Calculate the pH of 0.0167 M HNO3
Use this interactive nitric acid calculator to find hydrogen ion concentration, pH, pOH, and acidity classification for a monoprotic strong acid solution.
Click Calculate to refresh the values and chart.
How to calculate the pH of 0.0167 M HNO3
If you need to calculate the pH of 0.0167 M HNO3, the chemistry is straightforward because nitric acid is treated as a strong monoprotic acid in introductory and most general chemistry settings. That means each mole of nitric acid contributes essentially one mole of hydrogen ions to solution. Once you identify that relationship, the pH calculation becomes a logarithm problem rather than an equilibrium problem.
Why HNO3 is easy to handle in pH calculations
Nitric acid, written as HNO3, is one of the standard strong acids taught in chemistry. In water, it dissociates essentially completely:
HNO3(aq) → H+(aq) + NO3-(aq)Because there is only one ionizable hydrogen in each formula unit, nitric acid is monoprotic. For a solution concentration of 0.0167 M, the hydrogen ion concentration is therefore taken as:
[H+] = 0.0167 MOnce you know hydrogen ion concentration, use the standard pH definition:
pH = -log10[H+]Substitute the value:
pH = -log10(0.0167) = 1.777…Rounded appropriately, the result is:
pH ≈ 1.78Step by step solution
- Identify the acid as nitric acid, HNO3.
- Recognize that HNO3 is a strong acid and dissociates completely in water.
- Since it is monoprotic, set the hydrogen ion concentration equal to the acid molarity.
- Use the pH formula pH = -log10[H+].
- Evaluate -log10(0.0167).
- Round the final value to the desired precision, commonly 1.78.
Checking the math carefully
Students often get the right chemistry but the wrong calculator entry. The concentration 0.0167 M can also be written as 1.67 × 10^-2. The base-10 logarithm of 1.67 × 10^-2 is about -1.7773, and applying the negative sign gives a pH near 1.7773. If your calculator gives a value with the wrong sign, confirm that you entered the negative sign outside the logarithm.
What is the pOH for 0.0167 M HNO3?
At 25 C, the common classroom relationship between pH and pOH is:
pH + pOH = 14.00Using the pH we just calculated:
pOH = 14.00 – 1.7773 = 12.2227Rounded, the pOH is approximately 12.22. This is exactly what you should expect for an acidic solution. Low pH corresponds to high pOH, and vice versa.
Comparison table: nitric acid concentration versus pH
The table below shows how pH changes with nitric acid concentration under the same strong acid assumption. These values are directly calculated from pH = -log10[H+].
| HNO3 Concentration (M) | Hydrogen Ion Concentration [H+] (M) | Calculated pH | Acidity Description |
|---|---|---|---|
| 1.0 | 1.0 | 0.00 | Extremely acidic |
| 0.100 | 0.100 | 1.00 | Very strongly acidic |
| 0.0167 | 0.0167 | 1.78 | Strongly acidic |
| 0.0100 | 0.0100 | 2.00 | Strongly acidic |
| 0.00100 | 0.00100 | 3.00 | Moderately acidic |
Why the complete dissociation assumption works here
For weak acids, you usually need an acid dissociation constant and an equilibrium table. For nitric acid, that extra work is not normally needed because the acid dissociates so extensively that the concentration of undissociated HNO3 is negligible for this level of calculation. As a result, the simple shortcut applies:
[H+] ≈ acid molarityThis is one of the biggest time savers in introductory acid-base chemistry. Once you learn to recognize strong acids, many pH problems become almost immediate.
Common mistakes when calculating the pH of HNO3
- Forgetting that pH uses a logarithm. Some learners subtract from 7 or from 14 right away instead of using the logarithm first.
- Misreading the concentration. The value is 0.0167 M, not 0.167 M. A decimal place error changes the pH by exactly 1 unit.
- Using natural log instead of log base 10. pH uses the common logarithm.
- Assuming two hydrogens are released. Nitric acid has only one acidic hydrogen, so one mole of HNO3 gives one mole of H+.
- Rounding too early. If you keep extra digits until the end, your final pH will be more accurate.
How acidic is a pH of 1.78?
A pH of 1.78 is strongly acidic. Remember that the pH scale is logarithmic, not linear. A solution at pH 1.78 has a much larger hydrogen ion concentration than a solution at pH 2.78. In fact, a difference of one pH unit corresponds to a tenfold change in hydrogen ion activity. That is why even a small numerical change in pH represents a major change in acidity.
To make the value more intuitive, compare 0.0167 M HNO3 to a solution with pH 3.00. The pH 1.78 solution has hydrogen ion concentration of 0.0167 M, while a pH 3.00 solution has hydrogen ion concentration of 0.00100 M. Dividing these values shows that the nitric acid solution is about 16.7 times more acidic in terms of hydrogen ion concentration.
Comparison table: familiar pH ranges
The pH scale covers a broad range of substances and environmental systems. The table below gives representative pH values often cited in educational references and water science discussions. Exact values vary by sample, but the ranges are useful context for understanding where 0.0167 M HNO3 sits on the scale.
| Substance or System | Typical pH Range | Interpretation |
|---|---|---|
| Battery acid | 0 to 1 | Extremely acidic |
| 0.0167 M HNO3 | 1.78 | Strongly acidic |
| Lemon juice | 2 to 3 | Acidic food acid range |
| Pure water at 25 C | 7.00 | Neutral |
| Seawater | About 8.1 | Slightly basic |
| Household ammonia | 11 to 12 | Strongly basic |
Significant figures and reporting the answer
The concentration 0.0167 has three significant figures. In pH reporting, the digits after the decimal point correspond to significant figures in the concentration measurement. That means a reasonable reported answer is pH = 1.777 or, if your course expects a simpler rounded value, pH = 1.78. Either style is commonly accepted when the problem does not specify exact reporting rules.
What if the acid were weak instead of strong?
This question matters because the shortcut used here depends on HNO3 being strong. If the acid were weak, such as acetic acid, you could not simply say that hydrogen ion concentration equals the formal molarity. You would need:
- the acid dissociation constant, Ka,
- an equilibrium expression,
- possibly an ICE table, and
- sometimes a quadratic equation if approximation rules fail.
So when solving pH problems quickly, the first checkpoint is always acid identity: strong or weak, monoprotic or polyprotic.
Practical interpretation of the answer
Knowing that the pH is 1.78 helps you classify the solution, but it also tells you something about safe handling and chemical reactivity. Nitric acid is corrosive, oxidizing in many contexts, and can react vigorously with incompatible substances. Even relatively dilute nitric acid solutions require proper laboratory precautions, including eye protection, gloves appropriate for acid handling, and good ventilation. The pH number is not just an academic result. It reflects a chemically aggressive solution.
Formula summary for this exact problem
- HNO3 → H+ + NO3-
- [H+] = 0.0167 M
- pH = -log10(0.0167)
- pH = 1.7773…
- pH ≈ 1.78
Quick answer for students and exam review
If you are revising for a quiz and need the shortest method possible, memorize this logic: HNO3 is a strong monoprotic acid, so [H+] equals the molarity. Then take the negative log. For 0.0167 M HNO3, the answer is 1.78. That is the essential workflow.
Authoritative references for pH and acid chemistry context
Bottom line
To calculate the pH of 0.0167 M HNO3, treat nitric acid as a strong monoprotic acid, set hydrogen ion concentration equal to 0.0167 M, and apply the pH formula. The resulting pH is about 1.78. This value indicates a strongly acidic solution and matches what you would expect for a dilute but still powerful strong acid.