Calculate the pH of a Solution 1.5×10-5 M NH4OH
Use this premium weak-base calculator to determine pOH, pH, hydroxide concentration, and the degree of ionization for dilute ammonium hydroxide solutions.
How to Calculate the pH of a 1.5×10-5 M NH4OH Solution
If you need to calculate the pH of a solution 1.5×10-5 M NH4OH, you are solving a classic weak-base equilibrium problem. NH4OH, commonly treated in introductory chemistry as ammonium hydroxide, represents aqueous ammonia behaving as a weak base in water. Because it is not a strong base, it does not ionize completely. That means you cannot simply assume the hydroxide concentration equals the starting molarity. Instead, you must apply the base dissociation constant, Kb, and solve the equilibrium expression.
At 25 degrees C, a widely used Kb value for aqueous ammonia is approximately 1.8×10-5. For a starting concentration of 1.5×10-5 M, the concentration is in the same order of magnitude as Kb. That is an important clue: the usual shortcut for weak bases, where x is assumed small relative to the initial concentration, becomes much less reliable. In this case, the better approach is to use the quadratic form of the equilibrium equation.
1. Write the chemical equilibrium
The weak-base reaction can be represented as:
Many textbooks write the base as NH4OH, but the equilibrium behavior is equivalent to dissolved ammonia accepting a proton from water to produce ammonium and hydroxide. The key quantity that controls how far this reaction proceeds is Kb.
2. Set up an ICE table
Start with an initial concentration of 1.5×10-5 M for NH4OH and assume zero added products:
- Initial: [Base] = 1.5×10-5, [NH4+] = 0, [OH–] = 0
- Change: -x, +x, +x
- Equilibrium: [Base] = 1.5×10-5 – x, [NH4+] = x, [OH–] = x
3. Apply the Kb expression
Because x is not negligible compared with 1.5×10-5, solve this exactly instead of using the small-x approximation.
4. Rearrange into a quadratic equation
Solving with the quadratic formula gives:
Since x equals the equilibrium hydroxide concentration, [OH–] ≈ 9.44×10-6 M.
5. Convert hydroxide concentration to pOH and pH
Therefore, the pH of a solution 1.5×10-5 M NH4OH is approximately 8.98 under standard classroom assumptions at 25 degrees C.
Why this problem is trickier than it looks
Students often make one of two mistakes with this kind of question. The first is to treat NH4OH as a strong base and assume the hydroxide concentration is 1.5×10-5 M directly. If you do that, you would calculate pOH = 4.82 and pH = 9.18. That answer is too high because weak bases do not fully dissociate.
The second common mistake is to use the weak-base approximation x = √(KbC) without checking whether x is small compared with C. Here, because Kb and concentration are close in size, the approximation predicts x ≈ 1.64×10-5 M, which is physically impossible because x would exceed the starting concentration. That is your warning sign that the approximation breaks down and the quadratic solution is necessary.
| Method | Assumption | Calculated [OH-] | pH | Comment |
|---|---|---|---|---|
| Strong-base assumption | Complete dissociation | 1.50×10-5 M | 9.18 | Too high for NH4OH |
| Weak-base approximation | x small relative to C | 1.64×10-5 M | 9.22 | Invalid because x exceeds initial concentration |
| Quadratic equilibrium solution | No small-x shortcut | 9.44×10-6 M | 8.98 | Best standard chemistry answer |
Interpreting the result chemically
A pH of about 8.98 means the solution is basic, but only mildly so. That makes sense: the concentration is very low, and NH4OH is a weak base. The equilibrium strongly limits hydroxide production. In fact, the percent ionization is fairly high compared with more concentrated weak-base solutions, because dilution tends to favor ionization. Even so, the absolute hydroxide concentration remains small.
To estimate the degree of ionization:
That number may surprise you. Weak electrolytes can show large percent ionization at very low concentration, even though they still produce modest ion concentrations overall. This is one reason dilute equilibrium problems deserve careful treatment.
Real numerical reference points for pH scale context
Putting 8.98 on the pH scale into context can help you understand what the answer means. The pH scale is logarithmic, so a small numerical shift corresponds to a large change in hydrogen or hydroxide concentration. Standard educational and laboratory references routinely use pH 7.00 as neutral water at 25 degrees C, values below 7 as acidic, and values above 7 as basic.
| Reference Solution or Range | Typical pH | Comparison to 1.5×10-5 M NH4OH |
|---|---|---|
| Pure water at 25 degrees C | 7.00 | The NH4OH solution is about 1.98 pH units more basic |
| Typical drinking water guideline range | 6.5 to 8.5 | This solution is slightly above the usual upper aesthetic guideline range |
| Common classroom dilute ammonia solution | 9 to 11+ | This value sits at the lower end because the concentration is very low |
| Strong base laboratory solution | 12 to 14 | Far less basic than concentrated NaOH or KOH |
When should you consider water autoionization?
At extremely low solute concentrations, water itself contributes a meaningful amount of H+ and OH– through autoionization. In pure water at 25 degrees C, each is about 1.0×10-7 M. For this NH4OH problem, the equilibrium hydroxide concentration from the base is about 9.44×10-6 M, which is much larger than 1.0×10-7 M. That means the water contribution is comparatively small and the standard weak-base treatment remains acceptable.
If the initial base concentration were much closer to 10-7 M, then ignoring water autoionization could introduce noticeable error. In advanced analytical chemistry, more complete charge-balance and mass-balance equations are sometimes used for ultra-dilute systems. For ordinary homework or general chemistry exam work, however, the quadratic weak-base solution shown here is the correct and expected method.
Step-by-step summary for solving similar problems
- Identify whether the solute is a strong or weak acid/base.
- Write the equilibrium reaction with water.
- Build an ICE table using x for the amount ionized.
- Substitute equilibrium concentrations into the Ka or Kb expression.
- Check whether the small-x approximation is justified.
- If it is not justified, solve the quadratic equation.
- Convert [OH–] to pOH, then calculate pH using pH + pOH = 14 at 25 degrees C.
- Optionally compute percent ionization to understand how extensively the weak base dissociates.
Common student questions
Is NH4OH a real compound in solution?
In many educational settings, NH4OH is used as a convenient way to represent aqueous ammonia. More rigorously, the species present are ammonia, water, ammonium, and hydroxide in equilibrium. For pH calculations, using the Kb of ammonia is the key step.
Why is the pH not very high if the solution is basic?
Because the concentration is only 1.5×10-5 M, there is limited material available to produce hydroxide ions. Even though the percent ionization is relatively substantial, the total hydroxide formed is still small compared with more concentrated base solutions.
Can I always use pH = 14 – pOH?
At 25 degrees C, yes, that is the standard relationship because pKw = 14.00. At other temperatures, pKw changes slightly, so highly precise work may need a temperature-adjusted value.
Authoritative references for pH, equilibrium constants, and water quality
For deeper reading, consult high-quality science and regulatory references such as the U.S. Environmental Protection Agency pH overview, the LibreTexts Chemistry library, and university chemistry resources such as University of Minnesota Chemistry. For water-related pH guidance and interpretation, the U.S. Geological Survey pH and water resource is especially useful.
Final answer
Using Kb = 1.8×10-5 at 25 degrees C, the pH of a solution 1.5×10-5 M NH4OH is approximately 8.98. The corresponding pOH is about 5.02, and the hydroxide ion concentration is about 9.44×10-6 M.
Educational note: Different textbooks may round Kb slightly differently, which can shift the last decimal place. The expected answer remains very close to pH 8.98.