Calculate the pH of a 0.00050 M KOH Solution
Use this premium calculator to determine hydroxide concentration, pOH, and pH for a dilute potassium hydroxide solution. KOH is a strong base, so at ordinary classroom conditions it dissociates essentially completely in water.
Calculated Results
At 25 degrees C, a 0.00050 M KOH solution is basic. Because KOH dissociates completely, [OH-] is taken as equal to the KOH molarity in this common approximation.
Expert Guide: How to Calculate the pH of a 0.00050 M KOH Solution
Calculating the pH of a 0.00050 M KOH solution is a classic general chemistry problem that teaches several essential ideas at once: strong electrolyte dissociation, the relationship between hydroxide concentration and pOH, and the conversion from pOH to pH. While the arithmetic is straightforward, the chemistry behind it is important because it shows why potassium hydroxide behaves differently from a weak base such as ammonia. If you understand this one problem well, you will be able to solve a wide range of acid-base calculations much faster and with fewer mistakes.
KOH, or potassium hydroxide, is considered a strong base in introductory aqueous chemistry. That means that when KOH dissolves in water, it dissociates essentially completely into potassium ions and hydroxide ions:
Because the dissociation is effectively complete at ordinary concentrations used in most educational contexts, the hydroxide ion concentration is treated as equal to the original KOH concentration. For a 0.00050 M KOH solution, that means:
Once you know the hydroxide concentration, the next step is to calculate pOH. By definition:
Substituting the concentration gives:
At 25 degrees C, the familiar relationship between pH and pOH is:
So the pH is:
That is the standard answer: the pH of a 0.00050 M KOH solution is approximately 10.70 when rounded to two decimal places, or 10.699 to three decimal places.
Why KOH Makes the Calculation Easy
KOH belongs to the family of strong metal hydroxides. In first-year chemistry, substances such as NaOH, KOH, and often LiOH are treated as strong bases because they produce hydroxide ions nearly completely upon dissolution. This matters because the concentration of dissolved hydroxide comes directly from the formula stoichiometry. Since one mole of KOH gives one mole of OH–, there is a 1:1 relationship between KOH molarity and hydroxide molarity.
- If the solution is 0.10 M KOH, then [OH–] ≈ 0.10 M.
- If the solution is 0.0010 M KOH, then [OH–] ≈ 0.0010 M.
- If the solution is 0.00050 M KOH, then [OH–] ≈ 0.00050 M.
This direct conversion is what makes strong-base pH questions much simpler than weak-base equilibrium problems, where you would need a base dissociation constant, an ICE table, and an equilibrium approximation.
Step-by-Step Calculation in Full
- Write the dissociation equation: KOH → K+ + OH–.
- Assign hydroxide concentration: because KOH is a strong base, [OH–] = 0.00050 M.
- Calculate pOH: pOH = -log(0.00050) = 3.30103.
- Calculate pH: pH = 14.00 – 3.30103 = 10.69897.
- Round appropriately: pH ≈ 10.699 or 10.70 depending on the requested precision.
Common Student Mistakes to Avoid
Even though this problem is relatively easy, there are several errors students make repeatedly:
- Using pH = -log[OH–] instead of pOH = -log[OH–]. Remember that hydroxide gives pOH first.
- Forgetting to subtract from 14 at 25 degrees C.
- Treating KOH as a weak base and trying to use a Kb expression. That is unnecessary here.
- Entering concentration incorrectly into a calculator. 0.00050 is 5.0 × 10-4, not 5.0 × 10-5.
- Rounding too early. Keep extra digits through the pOH step and round only at the end.
Comparison Table: Strong Bases and Approximate pH at 25 Degrees C
The table below shows how changing concentration affects pOH and pH for common strong bases that release one hydroxide ion per formula unit, including KOH and NaOH. These values use the standard classroom approximation of complete dissociation at 25 degrees C.
| Base | Concentration (M) | Approx. [OH-] (M) | pOH | Approx. pH |
|---|---|---|---|---|
| KOH | 0.100 | 0.100 | 1.000 | 13.000 |
| KOH | 0.0100 | 0.0100 | 2.000 | 12.000 |
| KOH | 0.0010 | 0.0010 | 3.000 | 11.000 |
| KOH | 0.00050 | 0.00050 | 3.301 | 10.699 |
| NaOH | 0.00010 | 0.00010 | 4.000 | 10.000 |
How Significant Is Water Autoionization Here?
For very dilute acids and bases, the autoionization of water can become important. At 25 degrees C, pure water has:
[H+] = [OH–] = 1.0 × 10-7 M
In this problem, the KOH concentration is 5.0 × 10-4 M. That hydroxide concentration is 5000 times larger than the hydroxide from pure water alone. Because the added hydroxide overwhelms water’s own contribution, the standard simplification is excellent.
This is one reason the answer is reliable without a more complicated equilibrium treatment. If the concentration were closer to 10-7 M, then the contribution from water would no longer be negligible and a more careful calculation would be warranted.
Data Table: Pure Water vs. 0.00050 M KOH at 25 Degrees C
| System | [OH-] (M) | Relative to Pure Water | pOH | pH |
|---|---|---|---|---|
| Pure water | 1.0 × 10^-7 | 1 × | 7.000 | 7.000 |
| 0.00050 M KOH solution | 5.0 × 10^-4 | 5000 × | 3.301 | 10.699 |
What the Answer Means Chemically
A pH of 10.699 indicates a definitely basic solution, but not an extremely concentrated one. Household and laboratory bases can span a wide range. For example, a 0.10 M strong base has a pH around 13, which is much more alkaline than the present solution. By contrast, your 0.00050 M KOH solution is dilute enough to be considered mildly to moderately basic in comparison, yet still far above neutral pH 7.00.
The logarithmic nature of the pH scale is worth emphasizing. A change of 1 pH unit corresponds to a tenfold change in hydrogen ion concentration. So moving from pH 10.7 to pH 11.7 is not a small adjustment; it represents a tenfold chemical shift in acidity. That is why even a modest change in base concentration can noticeably change pH.
When the Standard 14.00 Relationship Changes
Students are often taught that pH + pOH = 14.00, and that is correct at 25 degrees C. However, the exact value depends on temperature because Kw changes with temperature. In more advanced chemistry, if the temperature is not 25 degrees C, you should use the temperature-appropriate value of Kw. For this calculator and for most general chemistry exercises, the standard assumption is room temperature, so the 14.00 relationship is appropriate and expected.
Authority Sources for Further Study
If you want to review acid-base theory, water ion-product data, or pH fundamentals from reliable sources, the following references are excellent starting points:
- National Institute of Standards and Technology (NIST)
- LibreTexts Chemistry hosted by university contributors
- United States Environmental Protection Agency (EPA) information on pH and water chemistry
Practical Summary
To calculate the pH of a 0.00050 M KOH solution, treat KOH as a strong base that dissociates completely. Set the hydroxide concentration equal to the KOH concentration, calculate pOH with the negative logarithm, and then convert to pH by subtracting from 14.00 at 25 degrees C. The complete sequence is:
- [OH–] = 0.00050 M
- pOH = -log(0.00050) = 3.301
- pH = 14.00 – 3.301 = 10.699
Therefore, the correct answer is pH = 10.699, or 10.70 if rounded to two decimal places. This result is robust, chemically meaningful, and consistent with the expected behavior of a dilute strong base in water.