Calculate the pH of a 0.14 M HNO2 Solution
Use this premium nitrous acid calculator to find the pH, hydrogen ion concentration, percent ionization, and equilibrium concentrations for a weak acid solution. The default setup is already configured for 0.14 M HNO2 at 25 degrees Celsius with a commonly used Ka value of 4.5 × 10-4.
Because HNO2 is a weak acid, it does not dissociate completely. That means the correct pH comes from the weak acid equilibrium expression, not from assuming full ionization as you would for a strong acid.
Tip: For 0.14 M HNO2, the exact pH is slightly above 2.11 when Ka = 4.5 × 10-4.
Expert Guide: How to Calculate the pH of a 0.14 M HNO2 Solution
To calculate the pH of a 0.14 M HNO2 solution, you need to recognize one central fact first: nitrous acid is a weak acid. That single idea determines the whole solution path. If HNO2 were a strong acid, you could set the hydrogen ion concentration equal to the starting molarity and immediately take the negative logarithm. But HNO2 only partially ionizes in water, so the concentration of H+ must be found from an equilibrium calculation.
The dissociation equation is:
HNO2 ⇌ H+ + NO2–
At 25 degrees Celsius, a frequently used acid dissociation constant for nitrous acid is Ka = 4.5 × 10-4. Starting from an initial concentration of 0.14 M, the equilibrium setup leads to a quadratic equation or, in some classroom settings, a square root approximation. The exact approach is more rigorous and is the preferred method when you want a dependable numerical answer.
Step 1: Write the Ka expression
For a generic weak acid HA, the dissociation constant is:
Ka = [H+][A–] / [HA]
For nitrous acid specifically:
Ka = [H+][NO2–] / [HNO2]
If the initial concentration of HNO2 is 0.14 M and the amount that dissociates is x, then at equilibrium:
- [HNO2] = 0.14 – x
- [H+] = x
- [NO2–] = x
Substitute these into the Ka expression:
4.5 × 10-4 = x2 / (0.14 – x)
Step 2: Solve the equilibrium expression
There are two ways to proceed. The exact method rearranges the equation into quadratic form:
x2 + Ka x – KaC = 0
With C = 0.14 and Ka = 4.5 × 10-4, this becomes:
x2 + 4.5 × 10-4x – 6.3 × 10-5 = 0
Using the quadratic formula:
x = [-Ka + √(Ka2 + 4KaC)] / 2
Substituting the values gives:
x ≈ 0.00771 M
Since x is the equilibrium hydrogen ion concentration, that means:
[H+] ≈ 7.71 × 10-3 M
Now calculate pH:
pH = -log[H+] = -log(0.00771) ≈ 2.11
Step 3: Check the approximation method
In many chemistry courses, you are also taught to simplify weak acid problems with the small x assumption. If x is small compared with the initial concentration, then 0.14 – x can be approximated as 0.14. The Ka expression becomes:
Ka ≈ x2 / 0.14
So:
x ≈ √(Ka × C) = √[(4.5 × 10-4)(0.14)] ≈ 0.00794 M
Then:
pH ≈ -log(0.00794) ≈ 2.10
This is extremely close to the exact answer. The approximation works fairly well here because the dissociation remains a small fraction of the starting concentration, although the exact solution is still better for polished work, lab reporting, and advanced coursework.
Why HNO2 does not behave like a strong acid
A common mistake is to treat every formula that begins with hydrogen as a strong acid. That is incorrect. Only certain acids, such as HCl, HBr, HI, HNO3, HClO4, and typically the first dissociation of H2SO4, are treated as strong acids in introductory chemistry. Nitrous acid, HNO2, is weak, so it establishes an equilibrium in water rather than dissociating nearly 100 percent.
If you incorrectly assumed complete dissociation for 0.14 M HNO2, you would set [H+] = 0.14 M and find:
pH = -log(0.14) ≈ 0.85
That result is far too low. The correct weak acid calculation gives a pH around 2.11, which is more than one pH unit higher. Since the pH scale is logarithmic, this difference is chemically significant.
ICE table setup for 0.14 M HNO2
Many instructors expect you to present the solution in ICE table form. This is a clean way to organize weak acid and weak base equilibrium problems.
| Species | Initial (M) | Change (M) | Equilibrium (M) |
|---|---|---|---|
| HNO2 | 0.14 | -x | 0.14 – x |
| H+ | 0 | +x | x |
| NO2– | 0 | +x | x |
From that table, the Ka expression follows naturally. This is why ICE tables remain such a useful problem-solving format in acid-base chemistry.
Comparison table: HNO2 versus other common weak acids
Acid strength among weak acids varies considerably. One way to compare them is by Ka values at 25 degrees Celsius. Higher Ka means stronger acid behavior and greater ionization at the same formal concentration.
| Acid | Formula | Typical Ka at 25 degrees Celsius | Relative strength comment |
|---|---|---|---|
| Nitrous acid | HNO2 | 4.5 × 10-4 | Moderately weak, stronger than acetic acid |
| Hydrofluoric acid | HF | 6.8 × 10-4 | Slightly stronger weak acid than HNO2 |
| Formic acid | HCOOH | 1.8 × 10-4 | Weaker than HNO2 |
| Acetic acid | CH3COOH | 1.8 × 10-5 | Much weaker than HNO2 |
This comparison helps explain why a 0.14 M HNO2 solution has a pH that is lower than an equal concentration of acetic acid but still much higher than a strong acid of the same molarity.
How concentration affects the pH of HNO2
For weak acids, pH changes with concentration, but not in the exact one-to-one way seen with strong acids. Because the equilibrium shifts as the concentration changes, the hydrogen ion concentration grows sublinearly. The table below shows exact pH values for several HNO2 concentrations using Ka = 4.5 × 10-4.
| Initial HNO2 concentration (M) | Exact [H+] at equilibrium (M) | Exact pH | Percent ionization |
|---|---|---|---|
| 0.010 | 0.00191 | 2.72 | 19.1% |
| 0.050 | 0.00452 | 2.34 | 9.05% |
| 0.140 | 0.00771 | 2.11 | 5.51% |
| 0.500 | 0.01478 | 1.83 | 2.96% |
Notice the trend: as the initial concentration rises, the pH falls, but the percent ionization decreases. That pattern is characteristic of weak acids and appears in many textbook and laboratory systems.
Percent ionization for 0.14 M HNO2
Once you know x, it is easy to compute the percent ionization:
Percent ionization = (x / C) × 100
For 0.14 M HNO2:
(0.00771 / 0.14) × 100 ≈ 5.51%
This tells you that only a small portion of the nitrous acid molecules donate protons to water at equilibrium. That is the essence of weak acid behavior.
Most common mistakes students make
- Treating HNO2 as a strong acid. This produces an unrealistically low pH.
- Using the wrong acid. HNO2 is nitrous acid, while HNO3 is nitric acid. They are very different in strength.
- Confusing Ka with pKa. If a problem gives pKa, convert first using Ka = 10-pKa.
- Ignoring significant figures. pH values are usually reported with decimal places based on the precision of the data.
- Applying the square root shortcut without checking. The approximation is useful, but exact solutions are safer when the ionization is not extremely small.
When to use the exact quadratic method
The exact method should be your default when:
- You are preparing a formal chemistry assignment or lab report.
- You want to compare the exact answer against the approximation.
- The percent ionization is not tiny.
- Your instructor explicitly asks for a full equilibrium treatment.
For 0.14 M HNO2, the approximation is close, but the exact method still provides the most defensible result. Modern calculators and software make the quadratic solution straightforward, so there is little downside to using it.
Context for pH values around 2.11
A pH near 2.11 indicates a significantly acidic solution, but not one as aggressive as a strong acid of the same molarity. In practical terms, such a solution contains enough hydrogen ion concentration to strongly influence acid-base indicators, corrosion behavior, and reaction rates in many aqueous systems. In environmental and analytical contexts, pH values in this range are treated as distinctly acidic and can affect solubility, metal mobility, and biological systems.
Authoritative references for acid-base chemistry and pH
If you want to deepen your understanding of pH, weak acid chemistry, and acidification concepts, these sources are useful starting points:
- U.S. Environmental Protection Agency: Alkalinity and Acidification
- University of Wisconsin Chemistry: Acid-Base Fundamentals
- U.S. Geological Survey: pH and Water
Quick summary
To calculate the pH of a 0.14 M HNO2 solution, set up the weak acid equilibrium using the dissociation reaction HNO2 ⇌ H+ + NO2–. Use the acid dissociation constant Ka = 4.5 × 10-4, solve for the equilibrium hydrogen ion concentration, and then compute pH from the negative logarithm of [H+]. The exact result is pH ≈ 2.11. The hydrogen ion concentration is about 7.71 × 10-3 M, and the percent ionization is roughly 5.51%.
That is the chemically correct way to solve this problem. If you are studying for an exam, remember the key idea: HNO2 is weak, so use equilibrium, not complete dissociation.