Calculate the pH of a 0.47 M KOH Solution
Use this interactive calculator to determine pOH, pH, hydroxide concentration, and hydrogen ion concentration for potassium hydroxide solutions. The default setup solves the exact problem of a 0.47 M KOH solution at 25 degrees Celsius under the standard strong-base assumption.
KOH pH Calculator
Assumption used: KOH is a strong base that dissociates essentially completely in dilute to moderately concentrated aqueous solution, so for introductory chemistry calculations, [OH-] is taken as equal to the formal KOH concentration.
Visual Breakdown
The chart compares the resulting pH and pOH and also shows the relative concentrations of hydroxide and hydronium ions on a logarithmic scale. For 0.47 M KOH, the solution is strongly basic.
How to calculate the pH of a 0.47 M KOH solution
To calculate the pH of a 0.47 M potassium hydroxide solution, start with the chemistry of KOH itself. Potassium hydroxide is a strong base, which means it dissociates almost completely in water:
KOH(aq) → K+ + OH-
Because each formula unit of KOH releases one hydroxide ion, a 0.47 M KOH solution produces approximately 0.47 M OH-. Once you know the hydroxide concentration, use the pOH equation:
pOH = -log10[OH-]
Substitute the concentration:
pOH = -log10(0.47) ≈ 0.33
At 25 degrees Celsius, the relationship between pH and pOH is:
pH + pOH = 14.00
So:
pH = 14.00 – 0.33 = 13.67
Why KOH is treated as a strong base
In general chemistry, KOH is classified as a strong Arrhenius base because it dissociates in water to produce hydroxide ions with very high efficiency. That matters because weak bases require an equilibrium expression and a base dissociation constant, but strong bases do not. For KOH, you normally skip an ICE table and go directly from the listed concentration to hydroxide concentration.
This is the key shortcut that makes the problem simple. A weak base such as ammonia would require a different method, since the concentration of OH- would have to be derived from equilibrium. But with potassium hydroxide, the stoichiometric relationship is enough:
- 1 mole of KOH gives 1 mole of OH-
- 0.47 M KOH gives 0.47 M OH-
- Then use logarithms to determine pOH and pH
For classroom and routine laboratory calculations, this assumption is standard unless a problem specifically asks you to account for activity effects at higher ionic strengths.
Step by step solution for 0.47 M KOH
- Write the dissociation equation: KOH → K+ + OH-
- Recognize that KOH is a strong base and dissociates essentially completely.
- Set hydroxide concentration equal to the formal base concentration: [OH-] = 0.47 M.
- Calculate pOH using pOH = -log10[OH-].
- Compute pOH = -log10(0.47) = 0.3279.
- Use pH = 14.00 – 0.3279 at 25 degrees C.
- Round appropriately: pH ≈ 13.67.
If your instructor emphasizes significant figures, the concentration 0.47 M has two significant figures, so reporting pH as 13.67 is typically appropriate because pH values are often expressed with decimal places corresponding to the precision of the logarithmic input.
What about hydrogen ion concentration?
Once pH is known, you can estimate the hydrogen ion concentration:
[H+] = 10^-pH = 10^-13.67 ≈ 2.13 × 10^-14 M
This extremely low hydrogen ion concentration is exactly what you expect for a strongly basic solution. Compare that with pure water at 25 degrees C, where [H+] is about 1.0 × 10^-7 M. The KOH solution has far less H+ and far more OH-, so the pH is much higher.
Important formulas used in this problem
- [OH-] = C for a strong monobasic base like KOH
- pOH = -log10[OH-]
- pH = 14.00 – pOH at 25 degrees C
- [H+] = 10^-pH
- Kw = [H+][OH-] = 1.0 × 10^-14 at 25 degrees C
Students often memorize pH = -log[H+] but forget that strong-base problems are usually faster through pOH first. In this problem, the hydroxide concentration is given indirectly through the concentration of a fully dissociated base, so pOH is the natural first step.
Comparison table: pH values for selected KOH concentrations
The table below shows how pH changes as KOH concentration changes under the same 25 degree C assumption. These values follow the standard strong-base model used in general chemistry.
| KOH Concentration (M) | [OH-] (M) | pOH | pH |
|---|---|---|---|
| 0.0010 | 0.0010 | 3.00 | 11.00 |
| 0.010 | 0.010 | 2.00 | 12.00 |
| 0.10 | 0.10 | 1.00 | 13.00 |
| 0.47 | 0.47 | 0.33 | 13.67 |
| 1.00 | 1.00 | 0.00 | 14.00 |
Why the answer is not exactly 14 unless the concentration is 1.0 M
A common mistake is to assume that any strong base automatically has a pH of 14. That is not true. The pH depends on concentration. A strong base simply means the base dissociates completely, not that every solution is equally basic. For KOH:
- 0.001 M KOH has pH 11
- 0.01 M KOH has pH 12
- 0.10 M KOH has pH 13
- 0.47 M KOH has pH 13.67
Only a 1.0 M strong base gives pOH 0 and therefore pH 14 under the simplest 25 degree C model. This is why concentration matters just as much as acid or base strength.
Second comparison table: ion concentrations and scale perspective
The next table compares a 0.47 M KOH solution with pure water and a mildly basic solution. This helps place the answer in context and shows just how dramatically hydroxide concentration changes across the pH scale.
| Solution | Approx. pH | [H+] (M) | [OH-] (M) |
|---|---|---|---|
| Pure water at 25 degrees C | 7.00 | 1.0 × 10^-7 | 1.0 × 10^-7 |
| Mildly basic solution | 9.00 | 1.0 × 10^-9 | 1.0 × 10^-5 |
| 0.47 M KOH solution | 13.67 | 2.13 × 10^-14 | 4.7 × 10^-1 |
Common mistakes when calculating the pH of KOH
1. Using pH directly from 0.47 M
Some students mistakenly calculate pH = -log(0.47). That is incorrect because 0.47 M in this problem is the hydroxide concentration, not the hydrogen ion concentration. The correct first step is pOH = -log(0.47), then convert to pH.
2. Forgetting that KOH gives one hydroxide ion
KOH contributes one OH- per formula unit. If the base were Ca(OH)2, you would need to account for two hydroxide ions per formula unit. For example, 0.47 M Ca(OH)2 would ideally produce 0.94 M OH-, which would change the pOH and pH.
3. Ignoring temperature assumptions
The equation pH + pOH = 14.00 is exact only at 25 degrees C in the standard introductory model. At other temperatures, the ionic product of water changes. Many textbook and exam questions silently assume 25 degrees C, which is also what this calculator uses.
4. Overthinking complete dissociation
In beginning chemistry, KOH is treated as fully dissociated. In advanced physical chemistry, concentrated solutions may require corrections using activities instead of raw concentrations. Unless your course specifically introduces activity coefficients, the direct strong-base approach is the expected method.
Practical chemistry context
Potassium hydroxide is used in laboratories, industrial cleaning formulations, alkaline batteries, biodiesel processing, and analytical chemistry. Because it is highly caustic, knowing its pH helps predict reactivity, material compatibility, and safety requirements. A 0.47 M KOH solution is strongly basic and can cause severe irritation or burns on contact.
In water chemistry, pH is one of the most fundamental measurements because it influences metal solubility, reaction rates, biological function, and corrosion behavior. Government and university resources consistently emphasize the importance of pH in environmental and laboratory systems. For further reading, see the USGS overview of pH and water, the U.S. EPA discussion of pH in aquatic systems, and the Purdue University guide to pH concepts.
When would a more advanced calculation be needed?
There are cases where a simple classroom pH calculation becomes less accurate:
- Very concentrated solutions with significant non-ideal behavior
- Solutions at temperatures far from 25 degrees C
- Mixed acid-base systems containing buffers or multiple equilibria
- Experiments requiring activity-based thermodynamic treatment
However, for a standard problem asking for the pH of a 0.47 M KOH solution, the correct and expected answer remains about 13.67.
Quick recap
- KOH is a strong base.
- Therefore, [OH-] = 0.47 M.
- pOH = -log10(0.47) = 0.33.
- pH = 14.00 – 0.33 = 13.67.
If you want a fast memory trick, remember this rule: for a strong base that releases one OH-, concentration gives hydroxide directly, then log to pOH, then subtract from 14 to get pH.