Calculate the pH of the Following Solutions: 0.12 M KNO2
Use this premium calculator to determine the pH of a potassium nitrite solution by applying weak base hydrolysis, equilibrium chemistry, and a precise quadratic solution. The default setup is for 0.12 M KNO2, but you can also change the concentration and acid dissociation data to explore how the pH shifts.
KNO2 pH Calculator
Potassium nitrite is the salt of a strong base, KOH, and a weak acid, HNO2. That means the solution is basic because NO2- hydrolyzes in water to produce OH-.
Results
Click Calculate pH to solve the default 0.12 M KNO2 problem.
Visualization
This chart compares pH, pOH, and hydroxide concentration for your selected KNO2 conditions.
How to Calculate the pH of 0.12 M KNO2
To calculate the pH of the following solution, 0.12 M KNO2, you need to recognize what kind of salt potassium nitrite is and how it behaves in water. Many students first see KNO2 and wonder whether it should be neutral because it is a salt. In reality, not all salts produce neutral solutions. The pH depends on the strengths of the parent acid and parent base that formed the salt.
Potassium nitrite, KNO2, comes from KOH, a strong base, and HNO2, nitrous acid, which is a weak acid. The potassium ion, K+, does not significantly react with water. The nitrite ion, NO2-, does react with water because it is the conjugate base of a weak acid. That hydrolysis reaction generates hydroxide ions, OH-, which makes the solution basic. Therefore, a 0.12 M KNO2 solution will have a pH above 7.
Step 1: Write the Hydrolysis Reaction
The nitrite ion accepts a proton from water according to the equilibrium:
NO2- + H2O ⇌ HNO2 + OH-
This tells you immediately that OH- is produced. Since pH and pOH are linked through the concentration of hydrogen and hydroxide ions, the rest of the problem is to determine how much OH- forms at equilibrium.
Step 2: Relate Kb to Ka
Most textbooks provide the acid dissociation constant, Ka, for nitrous acid rather than the base dissociation constant, Kb, for nitrite. To convert, use:
Kb = Kw / Ka
At 25 C, Kw is approximately 1.0 × 10-14. A commonly used Ka value for HNO2 is about 4.5 × 10-4. Substituting:
Kb = (1.0 × 10-14) / (4.5 × 10-4) = 2.22 × 10-11
This Kb value is quite small, which means nitrite is only a weak base. Even so, at a concentration of 0.12 M, it still creates enough hydroxide to make the solution distinctly basic.
Step 3: Set Up the ICE Table
For the hydrolysis reaction:
NO2- + H2O ⇌ HNO2 + OH-
Let the initial concentration of NO2- be 0.12 M. Assume the initial OH- from water is negligible compared with what the salt produces. Then the ICE table is:
| Species | Initial (M) | Change (M) | Equilibrium (M) |
|---|---|---|---|
| NO2- | 0.12 | -x | 0.12 – x |
| HNO2 | 0 | +x | x |
| OH- | 0 | +x | x |
The equilibrium expression for Kb is:
Kb = [HNO2][OH-] / [NO2-] = x2 / (0.12 – x)
Step 4: Solve for x
Using Kb = 2.22 × 10-11:
2.22 × 10-11 = x2 / (0.12 – x)
Because Kb is very small, the approximation 0.12 – x ≈ 0.12 is valid. Then:
x2 = (2.22 × 10-11)(0.12) = 2.67 × 10-12
x = 1.63 × 10-6 M
This x value represents the equilibrium concentration of hydroxide ion:
[OH-] = 1.63 × 10-6 M
Step 5: Convert to pOH and pH
Now determine pOH:
pOH = -log(1.63 × 10-6) ≈ 5.79
Then use:
pH = 14.00 – 5.79 = 8.21
Why the Solution Is Basic
Understanding the chemistry matters more than memorizing the answer. KNO2 dissociates completely into K+ and NO2- in water. The potassium ion is a spectator ion because it comes from a strong base and has negligible acid or base character in water. Nitrite, however, is the conjugate base of nitrous acid, a weak acid. Conjugate bases of weak acids are basic in aqueous solution. They react with water, pull off a proton, and generate OH-. That is why the pH exceeds 7.
Quick Classification Rules
- Strong acid + strong base salt: usually neutral
- Strong base + weak acid salt: basic
- Weak base + strong acid salt: acidic
- Weak acid + weak base salt: depends on relative Ka and Kb
KNO2 fits the second category, so a basic pH is expected before any calculation begins.
Exact Solution Versus Approximation
In many introductory problems, the approximation method is used because x is tiny relative to the starting concentration. For 0.12 M KNO2, the approximation is excellent. However, the exact quadratic solution is still the more rigorous method and is especially helpful when the base is stronger or the concentration is much smaller.
| Method | [OH-] (M) | pOH | pH | Comment |
|---|---|---|---|---|
| Approximation | 1.63 × 10-6 | 5.79 | 8.21 | Fast and valid because x is far smaller than 0.12 |
| Quadratic exact | 1.63 × 10-6 | 5.79 | 8.21 | More rigorous and preferred for calculators |
The percent ionization in this case is extremely small, confirming that the approximation works well. Since x / 0.12 × 100 is much less than 5%, the simplified approach is justified.
How Concentration Changes the pH of KNO2
One useful way to understand these equilibrium systems is to look at how concentration affects the pH. As the concentration of KNO2 increases, the amount of hydrolysis also changes, and the resulting pH moves upward, though not linearly. Because pH is logarithmic, doubling concentration does not simply add a fixed amount to pH.
| KNO2 Concentration (M) | Calculated [OH-] (M) | Approximate pOH | Approximate pH |
|---|---|---|---|
| 0.010 | 4.71 × 10-7 | 6.33 | 7.67 |
| 0.050 | 1.05 × 10-6 | 5.98 | 8.02 |
| 0.120 | 1.63 × 10-6 | 5.79 | 8.21 |
| 0.500 | 3.33 × 10-6 | 5.48 | 8.52 |
These numbers show a realistic trend: increasing concentration increases hydroxide concentration and raises pH. Still, because the reaction is governed by a weak base equilibrium, the pH remains moderately basic rather than strongly alkaline.
Common Mistakes When Solving KNO2 pH Problems
- Assuming all salts are neutral. This is one of the most common conceptual errors. KNO2 is not neutral because NO2- is basic.
- Using Ka directly instead of converting to Kb. Since NO2- acts as a base, use Kb for the hydrolysis reaction. If only Ka is given, convert using Kb = Kw / Ka.
- Using 0.12 M as [OH-]. The salt concentration is not the same as hydroxide concentration. Only a small fraction hydrolyzes.
- Forgetting to compute pOH first. Since the equilibrium directly gives OH-, calculate pOH, then convert to pH.
- Significant figure errors. Keep enough digits through the intermediate steps, then round the final pH appropriately.
Reference Data and Authoritative Sources
If you want to verify equilibrium concepts, water ion-product data, and broader acid-base principles, these authoritative educational and government resources are useful:
- University level chemistry resources and equilibrium tutorials
- United States Environmental Protection Agency for water chemistry context and pH significance
- National Institute of Standards and Technology for scientific standards and measurement context
- Princeton University Chemistry for advanced chemistry learning context
Interpretation of the Final Answer
A pH of about 8.21 means the solution is mildly basic. It is far from the pH values seen for strong bases such as sodium hydroxide, but it is clearly above neutral water. This is exactly what you should expect from a salt derived from a weak acid and strong base. The nitrite ion is basic, but only weakly so, and therefore the equilibrium creates a limited amount of hydroxide.
In laboratory settings, this type of salt solution can matter in buffer calculations, analytical chemistry, and environmental chemistry where nitrogen species influence water composition. Understanding how to move from salt identity to equilibrium expression to pH is an essential skill in general chemistry.
Summary Formula Path for 0.12 M KNO2
- Identify KNO2 as a salt of strong base KOH and weak acid HNO2.
- Recognize NO2- as a weak base in water.
- Use Kb = Kw / Ka.
- Set up Kb = x2 / (C – x).
- Solve for x = [OH-].
- Find pOH = -log[OH-].
- Find pH = 14 – pOH.
For the specific problem asked here, the final result is:
If you use the calculator above, you can instantly recompute the pH if your instructor gives a slightly different Ka value for HNO2 or asks you to test another nitrite concentration. That makes this tool useful both for homework practice and for building deeper intuition about weak base hydrolysis.