 0.35 – x |
| H+ | 0 | +x | x |
| CN- | 0 | +x | x |
After filling in the ICE table, substitute the equilibrium values into the Ka expression. This structure helps prevent sign errors and reminds you that weak acid problems are equilibrium problems, not simple stoichiometry problems.
Approximation vs exact solution
One of the most useful chemistry skills is knowing when an approximation is justified. For weak acids, chemists often check whether the amount ionized is less than 5 percent of the initial concentration. If it is, then replacing 0.35 – x with 0.35 is considered acceptable.
For 0.35 M HCN:
- Approximate x = 1.31 × 10^-5 M
- Percent ionization = (1.31 × 10^-5 / 0.35) × 100 ≈ 0.00374%
That percentage is far below 5 percent, so the approximation is excellent here. In practical terms, both methods return the same pH to two decimal places.
| Method | Equation Used | [H+] Result | pH | Comment |
|---|---|---|---|---|
| Weak acid approximation | x ≈ √(KaC) | 1.31 × 10^-5 M | 4.88 | Fast and highly accurate for this case |
| Exact quadratic solution | x = (-Ka + √(Ka^2 + 4KaC)) / 2 | 1.31 × 10^-5 M | 4.88 | Best if your instructor requires no approximation |
Comparison with other weak acids
Understanding HCN becomes easier when you compare it to familiar weak acids. Acid strength is commonly measured by Ka or pKa. A larger Ka means stronger acid behavior. HCN is a relatively weak weak acid, which is why even a moderately concentrated solution such as 0.35 M still has a pH near 4.88 instead of something dramatically lower.
| Acid | Typical Ka at 25 C | pKa | Relative Strength vs HCN |
|---|---|---|---|
| Hydrocyanic acid, HCN | 4.9 × 10^-10 | 9.31 | Reference |
| Acetic acid, CH3COOH | 1.8 × 10^-5 | 4.76 | About 36,700 times larger Ka than HCN |
| Hydrofluoric acid, HF | 6.8 × 10^-4 | 3.17 | More than 1,000,000 times larger Ka than HCN |
The comparison shows why HCN is often treated as a classic weak-acid equilibrium problem. If you were solving 0.35 M acetic acid or HF instead, the resulting pH would be significantly lower because those acids ionize more extensively.
How pH changes with HCN concentration
As the concentration of HCN changes, the pH also changes, but not linearly. Because the relationship is governed by equilibrium, reducing concentration does not increase pH by a fixed amount each time. For weak acids in the approximation regime, hydrogen ion concentration scales roughly with the square root of concentration. That means pH shifts more gradually than many students expect.
| HCN Concentration (M) | Estimated [H+] (M) | Approximate pH | Percent Ionization |
|---|---|---|---|
| 1.00 | 2.21 × 10^-5 | 4.66 | 0.00221% |
| 0.35 | 1.31 × 10^-5 | 4.88 | 0.00374% |
| 0.10 | 7.00 × 10^-6 | 5.15 | 0.00700% |
| 0.010 | 2.21 × 10^-6 | 5.66 | 0.0221% |
Notice that as concentration falls, percent ionization rises. This is a common trend for weak electrolytes. Even though the absolute amount of H+ decreases, the fraction of acid molecules that dissociate becomes larger.
Common mistakes when solving the pH of 0.35 M HCN
- Treating HCN as a strong acid. This leads to the incorrect assumption that [H+] = 0.35 M.
- Using pKa incorrectly. If your source gives pKa instead of Ka, convert using Ka = 10^-pKa.
- Forgetting the equilibrium setup. You need an ICE table or an equivalent expression.
- Skipping the 5 percent check. The approximation is valid here, but it is good practice to verify that x is small.
- Confusing concentration with amount. pH depends on molarity, not just moles of HCN present.
Authority sources for acid constants and chemical safety
For reliable chemistry reference data and safety information, use reputable government and university sources. A few strong starting points include:
- NIST Chemistry WebBook for chemical property data and reference information.
- PubChem at the National Institutes of Health for compound identification, hazards, and scientific summaries.
- Chemistry LibreTexts for educational explanations of weak acid equilibria and pH calculations.
Why the answer matters in real chemistry
Calculating the pH of a weak acid is more than a textbook exercise. It demonstrates how equilibrium constants control observable solution behavior. In analytical chemistry, pH affects speciation, buffering, extraction, and reactivity. In environmental chemistry, cyanide-containing species can change form depending on pH. In biochemistry and industrial contexts, even small pH shifts can alter reaction pathways, safety protocols, and waste treatment methods.
For HCN specifically, the weak-acid nature means pH can influence the balance between molecular HCN and ionic CN-. This matters because different forms behave differently in transport, volatility, and toxicity assessments. That is one reason chemists care about accurate equilibrium calculations and not just rough intuition.
Final answer for the pH of 0.35 M HCN
If you are looking for the short exam-style response, here it is:
- Write the dissociation: HCN ⇌ H+ + CN-
- Use Ka = 4.9 × 10^-10
- Set up Ka = x^2 / (0.35 – x)
- Approximate 0.35 – x ≈ 0.35
- Solve: x ≈ √((4.9 × 10^-10)(0.35)) = 1.31 × 10^-5
- Calculate pH: pH = -log(1.31 × 10^-5) ≈ 4.88
Therefore, the pH of 0.35 M HCN is approximately 4.88.