Calculate pH of 1.41 × 10-2 M NaOH
Use this premium calculator to find hydroxide concentration, pOH, and pH for sodium hydroxide solutions. The default setup solves the classic chemistry problem: calculate the pH of 1.41 × 10-2 M NaOH.
Enter concentration values in scientific notation and click Calculate pH. For 1.41 × 10-2 M NaOH, the expected answer is strongly basic with a pH a little above 12.
How to calculate pH of 1.41 × 10-2 M NaOH correctly
To calculate the pH of 1.41 × 10-2 M NaOH, you use the fact that sodium hydroxide is a strong base. In introductory and general chemistry, strong bases are treated as substances that dissociate essentially completely in water. That means each mole of NaOH releases one mole of hydroxide ions, OH–. As a result, the hydroxide concentration is taken to be equal to the formal concentration of the sodium hydroxide solution.
For this specific problem, the starting concentration is 1.41 × 10-2 M. Because NaOH dissociates completely, you can write:
Once you know the hydroxide concentration, the next step is to calculate pOH using the logarithmic relationship:
Substituting the value gives:
Then use the standard room temperature relationship between pH and pOH:
So the final answer is:
This means the pH of 1.41 × 10-2 M NaOH is approximately 12.15. That value makes chemical sense because the solution contains far more hydroxide ions than neutral water does, so it must be strongly basic.
Why NaOH is treated as a strong base
Sodium hydroxide is one of the classic strong bases introduced early in chemistry because it dissociates almost fully in aqueous solution:
NaOH(aq) → Na+(aq) + OH–(aq)
This complete dissociation is what simplifies the problem. If you were working with a weak base such as ammonia, NH3, you would need an equilibrium expression and a Kb value. But for NaOH, the stoichiometry is direct: one unit of NaOH gives one unit of OH–.
- NaOH is a Group 1 metal hydroxide.
- Group 1 hydroxides are commonly treated as strong electrolytes in water.
- One mole of NaOH produces one mole of OH–.
- The hydroxide concentration therefore matches the solution molarity.
Step by step method for scientific notation problems
Many students get tripped up when concentration is written in scientific notation. A reliable process helps avoid mistakes. Here is the exact sequence to use for a problem like calculate pH of 1.41 10 2 m NaOH, which is understood in standard notation as 1.41 × 10-2 M NaOH.
- Identify the compound as a strong base.
- Set [OH–] equal to the stated concentration.
- Convert the scientific notation to decimal if needed: 1.41 × 10-2 = 0.0141.
- Calculate pOH = -log(0.0141).
- Use pH = 14 – pOH at 25°C.
- Round appropriately, usually to match the significant figures of the concentration.
If you prefer a decimal-first method, you can rewrite the concentration as 0.0141 M. Then compute:
pOH = -log(0.0141) = 1.8508
pH = 14.0000 – 1.8508 = 12.1492
Rounded reasonably, the answer is 12.15.
Quick comparison table for strong base concentrations and pH
The following table shows how pH changes for several NaOH concentrations at 25°C. This is useful for checking whether your answer is in the right range.
| NaOH Concentration (M) | [OH-] (M) | pOH | pH at 25°C |
|---|---|---|---|
| 1.00 × 10-1 | 0.100 | 1.000 | 13.000 |
| 1.00 × 10-2 | 0.0100 | 2.000 | 12.000 |
| 1.41 × 10-2 | 0.0141 | 1.851 | 12.149 |
| 5.00 × 10-3 | 0.00500 | 2.301 | 11.699 |
| 1.00 × 10-3 | 0.00100 | 3.000 | 11.000 |
Notice where 1.41 × 10-2 M falls. It is slightly more concentrated than 1.00 × 10-2 M, so the pH should be slightly above 12.00. That is exactly what we obtained. This type of reasonableness check is important in chemistry because it catches common calculator and sign errors.
Most common mistakes when solving this problem
Even though the problem is straightforward, students often lose points because of a few repeat errors. Here are the ones to watch closely:
- Using pH = -log[OH-]. That formula is wrong. pOH = -log[OH-], not pH.
- Forgetting complete dissociation. For NaOH, [OH-] equals the NaOH molarity.
- Dropping the negative exponent. 10-2 means 0.01, not 100.
- Entering scientific notation incorrectly. On a calculator, 1.41E-2 is 0.0141.
- Subtracting in the wrong direction. The correct relationship is pH = 14 – pOH.
- Ignoring temperature context. The pH + pOH = 14 relationship is standard for 25°C problems.
Detailed breakdown of the logarithm
Some learners want to see why the pOH is about 1.85 without relying completely on a calculator. You can estimate it from the properties of logarithms:
log(1.41 × 10-2) = log(1.41) + log(10-2)
= log(1.41) – 2
≈ 0.1492 – 2 = -1.8508
Then, because pOH is the negative of that value:
pOH = 1.8508
This is a helpful habit because it lets you estimate whether your calculator output is sensible. If the concentration is around 10-2 M, then the pOH should be close to 2. Since 1.41 is a little bigger than 1, the pOH should be a little less than 2. That matches 1.85 perfectly.
Comparison of neutral water, weakly basic water, and this NaOH solution
The pH value becomes even more meaningful when compared to familiar reference points. The table below places this solution in context.
| Solution Type | Typical [OH-] (M) | Typical pH | Interpretation |
|---|---|---|---|
| Pure water at 25°C | 1.0 × 10-7 | 7.0 | Neutral |
| Mild household basic cleaner | About 1.0 × 10-4 to 1.0 × 10-3 | 10 to 11 | Moderately basic |
| 1.41 × 10-2 M NaOH | 1.41 × 10-2 | 12.15 | Strongly basic |
| 0.10 M NaOH | 1.0 × 10-1 | 13.0 | Very strongly basic |
This comparison shows why 12.15 is a realistic answer. The concentration is far above neutral water and firmly in the range of strong basicity, though still less concentrated than 0.10 M NaOH.
Why pH depends on temperature
In most classroom chemistry settings, you use pH + pOH = 14.00. That comes from the ionic product of water, Kw, at 25°C. At other temperatures, Kw changes slightly, so the exact sum of pH and pOH is not always exactly 14. However, unless your instructor or textbook specifically says otherwise, the standard assumption is 25°C. Under that assumption, the answer for 1.41 × 10-2 M NaOH remains 12.15.
Significant figures and reporting the answer
The concentration 1.41 × 10-2 has three significant figures. When reporting logarithmic values such as pH and pOH, the usual rule is that the number of decimal places in the pH or pOH should match the number of significant figures in the concentration. Because the given concentration has three significant figures, a polished answer is:
In many classroom contexts, this may be rounded to pH = 12.15. If your teacher expects strict sig fig treatment, using three decimal places is excellent.
Real chemistry context for sodium hydroxide
Sodium hydroxide is widely used in laboratories and industry. It appears in titrations, pH adjustment systems, drain cleaners, soap production, chemical manufacturing, and educational demonstrations. Because it is highly caustic, even moderate concentrations can irritate or damage skin and eyes. A solution with pH around 12.15 is very basic and should be handled with standard chemical safety practices.
- Wear splash-resistant eye protection.
- Use gloves compatible with caustic solutions.
- Avoid direct skin contact.
- Label the solution clearly with concentration and hazard information.
- Dispose of it according to institutional or local regulations.
Authoritative references for pH, hydroxide, and water chemistry
If you want to verify the chemistry principles behind this calculation, these sources are excellent places to start:
- U.S. Environmental Protection Agency: pH basics and water chemistry
- Chemistry educational materials hosted by academic institutions
- University of Wisconsin acid-base tutorial
Final answer
To summarize, when you are asked to calculate pH of 1.41 × 10-2 M NaOH, you treat NaOH as a strong base and assume complete dissociation. Therefore, [OH–] = 1.41 × 10-2 M, pOH = 1.8508, and pH = 12.1492. Rounded appropriately, the final answer is: