Calculate The Ph Of A 0.155 M Solution Of Koh

Chemistry Calculator

Use this interactive calculator to determine hydroxide concentration, pOH, and final pH for a potassium hydroxide solution. The default setup solves the exact problem of a 0.155 M KOH solution at 25°C, where KOH is treated as a strong base that dissociates completely in water.

Interactive Calculator

How to Calculate the pH of a 0.155 M Solution of KOH

To calculate the pH of a 0.155 M solution of KOH, you use the fact that potassium hydroxide is a strong base. In introductory and most intermediate chemistry settings, a strong base is assumed to dissociate completely in water. That means every mole of KOH contributes one mole of hydroxide ions, OH⁻, to the solution. Because pH is a logarithmic measure tied to hydrogen ion concentration, and because basic solutions are often easier to analyze through hydroxide concentration first, the standard route is to determine pOH and then convert pOH to pH.

The process is surprisingly straightforward once you know the rules. In this case, a 0.155 M KOH solution means the hydroxide ion concentration is approximately 0.155 M, assuming complete dissociation and ideal behavior. Once you have [OH⁻], you compute pOH using the negative base-10 logarithm. Finally, at 25°C, you subtract pOH from 14.00 to obtain pH.

Quick answer: For a 0.155 M KOH solution at 25°C, the pOH is about 0.810 and the pH is about 13.190.

Step 1: Recognize That KOH Is a Strong Base

KOH, or potassium hydroxide, belongs to the family of alkali metal hydroxides. These bases are highly soluble and are considered strong electrolytes in water. In a general chemistry problem, this means:

KOH(aq) → K⁺(aq) + OH⁻(aq)

Because the dissociation is effectively complete under standard assumptions, the concentration of hydroxide ions equals the concentration of dissolved KOH. So if the solution is 0.155 M KOH, then:

[OH⁻] = 0.155 M

This is the key simplification. You do not need an ICE table for a typical KOH pH problem because the extent of dissociation is not small or uncertain the way it is for weak bases such as ammonia.

Step 2: Calculate pOH

The definition of pOH is:

pOH = -log10[OH⁻]

Substitute the hydroxide concentration:

pOH = -log10(0.155)

Using a calculator:

pOH ≈ 0.8097

If you round to three decimal places, the pOH becomes 0.810.

Step 3: Convert pOH to pH

At 25°C, the standard relationship between pH and pOH is:

pH + pOH = 14.00

So:

pH = 14.00 – 0.8097 = 13.1903

Rounded appropriately:

pH ≈ 13.19

That is the correct pH of a 0.155 M KOH solution at 25°C under standard classroom assumptions.

Why This Result Makes Sense

A pH of 13.19 is very basic, which matches what you would expect from a moderately concentrated strong base. Neutral water at 25°C has pH 7.00, and any pH significantly above 7 indicates increasing basicity. Since 0.155 M is not a trace concentration but also not an extremely concentrated industrial solution, a pH in the low 13s is chemically reasonable.

Another good intuition check is to compare the hydroxide concentration to 1.0 M. If [OH⁻] were 1.0 M, then pOH would be 0 and pH would be 14 at 25°C. Since 0.155 M is less than 1.0 M, the pOH should be a little greater than 0, and the pH should be a little less than 14. That is exactly what we found.

Common Mistakes Students Make

• Using pH = -log(0.155) directly. That gives the pOH, not the pH, because 0.155 M refers to hydroxide concentration, not hydrogen ion concentration.
• Forgetting complete dissociation. KOH is a strong base, so [OH⁻] equals the initial KOH molarity in standard problems.
• Forgetting to subtract from 14. After finding pOH, you must calculate pH from pH = 14 – pOH at 25°C.
• Ignoring temperature assumptions. The equation pH + pOH = 14.00 is exact only at 25°C in standard textbook form. At other temperatures, pKw changes.
• Over-rounding too early. Keep several digits during intermediate steps, then round the final answer.

Worked Example in Full

1. Given concentration: 0.155 M KOH
2. Strong base assumption: [OH⁻] = 0.155 M
3. Calculate pOH: pOH = -log(0.155) = 0.8097
4. Calculate pH: pH = 14.00 – 0.8097 = 13.1903
5. Final answer: pH = 13.19

Comparison Table: pH of Different KOH Concentrations at 25°C

The following table shows how strongly pH responds to changing KOH concentration. These values are calculated using the same method: complete dissociation, pOH = -log[OH⁻], and pH = 14.00 – pOH at 25°C.

KOH Concentration (M)	[OH⁻] (M)	pOH	pH at 25°C
0.001	0.001	3.000	11.000
0.010	0.010	2.000	12.000
0.100	0.100	1.000	13.000
0.155	0.155	0.810	13.190
0.500	0.500	0.301	13.699
1.000	1.000	0.000	14.000

Temperature Matters More Than Many Learners Expect

Many chemistry exercises silently assume 25°C, but pH calculations are temperature dependent because the ion-product constant of water changes with temperature. In practical terms, this means the familiar relationship pH + pOH = 14.00 is a 25°C convention. At lower or higher temperatures, the sum is different. For classroom questions that specifically ask for the pH of a 0.155 M KOH solution without providing temperature data, 25°C is usually the intended assumption.

Still, it is useful to understand how pKw shifts. As temperature rises, water ionizes more extensively, which lowers pKw. This affects the pH scale itself, even though the solution remains strongly basic. The table below summarizes representative pKw values often used in chemistry references.

Temperature	Approximate pKw of Water	Neutral pH	Implication for KOH pH Calculations
0°C	14.94	7.47	For the same [OH⁻], the computed pH can be higher than the 25°C value because pKw is larger.
25°C	14.00	7.00	This is the standard textbook condition used for most pH and pOH problems.
50°C	13.26 to 13.60	6.63 to 6.80	The pH scale shifts downward, so pH + pOH is less than 14.

KOH Compared With Weak Bases

One reason this problem is easier than many acid-base calculations is that KOH is not a weak base. If you were dealing with ammonia, methylamine, or another weak base, the hydroxide concentration would not equal the starting concentration. Instead, you would need an equilibrium setup and the base dissociation constant, Kb. In contrast, KOH behaves as a strong electrolyte and contributes hydroxide ions directly and nearly quantitatively.

That difference matters in both speed and accuracy. A strong-base problem like this can often be solved in under a minute if you remember the formulas. A weak-base problem may require quadratic solving, approximation checks, or activity corrections in advanced settings.

Formula Summary for This Problem

• Strong base dissociation: [OH⁻] = [KOH]
• Hydroxide relation: pOH = -log[OH⁻]
• At 25°C: pH = 14.00 – pOH

Applying those formulas to 0.155 M KOH gives:

[OH⁻] = 0.155 M pOH = -log(0.155) ≈ 0.8097 pH = 14.00 – 0.8097 ≈ 13.1903

Does Significant-Figure Treatment Matter?

Yes, but not excessively. Since the given concentration 0.155 M contains three significant figures, reporting the final pH to three decimal places is often acceptable in educational contexts. That is why 13.190 is a clean and defensible final answer. Some instructors accept 13.19, especially if two decimal places are standard in the course. The most important thing is to avoid rounding too early in the calculation.

Practical Interpretation of pH 13.19

A solution with pH 13.19 is strongly caustic and should be treated with caution in any laboratory environment. Potassium hydroxide solutions can cause severe skin and eye irritation or burns. Even though this page focuses on the mathematics of the calculation, the chemistry has real safety consequences. Basicity at this level means the hydroxide ion concentration is far above that of neutral water.

In laboratory and industrial practice, KOH is used in cleaning solutions, chemical synthesis, battery manufacture, pH adjustment, and soap production. Understanding its pH is not only a textbook exercise but also a practical foundation for safe handling and process control.

Authoritative References for Further Study

• LibreTexts Chemistry for acid-base theory, pH, and strong base examples.
• NIST Chemistry WebBook for reliable chemical data resources.
• U.S. Environmental Protection Agency for water chemistry context and pH related environmental guidance.
• NIH NCBI Bookshelf for toxicology and safety context involving corrosive bases.

Final Takeaway

If you are asked to calculate the pH of a 0.155 M solution of KOH, the solution path is direct: treat KOH as a strong base, set [OH⁻] equal to 0.155 M, calculate pOH from the logarithm, and then convert to pH. At 25°C, the final result is pH = 13.19. This answer is chemically reasonable, mathematically correct, and fully consistent with standard acid-base conventions taught in chemistry courses.

Educational note: This calculator uses the standard strong-base assumption for KOH and the selected pKw value for the chosen temperature. In advanced physical chemistry, very concentrated solutions may require activity corrections rather than relying only on molarity.