Calculate The Ph Of A 0.300 M Hcn Solution.

Use this premium weak-acid calculator to solve the pH of hydrocyanic acid solutions with an exact equilibrium method, compare the exact answer to the common approximation, and visualize how much HCN remains undissociated at equilibrium.

Expert Guide: How to Calculate the pH of a 0.300 M HCN Solution

If you need to calculate the pH of a 0.300 M HCN solution, the key idea is that hydrocyanic acid is a weak acid, not a strong acid. That means it does not fully ionize in water. Instead, only a very small fraction of the HCN molecules donate protons to water, producing hydronium ions and cyanide ions. Because pH depends directly on the hydronium concentration, the problem becomes an equilibrium calculation rather than a simple concentration conversion.

Hydrocyanic acid dissociates according to the equilibrium:

HCN(aq) ⇌ H⁺(aq) + CN^–(aq)

The acid dissociation constant for HCN at 25 degrees C is commonly listed near 4.9 × 10^-10. Since that value is very small, HCN is a weak acid, which means a 0.300 M solution remains mostly as undissociated HCN at equilibrium. The practical consequence is that the pH of a 0.300 M HCN solution is not anywhere near as low as the pH of a 0.300 M strong acid such as HCl. Instead, the pH stays in the mildly acidic region.

The exact equilibrium setup

To calculate the pH of a 0.300 M HCN solution rigorously, set up an ICE table:

• Initial: [HCN] = 0.300, [H⁺] = 0, [CN^–] = 0
• Change: [HCN] = -x, [H⁺] = +x, [CN^–] = +x
• Equilibrium: [HCN] = 0.300 – x, [H⁺] = x, [CN^–] = x

Now substitute those equilibrium concentrations into the Ka expression:

Ka = [H⁺][CN^–] / [HCN]

So for this problem:

4.9 × 10^-10 = x² / (0.300 – x)

Because Ka is so small, x will be tiny compared with 0.300, and many chemistry courses allow the approximation 0.300 – x ≈ 0.300. That gives:

x ≈ √(Ka × C) = √[(4.9 × 10^-10)(0.300)]

This yields x ≈ 1.21 × 10^-5 M, which is the hydronium concentration. Then:

pH = -log[H⁺] = -log(1.21 × 10^-5) ≈ 4.92

If you use the exact quadratic solution instead of the approximation, you get essentially the same value to the usual number of reported decimal places. That is why the pH of a 0.300 M HCN solution is approximately 4.92.

Bottom line: For a 0.300 M HCN solution using Ka = 4.9 × 10^-10, the pH is about 4.92. The exact and approximate methods agree extremely well because HCN ionizes only slightly.

Why the answer is not close to pH 1

Students often expect any acid with a concentration around 0.300 M to have a very low pH. That intuition comes from strong acids, which dissociate essentially completely. If you had 0.300 M HCl, the hydronium concentration would be about 0.300 M, and the pH would be around 0.52. But HCN is weak. The Ka tells you that only a tiny fraction of molecules ionize, so the hydronium concentration is on the order of 10^-5 M rather than 10^-1 M. That difference of about four orders of magnitude completely changes the pH.

Step-by-step procedure you can use on exams

1. Write the balanced acid dissociation equation: HCN ⇌ H⁺ + CN^–.
2. Set up an ICE table with initial concentration 0.300 M for HCN and 0 for products.
3. Let x represent the amount dissociated.
4. Write the equilibrium expression: Ka = x² / (0.300 – x).
5. Use either the exact quadratic formula or the weak-acid approximation.
6. Find x, which equals [H⁺].
7. Calculate pH using pH = -log[H⁺].
8. Check whether the approximation is valid by verifying that x is less than 5% of 0.300.

For HCN, the approximation is excellent because the percent ionization is extremely small:

% ionization = (x / 0.300) × 100 ≈ (1.21 × 10^-5 / 0.300) × 100 ≈ 0.004%

That is far below 5%, so the shortcut is fully justified.

Exact solution versus approximation

It is useful to understand what the exact solver is doing. Rearranging the Ka equation gives:

x² + Ka x – KaC = 0

Using the quadratic formula:

x = [-Ka + √(Ka² + 4KaC)] / 2

This exact form avoids the assumption that 0.300 – x can be simplified to 0.300. In weak acids like HCN, the difference is negligible, but in somewhat stronger weak acids or more dilute solutions, the exact approach can matter more. A high-quality calculator should therefore let you switch between both methods, which is exactly what the calculator above does.

Comparison table: HCN versus stronger and weaker common acids

Acid	Typical Ka at 25 degrees C	pKa	Approximate pH at 0.300 M	Interpretation
Hydrochloric acid, HCl	Very large, effectively complete dissociation	Strong acid	0.52	Nearly all molecules donate H^+, so pH is very low.
Formic acid, HCOOH	1.8 × 10^-4	3.75	2.13	Weak acid, but much stronger than HCN.
Acetic acid, CH3COOH	1.8 × 10^-5	4.76	2.63	Classic weak acid example used in introductory chemistry.
Hydrocyanic acid, HCN	4.9 × 10^-10	9.31	4.92	Very weak acid, so only a tiny fraction ionizes.

This comparison makes the chemistry intuitive. The smaller the Ka, the less an acid dissociates and the higher the pH at the same formal concentration. HCN is many orders of magnitude weaker than acetic acid, so a 0.300 M HCN solution has a much less acidic pH than a 0.300 M acetic acid solution.

Data table: What equilibrium looks like in a 0.300 M HCN solution

Quantity	Approximate value	Meaning
Initial [HCN]	0.300 M	Formal concentration placed in water.
Equilibrium [H^+]	1.21 × 10^-5 M	Determines the pH of the solution.
Equilibrium [CN^–]	1.21 × 10^-5 M	Produced in a 1:1 ratio with H^+.
Remaining [HCN]	0.299988 M	Shows that almost all HCN remains undissociated.
Percent ionization	0.004%	Confirms that HCN is extremely weak under these conditions.

When the square-root shortcut works

The weak-acid shortcut is widely taught because it saves time. You can use it when the dissociation is small relative to the initial concentration. A common classroom check is the 5% rule. If x/C is less than 5%, then replacing C – x with C introduces little error. In this case, x/C is about 0.0000403, or 0.00403%, so the approximation is much more than acceptable.

Still, it is smart to know the exact method because not every weak-acid calculation behaves this cleanly. If Ka is larger, or if the initial concentration is much smaller, the difference between exact and approximate answers can become meaningful. That is particularly true in advanced chemistry, environmental analysis, and quantitative laboratory work.

Common mistakes when you calculate the pH of a 0.300 M HCN solution

• Treating HCN as a strong acid. This produces a wildly incorrect pH near 0.5 instead of 4.9.
• Using pKa directly as pH. pKa describes acid strength, not the pH of a particular solution.
• Forgetting the ICE table. Weak-acid calculations require equilibrium concentrations, not just the starting molarity.
• Ignoring significant figures. Most textbook answers report pH near 4.92 with reasonable precision based on Ka.
• Using the wrong Ka value. Different references may list slightly different values around the same order of magnitude, so small pH differences can occur.

Why HCN matters in chemistry and environmental science

Hydrocyanic acid is more than a textbook weak-acid example. It is also chemically and toxicologically important. In aqueous systems, the HCN/CN^– balance depends strongly on pH. At lower pH, the protonated form HCN is favored; at higher pH, cyanide ion becomes more important. Understanding this equilibrium is central in analytical chemistry, industrial safety, environmental monitoring, and toxicology. That is one reason weak-acid calculations involving HCN continue to appear in coursework and professional training.

The pKa of HCN is around 9.2 to 9.3, which means that near neutral pH most cyanide is present as HCN rather than CN^–. In strongly basic solutions, more cyanide shifts into the deprotonated CN^– form. That broader acid-base framework helps explain why the weak-acid calculation for a pure HCN solution gives a modestly acidic pH, not an extremely low one.

Authority sources for further reading

• CDC NIOSH: Hydrogen Cyanide reference information
• U.S. EPA cyanide chemistry and environmental guidance
• Purdue University: weak acid equilibrium methods

Final answer summary

To calculate the pH of a 0.300 M HCN solution, use the weak-acid equilibrium expression with Ka ≈ 4.9 × 10^-10. Solving for the hydronium concentration gives about 1.21 × 10^-5 M. Taking the negative logarithm gives a pH of approximately 4.92. Because the percent ionization is only about 0.004%, the approximation x ≈ √(KaC) is highly reliable here, although the exact quadratic method reaches essentially the same answer.

In short, if your chemistry assignment asks you to calculate the pH of a 0.300 M HCN solution, the correct result is pH ≈ 4.92, provided you use Ka near 4.9 × 10^-10 at 25 degrees C. Use the calculator above to confirm the number, test alternate Ka values from your textbook, and visualize how overwhelmingly the equilibrium favors undissociated HCN.