Calculate the pH of a 0.15 M Solution of NaOH
Use this interactive calculator to find hydroxide concentration, pOH, and pH for sodium hydroxide solutions. The default example is 0.15 M NaOH at 25 degrees Celsius.
NaOH pH Calculator
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Enter or keep the default value of 0.15 M NaOH, then click Calculate pH.
Expert Guide: How to Calculate the pH of a 0.15 M Solution of NaOH
Calculating the pH of a sodium hydroxide solution is one of the most common tasks in acid-base chemistry. If you want to calculate the pH of a 0.15 M solution of NaOH, the process is straightforward because sodium hydroxide is classified as a strong base. That means it dissociates almost completely in water, producing hydroxide ions that directly determine the solution’s basicity.
The short answer
For a 0.15 M NaOH solution at 25 degrees Celsius:
- [OH-] = 0.15 M
- pOH = -log10(0.15) = 0.824
- pH = 14.00 – 0.824 = 13.176
Final answer: the pH is approximately 13.18.
Why NaOH is easy to handle in pH calculations
Sodium hydroxide, NaOH, is a strong base. In introductory and most practical chemistry calculations, strong bases are treated as fully dissociated in water. Once dissolved, each formula unit of NaOH releases one hydroxide ion:
NaOH(aq) → Na+(aq) + OH-(aq)
This one-to-one relationship is what makes pH calculations for NaOH direct. If the concentration of NaOH is 0.15 M, then the hydroxide ion concentration is also 0.15 M, assuming ideal behavior.
That differs from weak bases such as ammonia, which do not ionize completely and require equilibrium expressions. With NaOH, there is usually no need to solve a quadratic equation or calculate a base dissociation constant. For classroom chemistry, general laboratory work, and many industrial approximations, this is exactly the right approach.
Step by step method to calculate the pH of 0.15 M NaOH
- Write the dissociation equation: NaOH dissociates fully into Na+ and OH-.
- Identify hydroxide concentration: because one NaOH gives one OH-, the hydroxide concentration is 0.15 M.
- Calculate pOH: pOH = -log10[OH-] = -log10(0.15).
- Evaluate the logarithm: pOH ≈ 0.8239.
- Convert pOH to pH: pH = 14.00 – 0.8239 = 13.1761.
- Round appropriately: pH ≈ 13.18.
This approach is the standard method taught in chemistry courses because it follows the definitions of pOH and pH. At 25 degrees Celsius, pH and pOH add to 14.00, which comes from the ionic product of water. At other temperatures, the pKw value shifts slightly, and our calculator above accounts for that by letting you choose a temperature.
Important note about M versus m
You may sometimes see the problem written as 0.15 m NaOH instead of 0.15 M NaOH. These are not exactly the same unit.
- Molarity (M) means moles of solute per liter of solution.
- Molality (m) means moles of solute per kilogram of solvent.
For many dilute aqueous solutions, molarity and molality are numerically close, which is why textbook problems often treat them almost interchangeably in simple pH examples. If your problem specifically says 0.15 m and gives no density information, many instructors still expect the same strong-base method and an answer near pH 13.18. In high precision work, however, you would need solution density and activity effects to convert accurately between concentration scales.
Comparison table: common NaOH concentrations and pH at 25 degrees Celsius
| NaOH concentration (M) | [OH-] (M) | pOH | pH at 25 degrees Celsius |
|---|---|---|---|
| 0.001 | 0.001 | 3.000 | 11.000 |
| 0.010 | 0.010 | 2.000 | 12.000 |
| 0.050 | 0.050 | 1.301 | 12.699 |
| 0.100 | 0.100 | 1.000 | 13.000 |
| 0.150 | 0.150 | 0.824 | 13.176 |
| 0.500 | 0.500 | 0.301 | 13.699 |
| 1.000 | 1.000 | 0.000 | 14.000 |
This table shows the logarithmic nature of the pH scale. Increasing NaOH concentration does not increase pH linearly. Instead, every tenfold change in hydroxide concentration changes pOH by 1 unit, which shifts pH by 1 unit in the opposite direction at 25 degrees Celsius.
How temperature changes the result
Many learners memorize the formula pH + pOH = 14, but that is strictly valid at 25 degrees Celsius. The ionic product of water changes with temperature, so pKw also changes. As temperature rises, pKw decreases, which means the calculated pH for the same hydroxide concentration changes slightly. This effect is usually small for basic classroom problems, but it matters in analytical chemistry and process control.
| Temperature | Approximate pKw | pOH for 0.15 M NaOH | Estimated pH |
|---|---|---|---|
| 0 degrees Celsius | 14.94 | 0.824 | 14.116 |
| 25 degrees Celsius | 14.00 | 0.824 | 13.176 |
| 50 degrees Celsius | 13.26 | 0.824 | 12.436 |
Notice that the same hydroxide concentration produces different pH values at different temperatures when pKw is adjusted. This does not mean the solution becomes weaker in a practical sense. It reflects how the water equilibrium changes with temperature.
Common mistakes when calculating pH for NaOH
- Using pH = -log[OH-]. That formula gives pOH, not pH.
- Forgetting complete dissociation. For NaOH, [OH-] equals the NaOH concentration in simple problems.
- Ignoring temperature assumptions. If no temperature is given, use 25 degrees Celsius.
- Confusing M and m. Molarity and molality are different concentration units.
- Rounding too early. Keep several digits during the logarithm step, then round at the end.
These small mistakes can produce answers that are close but not correct. If you are preparing for a chemistry exam, showing each step clearly can help you avoid unit confusion and sign errors.
What the result means chemically
A pH of about 13.18 indicates a strongly basic solution. Neutral water at 25 degrees Celsius has a pH of 7, so 0.15 M NaOH is far more alkaline than neutral water. Such a solution can cause chemical burns, react with acids, and alter the stability of many materials and biological systems.
In laboratory and industrial settings, sodium hydroxide is used for titrations, cleaning, soap production, pH adjustment, paper manufacturing, and chemical synthesis. Concentrations around 0.1 to 0.2 M are common in educational and practical work because they are strong enough to show clear basic behavior without reaching the extreme handling concerns of much more concentrated caustic solutions.
Real-world context and safety perspective
Sodium hydroxide is often called caustic soda for a reason. Even moderately concentrated solutions are hazardous to skin, eyes, and many surfaces. A solution with pH above 13 is considered strongly corrosive in practical handling terms. Always use proper protective equipment, including gloves and eye protection, and follow your institution’s safety rules.
If you are comparing household and laboratory basic solutions, a 0.15 M NaOH solution is much more alkaline than ordinary baking soda solutions and stronger than many cleaning products in terms of hydroxide concentration. It is therefore important to combine correct chemistry with correct safety habits.
Authoritative references for acid-base chemistry and sodium hydroxide
- LibreTexts Chemistry for general acid-base and pH explanations.
- U.S. Environmental Protection Agency for chemical safety and water chemistry context.
- CDC NIOSH for occupational safety information related to sodium hydroxide exposure.
- OpenStax for educational chemistry reference material hosted by a trusted academic source.
These sources are useful if you want to verify strong base behavior, review the pH scale, or understand safe handling guidance for caustic solutions.
Final conclusion
To calculate the pH of a 0.15 M solution of NaOH, assume complete dissociation, set hydroxide concentration equal to 0.15 M, calculate pOH using the negative logarithm, and then subtract from 14.00 if the temperature is 25 degrees Celsius. The result is:
pH = 13.18
That answer is the standard textbook result and the correct value for an ideal 0.15 M sodium hydroxide solution under normal room-temperature assumptions. If you need more precise work, you can also account for temperature, non-ideal activity, and concentration-unit differences. The calculator on this page handles the core chemistry instantly and provides a visual chart so you can understand how concentration, pOH, and pH relate to one another.