Calculate The Ph Of Hcn 4.9 10-10

Use this premium weak-acid calculator to find the pH of hydrocyanic acid at extremely low concentration, including the effect of water autoionization when the solution is close to neutral.

HCN pH Calculator

Default values are set to calculate the pH for an HCN solution with concentration 4.9 × 10^-10 M and acid dissociation constant K_a = 4.9 × 10^-10 at 25°C.

Model used: For very dilute weak acids, the calculator solves the full equilibrium with water autoionization:
K_a = [H⁺][CN^–] / [HCN], K_w = [H⁺][OH^–] = 1.0 × 10^-14
This is more accurate than the shortcut x = √(K_aC) when concentration is near or below 10^-7 M.

How to calculate the pH of HCN at 4.9 × 10^-10 M

If you need to calculate the pH of HCN 4.9 10-10, the most important idea is that this is an extremely dilute weak acid solution. Hydrocyanic acid, HCN, is a weak acid with a small acid dissociation constant. In ordinary textbook examples, weak-acid pH problems are often solved with the approximation:

x = √(K_aC)

where C is the formal concentration of the acid and x is the hydrogen ion concentration generated by dissociation. That shortcut works reasonably well when the acid concentration is not too small compared with the hydrogen ion concentration already present from water. Here, however, the concentration is only 4.9 × 10^-10 M, which is much lower than 1.0 × 10^-7 M, the hydrogen ion concentration in pure water at 25°C. Because of that, the autoionization of water cannot be ignored.

Bottom line: For HCN at 4.9 × 10^-10 M, the pH is only slightly below 7. The solution is acidic, but only very weakly acidic because water itself contributes most of the H⁺.

Step 1: Identify the chemistry

HCN dissociates in water according to:

HCN ⇌ H⁺ + CN^–

Its acid dissociation constant at 25°C is commonly taken as approximately:

K_a = 4.9 × 10^-10

Water also self-ionizes:

H₂O ⇌ H⁺ + OH^–

with:

K_w = 1.0 × 10^-14

Step 2: Understand why the usual approximation fails

If you tried the common weak-acid approximation,

[H⁺] ≈ √(K_aC)

then for K_a = 4.9 × 10^-10 and C = 4.9 × 10^-10, you would get:

[H⁺] ≈ √((4.9 × 10^-10)(4.9 × 10^-10)) = 4.9 × 10^-10 M

This would imply a pH around 9.31 if interpreted in isolation, which is physically wrong for an acid solution. The mistake comes from applying the weak-acid shortcut outside its valid range. When concentrations are extremely low, the background H⁺ and OH^– from water dominate the system.

Step 3: Use the full equilibrium model

A better method is to solve the full system using:

• Mass balance for cyanide species: C = [HCN] + [CN^–]
• Equilibrium expression: K_a = [H⁺][CN^–] / [HCN]
• Charge balance: [H⁺] = [CN^–] + [OH^–]
• Water relation: [OH^–] = K_w / [H⁺]

Combining these equations yields a nonlinear expression for [H⁺] that is best solved numerically. That is what the calculator above does automatically.

Step 4: Result for HCN at 4.9 × 10^-10 M

Using the exact equilibrium approach, the hydrogen ion concentration comes out only slightly greater than 1.0 × 10^-7 M. That means the pH is just under 7, typically around:

pH ≈ 6.99

The exact value depends on the K_a you use and the temperature, but at standard general chemistry conditions, the key conclusion is unchanged: the solution is almost neutral.

Why such a dilute acid stays near neutral

This result surprises many students because they expect any acid solution to have a noticeably low pH. The intuition is understandable, but concentration matters just as much as acid strength. HCN is already a weak acid, and here the concentration is tiny. Pure water has:

[H⁺] = 1.0 × 10^-7 M and pH = 7.00

Your HCN concentration is about 204 times smaller than 1.0 × 10^-7 M. So even if every HCN molecule dissociated completely, the additional hydrogen ions would still be a minor perturbation relative to the hydrogen ions already generated by water.

Quantity	Typical value at 25°C	Why it matters
Ka of HCN	4.9 × 10^-10	Shows HCN is a weak acid
pKa of HCN	9.31	High pKa means weak dissociation
Kw of water	1.0 × 10^-14	Sets [H^+] and [OH^–] in pure water
[H^+] in pure water	1.0 × 10^-7 M	Baseline that competes with very dilute acid
Given HCN concentration	4.9 × 10^-10 M	Far below 10^-7 M, so water cannot be ignored

Comparison: approximate vs exact method

One of the best ways to understand this topic is to compare the simplified method with the full calculation. The table below shows how the exact pH differs from the shortcut as the HCN concentration changes. These values use K_a = 4.9 × 10^-10 and 25°C water.

HCN concentration (M)	Approximate [H^+] = √(KaC)	Approximate pH	Exact pH with water
1.0 × 10^-2	2.21 × 10^-6	5.66	5.66
1.0 × 10^-4	2.21 × 10^-7	6.66	6.70
1.0 × 10^-6	2.21 × 10^-8	7.66	6.96
4.9 × 10^-10	4.90 × 10^-10	9.31	6.99

Notice what happens around 10^-6 M and below: the shortcut begins to break down badly. At 4.9 × 10^-10 M, it does not just introduce a small error; it predicts the wrong qualitative behavior. That is exactly why the full equilibrium method is essential for this problem.

Step by step reasoning you can use on exams

1. Write the acid dissociation equilibrium for HCN.
2. Check the concentration scale. If C is comparable to or below 10^-7 M, water autoionization matters.
3. Do not rely solely on √(K_aC) for ultradilute solutions.
4. Set up mass balance, charge balance, and the K_w expression.
5. Solve for [H⁺] numerically or with an exact calculator.
6. Compute pH = -log₁₀[H⁺].

Common mistakes when solving this HCN pH problem

• Ignoring water autoionization. This is the most common error.
• Assuming every acid solution must have a clearly acidic pH. Very dilute acids can sit extremely close to pH 7.
• Using Henderson-Hasselbalch incorrectly. That equation is for buffer systems, not a single weak acid in pure water.
• Confusing K_a with concentration. In this problem, both values happen to be 4.9 × 10^-10, but they represent different things.
• Forgetting units. pH calculations require concentration in molarity.

Practical interpretation of the answer

From a purely acid-base perspective, a 4.9 × 10^-10 M HCN solution is nearly neutral. That does not mean cyanide chemistry is unimportant in the real world. Toxicology, volatility, and speciation are separate issues from simple pH. If you are studying environmental chemistry, industrial hygiene, or laboratory safety, consult primary references for cyanide handling and exposure information.

Useful government references include the U.S. Environmental Protection Agency cyanide information page, the CDC NIOSH cyanide topic page, and the NIST Chemistry WebBook for chemical property data.

Why the chart in this calculator is useful

The interactive chart above shows the major species concentrations in the solution: H⁺, OH^–, CN^–, and undissociated HCN. For this problem, the chart makes one key point visually clear: the hydrogen ion concentration is driven primarily by water, while only a tiny amount of cyanide is formed by acid dissociation. In other words, the system behaves more like slightly perturbed water than like a conventional acid solution.

When should you use an exact weak-acid calculator?

You should prefer an exact solver when:

• The acid concentration is below about 10^-6 M.
• The acid is very weak and K_a is small.
• You need reliable values near neutral pH.
• You are comparing theoretical predictions with lab data.
• Your class or project explicitly asks whether water autoionization should be included.

Final answer for “calculate the pH of HCN 4.9 10-10”

For an HCN solution with concentration 4.9 × 10^-10 M, using K_a = 4.9 × 10^-10 and including water autoionization at 25°C, the pH is:

pH ≈ 6.99

The solution is acidic, but only slightly. That is the chemically correct conclusion because the concentration is so low that pure water largely controls the hydrogen ion concentration.

Educational note: pH values can shift slightly depending on the exact K_a source, ionic strength assumptions, and temperature. The calculator here is designed for standard general chemistry interpretation at 25°C.