Calculate Ph Of 10M Hcn That Is 0.007 Ionized

Use this interactive calculator to determine hydrogen ion concentration, remaining HCN concentration, cyanide ion concentration, percent ionization, and final pH for hydrocyanic acid.

Expert Guide: How to Calculate the pH of 10 M HCN That Is 0.007 Ionized

To calculate the pH of 10 M HCN that is 0.007 ionized, you only need a few core acid-base ideas. Hydrocyanic acid, HCN, is a weak acid. That means it does not fully dissociate in water. Instead, only a fraction of the dissolved acid molecules split into hydrogen ions and cyanide ions. Once you know the fraction ionized, you can find the hydrogen ion concentration directly and then convert that value into pH using the logarithmic definition of pH.

The dissociation process is:

HCN ⇌ H⁺ + CN^–

If a solution starts at 10 M HCN and 0.007 of it is ionized, then the fraction ionized, often called alpha, is 0.007. Since ionization means that same fraction of HCN becomes H⁺ and CN^–, the hydrogen ion concentration is:

[H⁺] = 10 × 0.007 = 0.07 M

Then use the pH formula:

pH = -log[H⁺] = -log(0.07) ≈ 1.155

So the final answer is:

The pH of 10 M HCN that is 0.007 ionized is approximately 1.15.

Why this method works

Students often confuse weak acids with dilute acids. A weak acid is one that dissociates only partially, but if its concentration is very high, the hydrogen ion concentration can still be large enough to produce a low pH. HCN is weak compared with strong acids like HCl, but in a concentrated solution, even a small ionized fraction can create a substantial amount of H⁺.

The key insight is that the phrase 0.007 ionized usually means 0.007 of the acid molecules ionize, not 0.007 M ionizes. This is a dimensionless fraction. In percentage terms, that is:

0.007 × 100 = 0.7%

That means only 0.7% of the HCN molecules dissociate, while 99.3% remain in molecular form. In this problem:

• Initial HCN = 10.00 M
• Ionized fraction = 0.007
• H⁺ formed = 0.070 M
• CN^– formed = 0.070 M
• HCN remaining = 10.000 – 0.070 = 9.930 M

Step by step calculation

1. Write the acid dissociation equation: HCN ⇌ H⁺ + CN^–
2. Identify the initial concentration: 10 M
3. Identify the ionized fraction: 0.007
4. Calculate hydrogen ion concentration: [H⁺] = 10 × 0.007 = 0.07 M
5. Apply the pH formula: pH = -log(0.07)
6. Evaluate: pH ≈ 1.1549, usually rounded to 1.15

Common shortcut formula

Whenever you know the initial concentration C of a monoprotic weak acid and its fraction ionized alpha, you can calculate pH directly from:

pH = -log(C × alpha)

For this problem:

pH = -log(10 × 0.007) = -log(0.07) = 1.15

Important interpretation note

Some textbooks and instructors use the phrase “0.007 ionized” to mean 0.007% ionization instead of a fraction. That wording is less common in chemistry problem sets, but it does happen. If the intended meaning were 0.007%, then the fraction would be 0.00007 and the pH would be much higher:

• [H⁺] = 10 × 0.00007 = 0.0007 M
• pH = -log(0.0007) ≈ 3.15

That is why it is essential to check whether the ionization number is given as a decimal fraction or a percentage. In the calculator above, you can switch between both formats using the dropdown menu.

Comparison table: pH at different ionization levels for 10 M HCN

The table below shows how strongly the pH changes as the ionized fraction changes. These values are calculated from the exact relationship pH = -log(10 × alpha).

Ionization fraction	Percent ionization	[H^+] produced (M)	Calculated pH	HCN remaining (M)
0.001	0.1%	0.010	2.00	9.990
0.003	0.3%	0.030	1.52	9.970
0.007	0.7%	0.070	1.15	9.930
0.010	1.0%	0.100	1.00	9.900
0.020	2.0%	0.200	0.70	9.800

Comparison table: HCN vs other common weak acids

HCN is classified as a weak acid. Its acidity is often compared using Ka or pKa values. Lower pKa means a stronger acid. The values below are standard approximate reference values commonly used in general chemistry and analytical chemistry instruction.

Acid	Approximate Ka at 25°C	Approximate pKa	Relative strength note
Hydrocyanic acid, HCN	4.9 × 10^-10	9.31	Very weak acid
Acetic acid, CH3COOH	1.8 × 10^-5	4.76	Much stronger than HCN
Formic acid, HCOOH	1.8 × 10^-4	3.75	Stronger weak acid
Hydrofluoric acid, HF	6.8 × 10^-4	3.17	Weak, but far stronger than HCN

How this relates to Ka and ICE tables

In many weak-acid problems, you are given the acid dissociation constant Ka and asked to solve for x using an ICE table. This problem is simpler because the degree of ionization is already supplied. If alpha is known, you do not need to derive it from Ka. You can move directly to concentration changes.

For a monoprotic weak acid HA:

• Initial concentration = C
• Ionized fraction = alpha
• [H⁺] = C alpha
• [A^–] = C alpha
• [HA] remaining = C(1 – alpha)

For the current problem:

• C = 10
• alpha = 0.007
• [H⁺] = 10(0.007) = 0.07 M
• [CN^–] = 0.07 M
• [HCN] remaining = 10(1 – 0.007) = 9.93 M

Why the pH is surprisingly low

At first glance, some learners expect a weak acid to have a pH near neutral. That expectation can be misleading. Weak only describes incomplete dissociation, not low concentration. A 10 M acid solution is extremely concentrated. Even if only 0.7% ionizes, the amount of H⁺ released is 0.07 M, which is high enough to give a pH close to 1.15. This is strongly acidic in practice.

This also highlights a broader chemistry principle: acid strength and acid concentration are different concepts. A concentrated weak acid can sometimes produce more hydrogen ions than a very dilute strong acid.

Safety and chemistry context

HCN is not just a weak acid. It is also a highly toxic compound, and cyanide chemistry has major importance in environmental monitoring, industrial hygiene, toxicology, and emergency response. If you are studying cyanide systems, it is useful to consult authoritative references for hazard and environmental background. Relevant sources include the CDC NIOSH cyanide information, the U.S. Environmental Protection Agency cyanide resources, and the U.S. Geological Survey guide to pH and water.

Frequent mistakes to avoid

• Confusing fraction with percent. A decimal like 0.007 means 0.7%, not 7%.
• Taking pH from the acid concentration directly. For weak acids, use the hydrogen ion concentration, not the original acid concentration.
• Ignoring the one-to-one stoichiometry. Each ionized HCN molecule gives one H⁺ and one CN^–.
• Rounding too early. Keep extra digits until the final pH step for cleaner results.
• Assuming weak acid means high pH. Concentration matters a lot.

Quick exam strategy

If you see a problem asking for the pH of a monoprotic acid with a known degree of ionization, use this fast path:

1. Convert percent ionization to a decimal fraction if needed.
2. Multiply initial molarity by the fraction ionized to get [H⁺].
3. Apply pH = -log[H⁺].
4. Report pH to an appropriate number of decimal places, usually two or three.

For the specific question here, the fast path is:

[H⁺] = 10 × 0.007 = 0.07 M

pH = -log(0.07) = 1.15

Final answer summary

If 10 M HCN is 0.007 ionized as a fraction, then:

• Hydrogen ion concentration = 0.070 M
• Cyanide ion concentration = 0.070 M
• Remaining HCN concentration = 9.930 M
• pH = 1.15

This is the value the calculator above returns by default. You can change the inputs to explore how pH changes with concentration or ionization level and visualize the species distribution directly on the chart.