Calculate The Ph Of A 0.20 M Solution Of Hcn

Use this interactive weak-acid calculator to find the pH, hydrogen ion concentration, percent ionization, and equilibrium concentrations for hydrocyanic acid. The default values are set for a 0.20 M HCN solution at 25 C.

How to calculate the pH of a 0.20 M solution of HCN

To calculate the pH of a 0.20 M solution of HCN, you need to remember that hydrocyanic acid is a weak acid, not a strong acid. That means it does not ionize completely in water. Instead of assuming that the hydrogen ion concentration equals the starting acid concentration, you must use an equilibrium expression based on the acid dissociation constant, Ka.

The acid dissociation reaction for HCN in water is:

HCN + H2O ⇌ H3O+ + CN-

For a common 25 C reference value, the acid dissociation constant of HCN is approximately 6.2 x 10^-10. This very small Ka tells you that HCN ionizes only slightly. Because the acid is weak, the equilibrium concentration of H3O+ is much smaller than the initial concentration of HCN.

Step by step setup

1. Write the balanced dissociation equation: HCN ⇌ H+ + CN-.
2. Set up an ICE table with initial, change, and equilibrium concentrations.
3. Let x represent the amount of HCN that ionizes.
4. At equilibrium, [H+] = x and [CN-] = x, while [HCN] = 0.20 – x.
5. Use the equilibrium expression: Ka = x^2 / (0.20 – x).
6. Solve for x exactly with the quadratic formula, or use the weak-acid approximation if x is very small compared with 0.20.
7. Convert hydrogen ion concentration to pH with pH = -log10[H+].

ICE table for 0.20 M HCN

Species	Initial (M)	Change (M)	Equilibrium (M)
HCN	0.20	-x	0.20 – x
H+	0	+x	x
CN-	0	+x	x

Plugging these equilibrium concentrations into the Ka expression gives:

6.2 x 10^-10 = x^2 / (0.20 – x)

Since HCN is a weak acid and Ka is tiny, x is much smaller than 0.20. In many introductory chemistry problems, you can use the approximation:

0.20 – x ≈ 0.20

That simplifies the equation to:

x^2 = (6.2 x 10^-10)(0.20) = 1.24 x 10^-10

x = 1.11 x 10^-5 M

Because x represents the hydrogen ion concentration, [H+] = 1.11 x 10^-5 M. Now convert to pH:

pH = -log10(1.11 x 10^-5) ≈ 4.95

So, the pH of a 0.20 M solution of HCN is approximately 4.95. If you solve with the exact quadratic equation instead of the approximation, you get essentially the same answer to ordinary significant figures.

Why HCN has a relatively high pH compared with strong acids

Students often find this result surprising. A 0.20 M acid solution sounds concentrated, so it is tempting to expect a very low pH. But acid strength and acid concentration are not the same thing. HCN is present at a substantial concentration, yet it donates protons only weakly. Most of the HCN molecules remain undissociated in water.

Compare HCN with a strong acid like HCl. If you had a 0.20 M HCl solution, the acid would dissociate nearly completely, so [H+] would be close to 0.20 M. The pH would then be:

pH = -log10(0.20) ≈ 0.70

That is more than four pH units lower than the HCN case. Since each pH unit corresponds to a factor of 10 in hydrogen ion concentration, the strong-acid solution is dramatically more acidic.

Key conceptual difference: strength versus concentration

• Concentration tells you how much acid is dissolved.
• Strength tells you how completely the acid ionizes.
• HCN is weak, so only a tiny fraction ionizes.
• HCl is strong, so almost all of it produces H+ in solution.

Exact solution versus approximation

In many chemistry classes, you are taught to check whether the weak-acid approximation is valid by comparing x to the initial concentration. The usual rule of thumb is that if x is less than 5 percent of the starting concentration, the approximation is considered acceptable.

For 0.20 M HCN:

percent ionization = (1.11 x 10^-5 / 0.20) x 100 ≈ 0.0056%

That is far below 5 percent, so the approximation is excellent here. Still, it is useful to know the exact formula for a weak monoprotic acid:

x = (-Ka + sqrt(Ka^2 + 4KaC)) / 2

In this expression, C is the initial acid concentration and x is the equilibrium [H+]. The calculator above can use either the exact method or the approximation so you can compare them directly.

Comparison data table: HCN versus other acids at 0.20 M

The table below highlights how weak HCN is compared with several familiar acids. The pH values for the weak acids are estimated using the standard weak-acid relation and typical 25 C Ka values, while the strong acid is treated as fully dissociated.

Acid	Typical Ka or behavior	Initial concentration (M)	Approximate [H+] (M)	Approximate pH
HCN	Ka = 6.2 x 10^-10	0.20	1.11 x 10^-5	4.95
CH3COOH	Ka = 1.8 x 10^-5	0.20	1.90 x 10^-3	2.72
HF	Ka = 6.8 x 10^-4	0.20	1.17 x 10^-2	1.93
HCl	Strong acid, nearly complete dissociation	0.20	0.20	0.70

This comparison makes the point very clearly: HCN is much weaker than acetic acid and dramatically weaker than hydrofluoric acid. Even at the same starting concentration, its pH is much higher because it generates far fewer hydrogen ions.

Derived values for a 0.20 M HCN solution

When instructors ask you to calculate the pH of a 0.20 M solution of HCN, they may also want related equilibrium quantities. These include the concentration of cyanide ion, the remaining concentration of un-ionized HCN, and the percent ionization. Since HCN is monoprotic, every mole of HCN that ionizes forms one mole of H+ and one mole of CN-.

Quantity	Value	Interpretation
Initial [HCN]	0.20 M	Starting concentration before ionization
Equilibrium [H+]	1.11 x 10^-5 M	Determines pH
Equilibrium [CN-]	1.11 x 10^-5 M	Equal to [H+] for a monoprotic weak acid
Equilibrium [HCN]	0.19999 M	Almost all HCN remains undissociated
Percent ionization	0.0056%	Confirms the weak-acid approximation is valid
pH	4.95	Mildly acidic compared with strong acids

Common mistakes when solving this problem

1. Treating HCN like a strong acid. If you set [H+] = 0.20 M directly, you will get pH 0.70, which is completely wrong for HCN.
2. Using pKa incorrectly. If your source gives pKa instead of Ka, convert using Ka = 10^-pKa.
3. Forgetting that water autoionization is negligible here. Because [H+] from HCN is around 10^-5 M, it is much larger than 10^-7 M from pure water.
4. Not checking the approximation. The approximation is valid here, but in other weak-acid problems you should verify percent ionization.
5. Dropping units or significant figures. Keep concentration in molarity and report pH with appropriate precision.

Why the equilibrium matters in real chemistry

Weak-acid calculations are not just classroom exercises. They are central to analytical chemistry, environmental chemistry, toxicology, and industrial process control. Hydrogen cyanide and cyanide-containing systems matter in environmental monitoring and occupational safety because cyanide species are chemically reactive and biologically significant. Understanding how much HCN dissociates helps chemists estimate species distribution, reactivity, and pH-dependent behavior.

In aqueous systems, pH controls whether cyanide is present primarily as HCN or as CN-. Since HCN is the protonated form and CN- is the conjugate base, equilibrium shifts with acidity. At low pH, more HCN is present. At higher pH, more cyanide ion is present. That broader acid-base perspective helps explain why weak-acid calculations remain relevant beyond a single textbook problem.

Authoritative reference sources

• NIST Chemistry WebBook entry for hydrogen cyanide
• CDC and NIOSH information on cyanide chemistry and safety
• Purdue University guide to acid dissociation constants and weak-acid equilibria

Fast exam shortcut for this exact question

If you see the exact prompt, “calculate the pH of a 0.20 M solution of HCN,” and your course allows the weak-acid approximation, you can move quickly:

1. Write x = sqrt(Ka x C).
2. Substitute Ka = 6.2 x 10^-10 and C = 0.20.
3. Get x = sqrt(1.24 x 10^-10) = 1.11 x 10^-5.
4. Take the negative log to get pH = 4.95.

Final answer: a 0.20 M solution of HCN has a pH of about 4.95 at 25 C when Ka is taken as 6.2 x 10^-10.

Final takeaway

The key to solving this problem correctly is recognizing that HCN is a weak acid. For a 0.20 M solution, the hydrogen ion concentration is not 0.20 M, but only about 1.11 x 10^-5 M because the acid dissociates to a very limited extent. Using the equilibrium expression or the valid weak-acid approximation gives a pH near 4.95. Once you understand this process, you can apply the same logic to any weak monoprotic acid problem involving Ka, ICE tables, and equilibrium pH.