Calculate The Ph Of A 1.10M Solution Of Hno2

Use this premium chemistry calculator to compute the pH of nitrous acid from its concentration and acid dissociation constant. The tool supports exact quadratic and weak-acid approximation methods, displays equilibrium values, and visualizes the chemistry with a responsive chart.

Nitrous Acid pH Calculator

How to Calculate the pH of a 1.10 M Solution of HNO2

To calculate the pH of a 1.10 M solution of HNO2, you need to recognize that nitrous acid is a weak acid, not a strong acid. That distinction is extremely important because weak acids do not dissociate completely in water. Instead, only a fraction of the dissolved acid molecules ionize to produce hydronium ions, and the pH must be determined from the acid dissociation equilibrium rather than by assuming that the hydrogen ion concentration is equal to the initial acid concentration.

Nitrous acid undergoes the equilibrium:

HNO2 ⇌ H+ + NO2-

The acid dissociation constant expression is:

Ka = [H+][NO2-] / [HNO2]

At 25 degrees Celsius, a commonly used value for the acid dissociation constant of nitrous acid is approximately Ka = 4.5 × 10^-4. Because the problem gives an initial concentration of 1.10 M, the goal is to find the equilibrium concentration of H+, then convert it to pH using:

pH = -log10[H+]

Step-by-Step Setup

Start with an ICE table, which tracks Initial, Change, and Equilibrium concentrations.

Species	Initial (M)	Change (M)	Equilibrium (M)
HNO2	1.10	-x	1.10 – x
H+	0	+x	x
NO2-	0	+x	x

Substitute the equilibrium concentrations into the Ka expression:

4.5 × 10^-4 = x² / (1.10 – x)

This equation can be solved exactly using the quadratic formula, or approximately if the ionization is very small compared with the initial concentration. Since the concentration is fairly large and Ka is still much smaller than 1, the approximation is usually reasonable here, but the exact method is still the most defensible approach in a formal chemistry setting.

Exact Quadratic Solution

Rearrange the equation:

4.5 × 10^-4(1.10 – x) = x²

4.95 × 10^-4 – 4.5 × 10^-4x = x²

x² + 4.5 × 10^-4x – 4.95 × 10^-4 = 0

Using the positive root of the quadratic formula gives:

x ≈ 0.0220 M

Since x equals the equilibrium hydrogen ion concentration,

[H+] ≈ 0.0220 M

Now compute pH:

pH = -log10(0.0220) ≈ 1.66

Final answer: The pH of a 1.10 M solution of HNO2 is approximately 1.66 when Ka is taken as 4.5 × 10^-4 at 25 degrees Celsius.

Approximation Method

If you assume that x is small relative to 1.10, then 1.10 – x is approximated as 1.10. The Ka expression becomes:

4.5 × 10^-4 = x² / 1.10

Solving for x:

x = √(4.5 × 10^-4 × 1.10) = √(4.95 × 10^-4) ≈ 0.0223 M

Then:

pH = -log10(0.0223) ≈ 1.65

This is extremely close to the exact value. The percent ionization is:

(0.0220 / 1.10) × 100 ≈ 2.0%

Because the ionization is only about 2%, the small-x approximation works well in this particular problem. Still, if you are using the value for a graded assignment, lab report, or engineering calculation, the exact quadratic result is usually the best choice.

Why HNO2 Is Not Treated as a Strong Acid

Students sometimes make the mistake of assigning pH by directly setting [H+] = 1.10 M. That would be correct only for a strong monoprotic acid that dissociates essentially completely in water. Nitrous acid does not behave that way. Its Ka is relatively modest, which means the equilibrium strongly favors the undissociated acid compared with the fully ionized form.

If HNO2 were strong, the pH would be:

pH = -log10(1.10) ≈ -0.04

That result is dramatically different from the actual weak-acid pH near 1.66. This comparison shows why identifying acid strength before calculating pH is one of the most important first steps in equilibrium chemistry.

Comparison Table: Exact vs Approximate vs Strong-Acid Assumption

Method	[H+] (M)	Calculated pH	Interpretation
Exact quadratic solution	0.0220	1.66	Best equilibrium-based answer for Ka = 4.5 × 10^-4
Weak-acid approximation	0.0223	1.65	Very close because ionization is only about 2.0%
Incorrect strong-acid assumption	1.10	-0.04	Not valid because HNO2 is a weak acid

How Concentration Changes pH for Nitrous Acid

One helpful way to understand weak-acid behavior is to compare the same acid at different concentrations. As the initial concentration increases, the equilibrium hydrogen ion concentration also increases, but not in direct one-to-one proportion. That is because weak-acid dissociation is governed by equilibrium, not complete ionization. Percent ionization typically decreases as the acid gets more concentrated.

Initial HNO2 Concentration (M)	Approximate [H+] (M)	Approximate pH	Percent Ionization
0.010	0.00212	2.67	21.2%
0.10	0.00671	2.17	6.7%
1.10	0.0220 to 0.0223	1.66 to 1.65	2.0%

This trend illustrates a classic weak-acid pattern: even though the solution gets more acidic as concentration rises, the fraction of molecules that ionize becomes smaller. That is exactly why equilibrium methods matter so much in acid-base calculations.

Common Mistakes to Avoid

• Assuming HNO2 is a strong acid and setting [H+] equal to 1.10 M.
• Using pKa directly without first converting it correctly or applying the proper weak-acid formula.
• Forgetting that pH must be based on the equilibrium hydrogen ion concentration, not the initial acid concentration.
• Dropping the negative sign in the pH formula.
• Rounding too early, which can noticeably affect the final pH value.

When to Use the Quadratic Formula

In introductory chemistry, the 5% rule is often used to judge whether the small-x approximation is acceptable. If x divided by the initial concentration is less than about 5%, the approximation is usually considered safe. For this 1.10 M HNO2 solution, the ionization fraction is close to 2.0%, so the approximation is acceptable. However, when precision matters, using the quadratic formula completely removes the need to justify the approximation.

1. Write the balanced ionization reaction.
2. Create an ICE table.
3. Insert equilibrium terms into the Ka expression.
4. Solve for x exactly or approximately.
5. Set [H+] = x.
6. Compute pH = -log10[H+].

Practical Interpretation of the Result

A pH of about 1.66 means the solution is strongly acidic in practical terms, even though the acid itself is weak. This sometimes confuses learners. The word weak refers to the degree of dissociation, not necessarily to whether the solution feels mild or has a high pH. A weak acid can still produce a very acidic solution if the concentration is high enough. Here, 1.10 M is a concentrated solution, so despite incomplete dissociation, the resulting [H+] is still substantial.

That distinction between acid strength and acid concentration is one of the most important conceptual lessons in general chemistry. Strength is an equilibrium property. Concentration is simply how much acid is present per liter. Both affect pH, but in different ways.

Authoritative References for Further Study

If you want to review pH fundamentals, acid dissociation, and nitrite or nitrous-acid related chemistry from authoritative sources, these references are excellent starting points:

• U.S. Environmental Protection Agency: pH Overview
• NIST Chemistry WebBook: Nitrous Acid Data
• Purdue University: Acid Ionization Constants and Equilibrium Concepts

Bottom Line

To calculate the pH of a 1.10 M solution of HNO2, treat nitrous acid as a weak monoprotic acid with a Ka of about 4.5 × 10^-4. Set up the equilibrium expression, solve for the hydrogen ion concentration, and then convert to pH. The exact solution gives a hydrogen ion concentration of about 0.0220 M, which corresponds to a pH of 1.66. The approximation method gives essentially the same answer, about 1.65, because the percent ionization is only around 2.0%. In both classroom and practical chemistry, this is the correct way to solve the problem.

Educational note: exact values can vary slightly depending on the Ka value selected from a textbook, database, or temperature-specific reference.