Calculate The Ph Of 0.0167M Hno3

Use this premium calculator to find the pH of nitric acid solution at 0.0167 M. Because HNO3 is a strong monoprotic acid, it dissociates essentially completely in water under typical classroom conditions, so the hydrogen ion concentration is approximately equal to the stated molarity.

Quick chemistry insight: For a strong monoprotic acid such as nitric acid, [H⁺] ≈ acid molarity. Therefore, for 0.0167 M HNO3, pH = -log₁₀(0.0167).

How to calculate the pH of 0.0167 M HNO3

To calculate the pH of 0.0167 M HNO3, you use one of the most direct relationships in introductory acid-base chemistry. Nitric acid, HNO3, is a strong acid. In dilute aqueous solution, it dissociates essentially completely into hydrogen ions and nitrate ions. That means the hydrogen ion concentration is approximately equal to the initial acid concentration. For a 0.0167 M nitric acid solution, you can set [H⁺] = 0.0167 M and then apply the pH formula:

pH = -log₁₀[H⁺]

Substituting the concentration gives:

pH = -log₁₀(0.0167) ≈ 1.777

Rounded to three decimal places, the pH is 1.777. Rounded to two decimal places, it is 1.78. This confirms that the solution is strongly acidic, but not as acidic as a 0.1 M or 1.0 M strong acid solution. Because pH is logarithmic, even a seemingly small numerical shift in concentration can move the pH noticeably.

Why HNO3 is treated as a strong acid

When students are asked to calculate the pH of 0.0167 M HNO3, the key chemistry assumption is acid strength. Nitric acid is classified as a strong acid in water. Strong acids are defined by near-complete ionization under normal aqueous conditions. In practical classroom calculations, this means you do not usually need to solve an equilibrium expression for HNO3 in the way you would for a weak acid such as acetic acid.

The dissociation can be written as:

HNO3(aq) → H⁺(aq) + NO3^–(aq)

Because each mole of nitric acid produces approximately one mole of hydrogen ions, the stoichiometric ratio is 1:1. That is why a 0.0167 M solution gives a hydrogen ion concentration of about 0.0167 M. This one-step logic is what makes the problem fast and reliable.

Core assumptions used in the calculation

• HNO3 behaves as a strong monoprotic acid in water.
• The solution is dilute enough that standard introductory approximations apply.
• Activity effects are ignored, so concentration is used in place of activity.
• Water autoionization is negligible compared with the acid concentration.

Step-by-step method for calculating pH

1. Identify the acid as strong and monoprotic.
2. Set hydrogen ion concentration equal to acid molarity: [H⁺] = 0.0167 M.
3. Apply the logarithmic pH equation: pH = -log₁₀(0.0167).
4. Use a calculator to evaluate the logarithm.
5. Round the answer according to your class or lab requirements.

This gives a pH of approximately 1.777. If your teacher expects significant figures to match the original concentration, you may report it as 1.78, depending on the convention being used in your course.

Worked example with interpretation

Suppose you are asked in a chemistry assignment: “Calculate the pH of 0.0167 M HNO3.” First, identify HNO3 as nitric acid. Next, remember that nitric acid is a strong acid, so it ionizes completely:

HNO3 → H⁺ + NO3^–

Therefore:

[H⁺] = 0.0167 M

Now apply the pH formula:

pH = -log₁₀(0.0167) = 1.777283528…

So the solution has a pH of about 1.78. This means it is much more acidic than neutral water, which has a pH close to 7 at 25 degrees Celsius. A pH near 1.8 indicates a substantial hydrogen ion concentration relative to everyday aqueous systems.

Quantity	Value for 0.0167 M HNO3	Meaning
Acid concentration	0.0167 mol/L	Initial molarity of nitric acid in solution
Hydrogen ion concentration	0.0167 mol/L	Because HNO3 is a strong monoprotic acid
pH	1.777	Calculated from -log10(0.0167)
pOH at 25 degrees Celsius	12.223	Using pH + pOH = 14.00

Common mistakes when calculating the pH of nitric acid

Even though this is considered a straightforward problem, students still make several predictable errors. Knowing what to avoid can help you get the answer right quickly and confidently.

1. Forgetting that HNO3 is a strong acid

The most common mistake is treating nitric acid like a weak acid and trying to use a Ka expression. For standard general chemistry problems, this is unnecessary. You can assume complete dissociation.

2. Using the concentration directly as the pH

Another mistake is writing pH = 0.0167. That is incorrect because pH is not equal to concentration. You must take the negative base-10 logarithm of the hydrogen ion concentration.

3. Missing the negative sign in the formula

If you compute log(0.0167) and stop there, you will get a negative value. The pH formula includes a negative sign, so the final pH is positive.

4. Reporting too many or too few digits

Depending on the context, your final answer may be shown as 1.777, 1.78, or 1.7773. In educational settings, matching the expected degree of precision matters.

Comparison of nitric acid concentrations and pH values

Because pH is logarithmic, concentration changes are not reflected in a simple linear way on the pH scale. The table below compares several realistic HNO3 concentrations with their corresponding pH values under the same strong-acid assumption.

HNO3 Concentration (M)	Hydrogen Ion Concentration (M)	Calculated pH
1.0	1.0	0.000
0.100	0.100	1.000
0.0167	0.0167	1.777
0.0100	0.0100	2.000
0.00100	0.00100	3.000

This comparison shows that 0.0167 M HNO3 falls between 0.01 M and 0.1 M on the concentration scale, with a pH between 2 and 1. Because the relationship is logarithmic, multiplying concentration by 10 lowers pH by 1 unit for strong monoprotic acids under idealized assumptions.

How the answer connects to the pH scale

The pH scale is a logarithmic representation of acidity and basicity. At 25 degrees Celsius, a neutral aqueous solution has a pH of about 7. Values below 7 are acidic, while values above 7 are basic. A solution with pH 1.777 is strongly acidic. The lower the pH, the greater the hydrogen ion concentration.

One useful way to understand this result is to compare it with neutral water. Neutral water has [H⁺] around 1.0 × 10^-7 M. In contrast, 0.0167 M HNO3 has [H⁺] around 1.67 × 10^-2 M. That is about 167,000 times greater hydrogen ion concentration than neutral water, which explains why the pH is so much lower than 7.

Does temperature matter?

In many introductory problems, the temperature is assumed to be 25 degrees Celsius, and the standard relationship pH + pOH = 14.00 is used. For the direct pH calculation of a strong acid concentration, the answer from -log[H⁺] remains the main step. However, temperature can influence equilibrium constants, water ionization, and exact activity behavior. In basic coursework, these refinements are usually ignored unless the problem explicitly asks for them.

Advanced note: concentration versus activity

In more advanced chemistry, pH is technically defined using hydrogen ion activity rather than raw molar concentration. At low to moderate concentrations, introductory courses usually approximate activity with molarity. For 0.0167 M HNO3, this approximation is generally acceptable in classroom and homework settings. In high-precision analytical chemistry, researchers may apply activity coefficients for more exact calculations, especially in more concentrated solutions or complex ionic mixtures.

Exam shortcut: If the acid is strong and monoprotic, you can often move straight from molarity to [H⁺] and then use the pH formula. For 0.0167 M HNO3, the answer is approximately 1.78.

Useful authoritative chemistry references

If you want to verify definitions, pH concepts, and acid behavior from trusted educational or government sources, these references are excellent starting points:

• U.S. Environmental Protection Agency: Acidity and pH
• LibreTexts Chemistry: Strong and Weak Acids and Bases
• NIST Chemistry WebBook

Final answer

To calculate the pH of 0.0167 M HNO3, assume complete dissociation because nitric acid is a strong acid. Then set [H⁺] = 0.0167 M and calculate:

pH = -log₁₀(0.0167) = 1.777

So, the pH of 0.0167 M HNO3 is approximately 1.78.

Educational note: This calculator is designed for standard chemistry learning scenarios. In advanced laboratory settings, activity corrections and non-ideal solution behavior may be considered for higher precision.