Calculate the pH of 0.208 M HNO3(aq)
Use this premium nitric acid pH calculator to find the hydrogen ion concentration, pH, pOH, and hydroxide ion concentration for an aqueous HNO3 solution. For 0.208 M HNO3(aq), nitric acid is treated as a strong acid that dissociates completely in water under standard general chemistry assumptions.
How to calculate the pH of 0.208 M HNO3(aq)
To calculate the pH of 0.208 M HNO3(aq), the key idea is that nitric acid, HNO3, is a strong acid. In standard aqueous solution problems from general chemistry, strong acids are assumed to dissociate essentially completely. That means every mole of nitric acid contributes one mole of hydrogen ions, written as H+ or more precisely hydronium, H3O+. Because HNO3 is monoprotic, the stoichiometric relationship is 1:1. So for a solution with a molarity of 0.208 M, the hydrogen ion concentration is also 0.208 M.
Once the hydrogen ion concentration is known, the pH formula is straightforward:
pH = -log10[H+]
Substitute the concentration into the equation:
pH = -log10(0.208) = 0.6819, which rounds to about 0.68
This result makes chemical sense. A pH below 1 indicates a highly acidic solution, and 0.208 M nitric acid is indeed a relatively concentrated strong acid compared with the dilute examples often used in beginning pH problems. The important conceptual step is recognizing that nitric acid is not treated like a weak acid that requires an equilibrium ICE table and Ka expression. Instead, its complete ionization gives a direct route from molarity to hydrogen ion concentration.
Step by step method
- Identify the acid as HNO3, a strong monoprotic acid.
- Assume complete dissociation in water: HNO3(aq) → H+(aq) + NO3−(aq).
- Set the hydrogen ion concentration equal to the acid molarity: [H+] = 0.208 M.
- Apply the pH formula: pH = -log10(0.208).
- Evaluate the logarithm to obtain pH ≈ 0.6819.
- Round appropriately, usually to pH ≈ 0.68.
Why HNO3 is treated as a strong acid
Nitric acid belongs to the common list of strong acids taught in chemistry courses. Strong acids ionize to a very high extent in water, which means the equilibrium lies overwhelmingly toward products. For routine pH calculations, this allows students and professionals to bypass a detailed equilibrium solution. Since HNO3 contributes one acidic proton per molecule, its molarity directly determines the concentration of hydrogen ions in solution.
In contrast, if the problem involved a weak acid such as acetic acid, you would need the acid dissociation constant and solve an equilibrium expression. That is not necessary here. For 0.208 M HNO3(aq), the chemistry is simple and elegant: concentration in, pH out through the negative logarithm.
Core equations used in this calculator
- Complete dissociation: HNO3(aq) → H+(aq) + NO3−(aq)
- Hydrogen ion concentration: [H+] = 0.208 M
- pH equation: pH = -log10[H+]
- pOH equation: pOH = 14.00 – pH at 25 °C
- Hydroxide concentration: [OH−] = 10-pOH
If pH is approximately 0.682, then pOH is approximately 13.318 at 25 °C. The hydroxide ion concentration is therefore very small, as expected in a strongly acidic solution. This complements the pH result and gives a fuller picture of the acid base character of the system.
| Quantity | Value for 0.208 M HNO3(aq) | Meaning |
|---|---|---|
| Molarity of HNO3 | 0.208 M | Starting concentration of nitric acid in water |
| [H+] | 0.208 M | Equal to acid concentration for a strong monoprotic acid |
| pH | 0.6819 | Negative base 10 logarithm of hydrogen ion concentration |
| pOH at 25 °C | 13.3181 | Computed from 14.00 – pH |
| [OH−] | 4.80 × 10-14 M | Extremely low hydroxide level in a strongly acidic solution |
Interpreting a pH of about 0.68
Many learners are surprised to see a pH below 1, but this is perfectly valid. The pH scale is logarithmic, not linear. Each whole number change in pH corresponds to a tenfold change in hydrogen ion concentration. Therefore, a solution with pH 0.68 is significantly more acidic than a solution with pH 1.68, even though the numbers differ by only 1.00 unit. Specifically, the pH 0.68 solution has about ten times the hydrogen ion concentration.
It is also worth noting that pH values can be negative for extremely concentrated acids and can exceed 14 for very concentrated bases, depending on the system and the level of idealization used. In high school and introductory college chemistry, however, values generally stay in the familiar 0 to 14 range for common aqueous examples. Here, 0.68 falls well within that standard instructional range.
Comparison with other nitric acid concentrations
Because nitric acid is a strong acid, the relationship between concentration and pH is simple to compare across multiple examples. Increasing concentration lowers pH. Since pH is based on the logarithm of concentration, the pH does not decrease linearly with molarity, but it follows a clear predictable trend.
| HNO3 Concentration | [H+] | Calculated pH | Relative acidity compared with 0.208 M |
|---|---|---|---|
| 0.001 M | 0.001 M | 3.000 | 208 times less concentrated in H+ |
| 0.010 M | 0.010 M | 2.000 | 20.8 times less concentrated in H+ |
| 0.100 M | 0.100 M | 1.000 | 2.08 times less concentrated in H+ |
| 0.208 M | 0.208 M | 0.682 | Reference case |
| 0.500 M | 0.500 M | 0.301 | 2.40 times more concentrated in H+ |
| 1.000 M | 1.000 M | 0.000 | 4.81 times more concentrated in H+ |
Common mistakes when solving this problem
- Using Ka unnecessarily: HNO3 is a strong acid, so equilibrium calculations are usually not needed.
- Forgetting the negative sign: pH uses the negative logarithm. Without the negative sign, the answer is incorrect.
- Confusing molarity with pH: 0.208 M does not mean pH 0.208. You must take the logarithm.
- Assuming pH cannot be below 1: A strong acid at moderate concentration can absolutely have pH less than 1.
- Rounding too early: Keep extra digits in the calculator, then round the final pH.
Real chemistry context for nitric acid in water
Nitric acid is a highly important industrial and laboratory chemical. It is used in fertilizer production, metal processing, and synthesis of numerous compounds. In water, it donates protons very effectively, which is why it behaves as a strong acid. The nitrate ion, NO3−, is the conjugate base, but it is a very weak base and does not significantly reverse the proton transfer under ordinary conditions.
In practical lab work, concentration matters greatly. A 0.208 M solution is much more dilute than concentrated commercial nitric acid, yet it is still strongly acidic and must be handled with care. The pH value of about 0.68 signals that the solution can irritate tissue and react with acid sensitive materials. Chemical safety data and standard lab protocols should always be followed for preparation, dilution, storage, and disposal.
Relationship between pH, pOH, and water autoionization
At 25 °C, pure water satisfies the ionic product relation Kw = 1.0 × 10-14, which leads to pH + pOH = 14.00 for many introductory calculations. Once pH is known, pOH follows immediately. For 0.208 M HNO3(aq), the pH is about 0.682, so pOH is about 13.318. This high pOH value simply reflects the extremely low concentration of hydroxide ions in an acidic medium.
Advanced chemistry courses discuss activities, non ideal behavior, and temperature dependent changes in Kw. Those refinements can matter in precise analytical work, especially at high ionic strength. However, for the problem of calculating the pH of 0.208 M HNO3(aq), the standard assumption of complete dissociation and pH + pOH = 14.00 at 25 °C is fully appropriate.
Authoritative references for acid strength and pH fundamentals
If you want to verify the theory behind strong acids, hydrogen ion concentration, and pH definitions, these authoritative educational and government sources are useful:
- Chemistry LibreTexts educational reference
- United States Environmental Protection Agency resources on pH
- NIST Chemistry WebBook
Worked example in one line
For anyone who wants the fastest possible answer: because HNO3 is a strong acid, set [H+] = 0.208 M, then compute pH = -log10(0.208) = 0.6819, so the pH is approximately 0.68.
Final answer summary
The pH of 0.208 M HNO3(aq) is approximately 0.68. This comes from the fact that nitric acid dissociates completely in water, giving [H+] = 0.208 M. Applying the logarithmic pH formula yields a strongly acidic solution with pOH near 13.32 and an extremely small hydroxide ion concentration. If your course expects a standard general chemistry treatment, this is the correct and complete approach.