Calculate the pH of a 0.0150 M Solution of NaOH
Use this premium calculator to find hydroxide concentration, pOH, and final pH for a sodium hydroxide solution. For 0.0150 M NaOH at 25 degrees Celsius, the expected solution is strongly basic because NaOH dissociates essentially completely in water.
Interactive NaOH pH Calculator
Enter the concentration and choose the calculation conditions. The default value is set to 0.0150 M to match the target problem.
Enter concentration in mol/L. Example: 0.0150
For introductory and most general chemistry problems, NaOH is treated as a strong base that fully dissociates: NaOH → Na+ + OH−.
Results
Click Calculate pH to see the step by step result for a 0.0150 M NaOH solution.
How to Calculate the pH of a 0.0150 M Solution of NaOH
Calculating the pH of a sodium hydroxide solution is a classic general chemistry problem because it combines acid-base definitions, logarithms, solution concentration, and the relationship between pH and pOH. In this specific case, the question asks for the pH of a 0.0150 M solution of NaOH. The solution process is straightforward once you recognize that sodium hydroxide is a strong base. That means it dissociates essentially completely in water, producing sodium ions and hydroxide ions in a one-to-one ratio.
Because NaOH is a strong base, the hydroxide ion concentration is taken directly from the molarity of the dissolved base. So, a 0.0150 M NaOH solution gives an OH− concentration of 0.0150 M under the usual assumptions used in chemistry coursework. From there, you calculate pOH using the negative base-10 logarithm of hydroxide concentration, then use the relationship between pH and pOH to determine the pH.
So the pH of a 0.0150 M solution of NaOH is approximately 12.18 when rounded to two decimal places, or 12.176 when rounded to three decimal places. This result is consistent with what we expect for a moderately concentrated strong base: a low pOH and a pH well above 7.
Step by Step Method
- Identify the substance. NaOH is sodium hydroxide, a strong base.
- Write the dissociation equation. Sodium hydroxide dissociates completely into Na+ and OH− ions.
- Set hydroxide concentration equal to base concentration. Since one mole of NaOH gives one mole of OH−, [OH−] = 0.0150 M.
- Calculate pOH. pOH = -log10(0.0150) = 1.824 approximately.
- Convert pOH to pH. At 25 degrees Celsius, pH + pOH = 14.00, so pH = 14.00 – 1.824 = 12.176.
Why NaOH Is Treated as a Strong Base
Sodium hydroxide belongs to the class of metal hydroxides that dissociate very effectively in aqueous solution. In practical educational calculations, this means the concentration of hydroxide ions is equal to the initial concentration of dissolved NaOH, provided the solution is not so dilute that water autoionization must be handled more carefully. For 0.0150 M, that issue is negligible. The hydroxide concentration coming from NaOH is far larger than the 1.0 × 10-7 M contribution that comes from water at 25 degrees Celsius.
This is why chemistry instructors usually want students to recognize the shortcut immediately: for strong monohydroxide bases such as NaOH and KOH, [OH−] is the same as the stated molarity. In contrast, weak bases such as ammonia require an equilibrium expression and a base dissociation constant, Kb.
Common Mistakes Students Make
- Using pH directly from concentration. You should not calculate pH as -log10(0.0150) for NaOH. That gives pOH, not pH.
- Forgetting the strong base dissociation ratio. NaOH produces one OH− per formula unit, so the stoichiometric ratio is 1:1.
- Rounding too early. If you round pOH too aggressively before subtracting from 14, your final pH can shift slightly.
- Ignoring temperature assumptions. The familiar relation pH + pOH = 14.00 is exact only at 25 degrees Celsius. At other temperatures, pKw changes.
- Confusing M with mmol/L. A value of 0.0150 M is equal to 15.0 mmol/L, not 0.0150 mmol/L.
Worked Example for 0.0150 M NaOH
Let us walk through the calculation carefully. The problem gives a concentration of 0.0150 M sodium hydroxide. Since sodium hydroxide is a strong base, we assume complete dissociation:
NaOH → Na+ + OH−
The coefficient of OH− is 1, so the hydroxide concentration is:
[OH−] = 0.0150 M
Now compute pOH:
pOH = -log10(0.0150) = 1.8239
At 25 degrees Celsius:
pH = 14.0000 – 1.8239 = 12.1761
Depending on the desired significant figures, the answer may be reported as 12.18 or 12.176. Because the original concentration has four significant figures, many instructors are comfortable with pH = 12.176 in intermediate calculations and 12.18 as a neatly rounded final answer.
Comparison Table: Strong Base Concentration vs pOH and pH
The table below helps place the 0.0150 M NaOH result into context. Values are calculated at 25 degrees Celsius under the complete dissociation assumption.
| NaOH Concentration (M) | [OH−] (M) | pOH | pH | Interpretation |
|---|---|---|---|---|
| 0.0010 | 0.0010 | 3.000 | 11.000 | Basic, but less concentrated |
| 0.0100 | 0.0100 | 2.000 | 12.000 | Strongly basic |
| 0.0150 | 0.0150 | 1.824 | 12.176 | Target problem result |
| 0.0500 | 0.0500 | 1.301 | 12.699 | More strongly basic |
| 0.1000 | 0.1000 | 1.000 | 13.000 | Very basic laboratory solution |
Why the Logarithm Matters
The pH scale is logarithmic, not linear. That means a tenfold change in hydroxide concentration changes pOH by 1 unit and pH by 1 unit in the opposite direction. Because of this, concentration changes that look small numerically can still produce meaningful pH differences. Going from 0.0100 M to 0.0150 M NaOH does not seem dramatic, but it still moves the pH from 12.000 to about 12.176.
This is also why pH is such a useful practical scale. It compresses a wide range of hydrogen and hydroxide concentrations into manageable numbers. In environmental chemistry, biology, medicine, and industrial processing, this allows chemists to compare solution basicity or acidity quickly without handling cumbersome scientific notation every time.
Temperature Effects and pKw
Students are often taught the relationship pH + pOH = 14, and for ordinary classroom work that is correct because most examples assume 25 degrees Celsius. However, the more precise statement is pH + pOH = pKw, and pKw varies with temperature. As temperature changes, the ion product of water changes too, so the neutral point shifts slightly.
For that reason, this calculator includes a temperature option. At 20 degrees Celsius, pKw is about 14.16, and at 30 degrees Celsius it is about 13.83. The hydroxide concentration coming from NaOH does not change just because you changed a dropdown, but the conversion from pOH to pH changes slightly. In many basic courses, unless stated otherwise, you should use 25 degrees Celsius and pKw = 14.00.
| Temperature | Approximate pKw | pOH for 0.0150 M NaOH | Calculated pH | Neutral pH at That Temperature |
|---|---|---|---|---|
| 20 degrees Celsius | 14.16 | 1.824 | 12.336 | About 7.08 |
| 25 degrees Celsius | 14.00 | 1.824 | 12.176 | 7.00 |
| 30 degrees Celsius | 13.83 | 1.824 | 12.006 | About 6.92 |
Real World Relevance of Sodium Hydroxide pH
Sodium hydroxide is one of the most important industrial bases in the world. It is used in soap manufacturing, paper pulping, chemical synthesis, food processing, water treatment, and cleaning formulations. Knowing the pH of NaOH solutions matters because highly basic solutions are chemically reactive and can be corrosive to skin, metals, and some materials.
For a 0.0150 M solution, the pH is strongly basic but far less extreme than concentrated stock solutions used in laboratories and industry. Even so, proper handling remains important. Basicity affects reaction rates, solubility, and equilibrium behavior. In titrations, for example, NaOH concentration directly controls the shape of the titration curve and the position of the equivalence point when reacting with acids.
Authority Sources for Further Study
If you want to verify core acid-base concepts or explore water chemistry in more depth, these authoritative sources are excellent references:
- U.S. Environmental Protection Agency: Water Quality Criteria
- LibreTexts Chemistry educational resources
- U.S. Geological Survey: pH and Water
Quick Summary
- NaOH is a strong base and dissociates completely in water.
- A 0.0150 M NaOH solution has [OH−] = 0.0150 M.
- pOH = -log10(0.0150) ≈ 1.824.
- At 25 degrees Celsius, pH = 14.00 – 1.824 = 12.176.
- The practical rounded answer is pH ≈ 12.18.
Final Takeaway
To calculate the pH of a 0.0150 M solution of NaOH, the key is recognizing that sodium hydroxide is a strong base with complete dissociation. That allows you to equate the hydroxide ion concentration directly to the molarity of the base. Once you do that, the rest is a straightforward logarithm and subtraction. The result, at standard 25 degree Celsius conditions, is a pH of about 12.18. This is a textbook example of how acid-base theory, stoichiometry, and logarithms work together in a clean and practical chemical calculation.