Calculate The Ph Of A 0.200 M Hcn Solution.

This premium weak-acid calculator solves the equilibrium for hydrocyanic acid using the acid dissociation constant, displays pH, hydrogen ion concentration, percent ionization, and a visual concentration chart. The default settings are preloaded for a 0.200 M HCN solution.

HCN pH Calculator

Weak Acid Equilibrium Summary

• Reaction: HCN ⇌ H⁺ + CN^–
• Ka = [H⁺][CN^–] / [HCN]
• If the initial concentration is C and dissociation is x, then:
• [H⁺] = x
• [CN^–] = x
• [HCN] = C – x
• Ka = x² / (C – x)
• Exact solution: x = (-Ka + √(Ka² + 4KaC)) / 2
• pH = -log₁₀[H⁺]

Expected Result for Default Inputs

For 0.200 M HCN using Ka = 6.2 × 10^-10, the pH is approximately 4.95. Because HCN is a weak acid, only a tiny fraction ionizes in water.

What this calculator shows

• Exact hydrogen ion concentration from equilibrium
• Calculated pH
• Remaining undissociated HCN concentration
• Produced cyanide ion concentration
• Percent ionization

Expert Guide: How to Calculate the pH of a 0.200 M HCN Solution

Calculating the pH of a 0.200 M HCN solution is a classic weak-acid equilibrium problem. HCN, or hydrocyanic acid, is not a strong acid, so it does not dissociate completely in water. That single fact changes the math entirely. 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. For HCN at about 25 degrees C, a commonly used Ka is approximately 6.2 × 10^-10, which tells you that dissociation is very limited. As a result, the pH of a 0.200 M HCN solution is acidic, but not nearly as acidic as a strong acid with the same formal concentration.

The equilibrium reaction is:

HCN(aq) ⇌ H⁺(aq) + CN^–(aq)

Because HCN is weak, most of the dissolved acid remains as HCN molecules, while only a small amount becomes H⁺ and CN^–. The key to solving the problem is to define the amount dissociated as x, write an ICE setup, substitute into the Ka expression, and then solve for x. Once x is known, it becomes the equilibrium hydrogen ion concentration and can be converted into pH with the logarithm formula.

Step-by-Step Setup

Start with the initial concentration of hydrocyanic acid:

• Initial [HCN] = 0.200 M
• Initial [H⁺] ≈ 0 M from the acid itself
• Initial [CN^–] = 0 M

Let x represent the amount of HCN that dissociates:

• Change in [HCN] = -x
• Change in [H⁺] = +x
• Change in [CN^–] = +x

At equilibrium, the concentrations become:

• [HCN] = 0.200 – x
• [H⁺] = x
• [CN^–] = x

Now insert these into the acid dissociation expression:

Ka = [H⁺][CN^–] / [HCN] = x² / (0.200 – x)

Using Ka = 6.2 × 10^-10:

6.2 × 10^-10 = x² / (0.200 – x)

Approximate Method

Because HCN is such a weak acid, x is very small compared with 0.200. That means the denominator 0.200 – x is extremely close to 0.200, so chemists often use the weak-acid approximation:

x² / 0.200 = 6.2 × 10^-10

Rearrange:

x² = (6.2 × 10^-10)(0.200) = 1.24 × 10^-10

Take the square root:

x = 1.11 × 10^-5 M

Since x = [H⁺], the pH is:

pH = -log(1.11 × 10^-5) ≈ 4.95

This is the standard textbook answer for the pH of a 0.200 M HCN solution when using a Ka near 6.2 × 10^-10.

Exact Quadratic Method

For a more rigorous answer, use the exact solution to the equilibrium equation rather than dropping x from the denominator. Starting from:

Ka = x² / (C – x)

Multiply through:

Ka(C – x) = x²

x² + Kax – KaC = 0

Apply the quadratic formula:

x = (-Ka + √(Ka² + 4KaC)) / 2

Substituting Ka = 6.2 × 10^-10 and C = 0.200 gives virtually the same x value, around 1.11 × 10^-5 M. The resulting pH still rounds to about 4.95. In other words, the approximation is excellent here because the amount of ionization is tiny.

The 5 percent rule is satisfied comfortably. Since x is only about 1.11 × 10^-5 M, the percent ionization is about 0.0056 percent, far below 5 percent. That is why the approximation works so well for this HCN problem.

Why HCN Has a Relatively High pH Compared with Strong Acids

Students often expect a 0.200 M acid to have a very low pH. That would be true for a strong acid such as HCl, which dissociates essentially completely. In that case, [H⁺] would be close to 0.200 M and the pH would be around 0.70. HCN behaves very differently because Ka is so small. Only a tiny fraction of the acid molecules produce hydrogen ions. As a result, the pH stays near 4.95, which is acidic but much less acidic than a strong acid of equal concentration.

Acid	Typical Acid Strength Metric	Initial Concentration	Approximate [H^+]	Approximate pH
HCN	Ka ≈ 6.2 × 10^-10	0.200 M	1.11 × 10^-5 M	4.95
Acetic acid	Ka ≈ 1.8 × 10^-5	0.200 M	1.90 × 10^-3 M	2.72
Hydrochloric acid	Strong acid, near complete dissociation	0.200 M	0.200 M	0.70

The comparison above is useful because it highlights what Ka means in practical terms. A lower Ka means less ionization and therefore a higher pH, all else being equal. HCN sits far toward the weak-acid side of the spectrum, so even at 0.200 M it does not flood the solution with hydrogen ions.

Percent Ionization of 0.200 M HCN

Percent ionization is another important quantity because it tells you how much of the original weak acid actually dissociates. The formula is:

Percent ionization = ([H⁺]_eq / [HCN]_initial) × 100

Substitute the values:

Percent ionization = (1.11 × 10^-5 / 0.200) × 100 ≈ 0.0056 percent

That is extremely small. In practical terms, more than 99.994 percent of the dissolved HCN remains undissociated at equilibrium. This small ionization fraction explains why the exact and approximate methods are almost identical for this problem.

Equilibrium Quantity	Value for 0.200 M HCN	Interpretation
[H^+]	1.11 × 10^-5 M	Hydrogen ion formed by weak acid dissociation
[CN^–]	1.11 × 10^-5 M	Conjugate base formed in the same amount as H^+
[HCN] remaining	0.199989 M	Nearly all HCN stays undissociated
pH	4.95	Weakly acidic solution
Percent ionization	0.0056%	Confirms very weak acid behavior

Common Mistakes When Solving HCN pH Problems

1. Treating HCN like a strong acid. If you assume [H⁺] = 0.200 M, you would get pH 0.70, which is completely wrong for a weak acid like HCN.
2. Using the wrong Ka value. Different tables may list slightly different Ka values because of temperature, rounding, or source differences. The answer usually remains close to pH 4.95 when Ka is in the 10^-10 range.
3. Forgetting the equilibrium denominator. Ka always includes the concentration of undissociated acid in the denominator for HA ⇌ H⁺ + A^–.
4. Mistyping scientific notation. Entering 6.2e-10 incorrectly in a calculator can produce wildly incorrect results.
5. Ignoring the 5 percent rule check. Although the approximation is valid here, good chemistry practice is to verify it.

How Changes in Concentration Affect pH

If the HCN concentration changes, the pH changes too, but not in the same dramatic way seen with strong acids. For weak acids, lowering the starting concentration reduces [H⁺] and raises the pH, but because ionization behavior is equilibrium controlled, the relationship is not simply one-to-one. In general, the square-root approximation for weak acids suggests that [H⁺] is roughly proportional to √(KaC). That means if concentration drops by a factor of 100, the hydrogen ion concentration drops by a factor of about 10, assuming Ka remains constant.

This is one reason weak-acid equilibrium problems are so important in general chemistry. They teach the difference between complete dissociation and equilibrium-limited dissociation, and they prepare you to understand buffers, titrations, and conjugate acid-base relationships later in the course.

Safety and Chemical Context for HCN

Hydrocyanic acid and cyanide-containing systems are significant in chemistry, toxicology, environmental science, and industrial safety. While this page focuses on acid-base equilibrium math, HCN itself is a hazardous substance and should never be handled outside proper professional or academic laboratory protocols. If you are studying HCN chemistry, it is smart to pair your equilibrium calculations with reputable health and chemical data from government and university sources.

• NIST Chemistry WebBook: Hydrogen cyanide data
• CDC ATSDR Toxic Substances Portal: Cyanide overview
• U.S. EPA: Cyanide sources and pathways

Final Answer

Using a typical Ka of 6.2 × 10^-10 for HCN at about 25 degrees C, the pH of a 0.200 M HCN solution is approximately 4.95. The equilibrium hydrogen ion concentration is about 1.11 × 10^-5 M, the cyanide ion concentration is the same, and the percent ionization is only about 0.0056 percent. These values confirm that HCN is a very weak acid and remains mostly undissociated in aqueous solution.

If you want the quickest route to the answer, remember this workflow: write the weak-acid equilibrium, assign x, use Ka = x²/(C – x), solve for x, and convert x to pH. For this specific case, both the exact quadratic and the common approximation lead to essentially the same result: pH ≈ 4.95.