Calculate the pH of a 0.075 M Solution of KOH
Use this interactive strong-base calculator to find hydroxide concentration, pOH, and pH for potassium hydroxide solutions. The default example is 0.075 M KOH at 25°C.
KOH pH Calculator
How to calculate the pH of a 0.075 M solution of KOH
To calculate the pH of a 0.075 M solution of KOH, you use the fact that potassium hydroxide is a strong base. Strong bases dissociate essentially completely in water under ordinary introductory chemistry conditions. That means each formula unit of KOH separates into one potassium ion, K+, and one hydroxide ion, OH–. Because there is a one-to-one stoichiometric relationship, the hydroxide concentration is the same as the molar concentration of KOH.
Step 1: Write the dissociation equation
The reaction of potassium hydroxide in water is:
KOH(aq) → K+(aq) + OH–(aq)
Since KOH is a strong base, this reaction goes essentially to completion in dilute aqueous solution. For many textbook and general chemistry calculations, we treat dissociation as complete.
Step 2: Determine the hydroxide concentration
If the KOH concentration is 0.075 M, then:
[OH–] = 0.075 M
This works because each mole of KOH produces one mole of hydroxide ions. If you were dealing with a base that produced more than one hydroxide ion per formula unit, the stoichiometry would change. For example, Ba(OH)2 produces two OH– ions for each formula unit dissolved.
Step 3: Calculate pOH
The formula for pOH is:
pOH = -log[OH–]
Substitute the hydroxide concentration:
pOH = -log(0.075)
Using a base-10 logarithm:
pOH ≈ 1.1249
Step 4: Convert pOH to pH
At 25°C, the relationship between pH and pOH is:
pH + pOH = 14.00
Therefore:
pH = 14.00 – 1.1249 = 12.8751
Rounded appropriately, the pH of a 0.075 M KOH solution is 12.88.
Why KOH gives a high pH
Potassium hydroxide is one of the classic examples of a strong Arrhenius base. It directly increases hydroxide ion concentration in water. The pH scale is logarithmic, so even moderate changes in concentration can shift pH in meaningful ways. A 0.075 M concentration is not dilute enough to be close to neutral, so the pH lands well above 12. In practical terms, that means the solution is strongly basic and should be handled with proper laboratory precautions.
When students first learn pH calculations, they often wonder why you cannot simply “see” the pH from the concentration. The reason is that pH and pOH are logarithmic transforms of hydrogen ion and hydroxide ion concentrations. A hydroxide concentration of 0.075 M does not correspond to pH 7.5 or 0.75. Instead, you must apply the logarithm to convert concentration into the pOH scale and then convert to pH.
Detailed worked example for 0.075 M KOH
- Start with the concentration of KOH: 0.075 mol/L.
- Recognize that KOH is a strong base and dissociates completely.
- Use stoichiometry: [OH–] = 0.075 M.
- Apply the pOH formula: pOH = -log(0.075).
- Compute pOH: 1.1249.
- Use pH = 14.00 – pOH at 25°C.
- Find pH: 12.8751.
- Round based on the precision of the original concentration: pH ≈ 12.88.
Common mistakes when calculating the pH of KOH
- Using the acid formula instead of the base formula. For KOH, start with hydroxide concentration and calculate pOH first.
- Forgetting that KOH is a strong base. You do not typically need an equilibrium ICE table for this basic textbook problem.
- Typing the logarithm incorrectly. Make sure you use -log(0.075), not log(0.075) without the negative sign.
- Confusing pOH with pH. A pOH of 1.125 means the pH is 12.875 at 25°C.
- Ignoring temperature assumptions. The familiar equation pH + pOH = 14.00 is exact only at about 25°C in many classroom settings.
Comparison table: KOH concentration vs pOH and pH 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 |
| 0.050 | 0.050 | 1.301 | 12.699 |
| 0.075 | 0.075 | 1.125 | 12.875 |
| 0.100 | 0.100 | 1.000 | 13.000 |
This table shows the logarithmic character of the pH scale. Moving from 0.010 M to 0.100 M is a tenfold increase in hydroxide concentration, but pOH changes by only 1 unit and pH changes by only 1 unit. Your 0.075 M KOH example falls between 0.050 M and 0.100 M, which is why the pH is between 12.699 and 13.000.
What “0.075 M” means in chemical terms
A molarity of 0.075 M means there are 0.075 moles of KOH dissolved per liter of solution. Because the molar mass of KOH is approximately 56.11 g/mol, this corresponds to about 4.21 grams of KOH per liter if the solution were prepared ideally from pure KOH and adjusted to a final volume of one liter.
| Property | KOH Value | Why It Matters |
|---|---|---|
| Molar mass | 56.11 g/mol | Useful when converting between grams and moles |
| Stoichiometric OH- yield | 1 mol OH- per 1 mol KOH | Lets you set [OH-] equal to KOH concentration |
| Example concentration | 0.075 mol/L | Given starting value for the pH calculation |
| Approximate mass in 1.00 L | 4.21 g | Helps connect solution chemistry with lab preparation |
Why the answer depends on temperature
Students are often taught that pH + pOH = 14.00, but that value is tied to the ion-product constant of water, Kw, which changes with temperature. In many classroom and calculator problems, 25°C is assumed unless otherwise stated. For your 0.075 M KOH solution, the standard classroom answer is therefore based on pKw = 14.00 and gives pH ≈ 12.88.
If the temperature is not 25°C, then pKw changes slightly and the pH changes too. The hydroxide concentration from fully dissociated KOH remains the main driver, but the conversion from pOH to pH shifts with temperature. This is why professional chemistry work often specifies temperature alongside concentration and measurement conditions.
Strong base theory behind this calculation
KOH belongs to a group of ionic hydroxides that are treated as strong bases in water. This means their equilibrium lies so far to the products side that for ordinary calculations, the dissolved base is considered completely dissociated. In contrast, weak bases such as ammonia require an equilibrium constant, Kb, and usually an ICE table or approximation strategy.
For KOH, the chemistry is simpler:
- There is no need to solve for an equilibrium concentration of OH–.
- The hydroxide concentration comes directly from stoichiometry.
- The logarithmic transformation to pOH and pH is the main mathematical step.
Real-world context for KOH solutions
Potassium hydroxide is used in analytical chemistry, biodiesel production, alkaline batteries, soap manufacturing, pH adjustment, and chemical cleaning processes. Solutions in this pH range are caustic and can damage skin, eyes, and many materials. That practical reality matches the high pH value you calculate. A pH of roughly 12.88 indicates a strongly basic solution, not a mildly alkaline one.
In laboratories and industry, actual measured pH can differ slightly from ideal calculations because of activity effects, calibration quality, ionic strength, temperature drift, and contamination from atmospheric carbon dioxide. CO2 can react with hydroxide, slightly lowering the effective basicity over time in exposed solutions. For general chemistry coursework, however, the ideal strong-base approach is exactly the right method.
Authoritative references for pH, strong bases, and water chemistry
For more background, consult these authoritative educational and government resources:
- LibreTexts Chemistry for general acid-base theory and pH calculations.
- U.S. Environmental Protection Agency for water pH fundamentals and environmental chemistry context.
- NIST Chemistry WebBook for trusted chemical data and reference information.
Final answer
If you need the direct answer only: for a 0.075 M solution of KOH at 25°C, assume complete dissociation, set [OH–] = 0.075 M, calculate pOH = -log(0.075) = 1.125, then compute pH = 14.00 – 1.125 = 12.875. Rounded to two decimal places, the pH is 12.88.