Calculate the pH of 5 M NH3
Use this premium weak-base calculator to find the pH, pOH, hydroxide concentration, ammonium concentration, and percent ionization for ammonia solutions. The default setup solves the exact equilibrium for a 5.00 M NH3 solution using the accepted base dissociation constant at 25 degrees Celsius.
Ammonia pH Calculator
Click Calculate pH to solve the equilibrium for the entered ammonia concentration.
Equilibrium Chart
This chart compares the initial NH3 concentration with the equilibrium concentrations of NH3, NH4+, and OH- after the weak-base equilibrium is established.
How to calculate the pH of 5 M NH3
To calculate the pH of 5 M NH3, you treat ammonia as a weak base in water. Ammonia does not fully dissociate the way sodium hydroxide does. Instead, only a small fraction of NH3 molecules react with water to produce ammonium ions, NH4+, and hydroxide ions, OH-. Because hydroxide is produced, the solution is basic and the pH will be greater than 7.
The equilibrium reaction is:
The corresponding base dissociation expression is:
For ammonia at 25 degrees Celsius, many chemistry texts use Kb = 1.8 × 10^-5. If the initial concentration of NH3 is 5.00 M, then you can set up an ICE table. Let x be the amount of NH3 that reacts.
- Initial: [NH3] = 5.00, [NH4+] = 0, [OH-] = 0
- Change: [NH3] = -x, [NH4+] = +x, [OH-] = +x
- Equilibrium: [NH3] = 5.00 – x, [NH4+] = x, [OH-] = x
Substitute those values into the Kb expression:
Because 5.00 M is much larger than x, many introductory problems use the approximation 5.00 – x ≈ 5.00. That gives:
Then calculate pOH:
Finally convert to pH:
So, the ideal textbook answer for the pH of 5 M NH3 is approximately 11.98.
Why ammonia does not give an extremely high pH despite being 5 M
This is a point that often confuses students. A 5 M solution sounds extremely concentrated, so some learners expect a pH close to 14. That would be reasonable for a strong base, but ammonia is not a strong base. Its Kb is relatively small, which means only a limited portion of NH3 molecules convert into OH-. Even though the solution contains a lot of ammonia overall, the amount that actually forms hydroxide is still modest compared with the total concentration.
In other words, the basicity comes from the equilibrium position, not just the starting concentration. Increasing concentration does raise pH, but because NH3 is weak, the increase is not linear and never behaves like a fully dissociated strong base.
Exact calculation versus approximation
For a weak base problem, your teacher may allow the common approximation if the percent ionization is small. The exact quadratic form is:
where:
- x = equilibrium [OH-]
- Kb = base dissociation constant
- C = initial concentration of NH3
Using the quadratic formula:
For C = 5.00 M and Kb = 1.8 × 10^-5, the exact result is still essentially 9.48 × 10^-3 M for [OH-], so the final pH remains about 11.98. The approximation works well here because the ionized fraction is tiny relative to 5.00 M.
| Method | [OH-] (M) | pOH | pH | Percent ionization |
|---|---|---|---|---|
| Approximation | 9.4868 × 10^-3 | 2.023 | 11.977 | 0.1897% |
| Exact quadratic | 9.4774 × 10^-3 | 2.024 | 11.976 | 0.1895% |
| Difference | 9.4 × 10^-6 | Less than 0.001 | Less than 0.001 | 0.0002 percentage points |
The comparison shows why the shortcut is accepted in many general chemistry classrooms. The equilibrium shift is so small relative to the initial concentration that subtracting x from 5.00 makes almost no practical difference in the final pH.
Step-by-step method you can use on exams
- Write the balanced equilibrium reaction for NH3 in water.
- Use the known Kb value for ammonia.
- Set up an ICE table with initial concentration 5.00 M.
- Express equilibrium concentrations in terms of x.
- Substitute into the Kb expression.
- Solve for x, which equals [OH-].
- Calculate pOH = -log[OH-].
- Calculate pH = 14 – pOH.
If you remember those eight steps, you can solve not only this exact problem but also similar weak-base questions involving methylamine, pyridine, or other nitrogen bases.
Concentration effects: how 5 M NH3 compares with weaker and stronger solutions
It helps to compare 5 M ammonia with less concentrated ammonia solutions. The table below uses the same weak-base model and Kb = 1.8 × 10^-5 at 25 degrees Celsius. The numbers are useful for building intuition: as concentration rises, pH increases, but not nearly as dramatically as it would for a strong base.
| Initial NH3 concentration (M) | Calculated [OH-] (M) | Calculated pOH | Calculated pH | Percent ionization |
|---|---|---|---|---|
| 0.10 | 1.333 × 10^-3 | 2.875 | 11.125 | 1.333% |
| 0.50 | 2.992 × 10^-3 | 2.524 | 11.476 | 0.598% |
| 1.00 | 4.234 × 10^-3 | 2.373 | 11.627 | 0.423% |
| 5.00 | 9.477 × 10^-3 | 2.023 | 11.976 | 0.190% |
Notice two key trends:
- The pH rises as NH3 concentration rises.
- The percent ionization falls as the solution becomes more concentrated.
This inverse relationship between concentration and percent ionization is common for weak acids and weak bases. In concentrated solutions, the equilibrium does not need to shift as far to satisfy the equilibrium constant.
Important real-world chemistry note for concentrated ammonia solutions
The standard textbook result for 5 M NH3 assumes ideal behavior, where concentrations are treated as if they were equal to activities. In real concentrated solutions, that simplification becomes less accurate. At high ionic strengths and high solute concentrations, activity coefficients deviate from 1, and measured pH can differ somewhat from simple classroom calculations. This does not mean the equilibrium setup is wrong; it means the model is an approximation designed for instructional chemistry.
That distinction matters if you work in analytical chemistry, industrial process chemistry, or environmental chemistry. In those fields, highly concentrated ammonia solutions may require activity corrections, temperature corrections, and calibration against actual instrument readings. For most homework, quizzes, and introductory lab calculations, however, the accepted answer remains very close to pH 11.98.
Common mistakes students make
- Treating NH3 as a strong base. If you assume complete dissociation, you will drastically overestimate pH.
- Using Ka instead of Kb. Ammonia is a base, so use Kb unless the problem is framed through NH4+ and Ka.
- Forgetting that x equals OH-. Since ammonia produces hydroxide, the first logarithm gives pOH, not pH.
- Skipping the 14 – pOH step. This is probably the most common arithmetic mistake.
- Ignoring units. Concentrations must be in molarity for the standard expression used here.
Relationship between NH3 and NH4+
Ammonia and ammonium form a conjugate acid-base pair. When NH3 accepts a proton from water, it becomes NH4+. This pair is central to buffer chemistry, biological nitrogen chemistry, and wastewater treatment. If you know the pKa of NH4+ or the Kb of NH3, you can move between the two using the relation:
For ammonia, the conjugate acid NH4+ has a pKa near 9.25, which is consistent with ammonia being a weak but important base in aqueous systems.
Authoritative references for ammonia acid-base chemistry
If you want to cross-check constants, equilibrium concepts, or ammonia handling information, these sources are useful:
- U.S. Environmental Protection Agency: ammonia resources
- Purdue University: acid-base equilibrium review
- University of Wisconsin: weak acids and weak bases equilibrium concepts
Final answer
Using the standard general chemistry equilibrium model with Kb = 1.8 × 10^-5, the pH of 5 M NH3 is approximately 11.98. The corresponding hydroxide concentration is about 9.48 × 10^-3 M, the pOH is about 2.02, and the percent ionization is only about 0.19%.
If your course expects an exact quadratic solution, you still arrive at essentially the same answer. If your course allows the weak-base approximation, it is fully justified because the ionized amount is extremely small compared with the initial 5.00 M concentration.