Calculate the pH of a 6.71 × 10-2 M NaOH Solution
Use this interactive chemistry calculator to find hydroxide concentration, pOH, and pH for a sodium hydroxide solution. Since NaOH is a strong base, it dissociates essentially completely in water, making the calculation direct and ideal for students, lab workers, and exam review.
Default values are set to calculate the pH of 6.71 × 10-2 M NaOH. For NaOH, the hydroxide ion concentration is taken as equal to the molarity because it dissociates completely into Na+ and OH–.
How to Calculate the pH of a 6.71 × 10-2 M NaOH Solution
To calculate the pH of a 6.71 × 10-2 M sodium hydroxide solution, the key concept is that NaOH is a strong base. In introductory and most general chemistry settings, a strong base is assumed to dissociate completely in water. That means every mole of NaOH added to the solution contributes one mole of hydroxide ions, OH–. Because of that one-to-one dissociation, the hydroxide concentration is the same as the formal molarity of the sodium hydroxide solution. For this problem, the concentration of OH– is 6.71 × 10-2 M, which is 0.0671 M.
[OH–] = 6.71 × 10-2 M = 0.0671 M
pOH = -log10[OH–]
pH = 14.00 – pOH
Now evaluate the logarithm. The pOH is equal to the negative base-10 logarithm of 0.0671. That gives a pOH of approximately 1.17. Once pOH is known, use the relationship pH + pOH = 14.00 at 25°C. Subtracting 1.17 from 14.00 gives a pH of about 12.83. This is the expected result for a moderately concentrated strong base solution.
Final Answer
The pH of a 6.71 × 10-2 M NaOH solution is approximately 12.83 at 25°C.
Why This Calculation Is So Direct for NaOH
Sodium hydroxide is one of the classic strong bases used in chemistry education, industrial processing, and laboratory titrations. The reason it is so convenient in pH calculations is that it dissociates essentially completely in dilute aqueous solution. In contrast, weak bases such as ammonia require equilibrium expressions and often the use of Kb. With NaOH, none of that is necessary for standard textbook problems. If the concentration is known, then the hydroxide concentration is known immediately.
This is why chemistry instructors often use compounds such as NaOH, KOH, and LiOH to teach the difference between pOH and pH. The steps are systematic, consistent, and ideal for learning logarithms in chemistry. Once students understand how to convert from scientific notation to decimal form and apply the pOH formula, they can solve a wide range of similar questions quickly and accurately.
Step-by-Step Method
- Write the dissociation equation: NaOH → Na+ + OH–.
- Identify the hydroxide concentration: because NaOH provides one OH– per formula unit, [OH–] = 6.71 × 10-2 M.
- Convert scientific notation if helpful: 6.71 × 10-2 = 0.0671.
- Calculate pOH: pOH = -log(0.0671) ≈ 1.17.
- Calculate pH: pH = 14.00 – 1.17 = 12.83.
That is the entire method. If your teacher or exam expects the answer to the correct number of decimal places, you would generally report the final pH to match the significant figure precision implied by the concentration. For most practical classroom use, pH = 12.83 is suitable.
Common Mistakes When Solving This Problem
- Using pH = -log[OH–] directly. That formula gives pOH, not pH.
- Forgetting scientific notation conversion. 6.71 × 10-2 is 0.0671, not 6.71 or 0.00671.
- Treating NaOH as a weak base. For general chemistry, NaOH is considered a strong base and fully dissociated.
- Subtracting incorrectly from 14. If pOH ≈ 1.17, then pH must be above 12, not near 13.8 or 11.2 by random estimation.
- Ignoring temperature assumptions. The equation pH + pOH = 14.00 is tied to 25°C unless another Kw is provided.
Strong Base Comparison Table
The following table shows how the pH shifts for different concentrations of strong monohydroxide bases at 25°C. Since NaOH releases one hydroxide ion per formula unit, these values apply broadly to ideal strong base solutions with the same molarity.
| Base Concentration (M) | [OH–] (M) | pOH | pH at 25°C | Relative Basicity vs 6.71 × 10-2 M |
|---|---|---|---|---|
| 1.0 × 10-4 | 0.0001 | 4.00 | 10.00 | 671 times less concentrated |
| 1.0 × 10-3 | 0.001 | 3.00 | 11.00 | 67.1 times less concentrated |
| 1.0 × 10-2 | 0.01 | 2.00 | 12.00 | 6.71 times less concentrated |
| 6.71 × 10-2 | 0.0671 | 1.17 | 12.83 | Reference value |
| 1.0 × 10-1 | 0.1 | 1.00 | 13.00 | 1.49 times more concentrated |
How pH Scale Values Compare in Real Chemistry
The pH scale is logarithmic. That means even a modest change in pH corresponds to a tenfold change in hydrogen ion concentration. A solution with pH 12.83 is strongly basic and far more alkaline than neutral water. In practical lab terms, a 0.0671 M NaOH solution is corrosive enough that it must be handled with care. Gloves, splash protection, and proper glassware technique are not optional in a real laboratory.
Students often remember pH values more easily by anchoring them to familiar categories. Pure water at 25°C has pH 7. A weak base may land around pH 8 to 11 depending on concentration. Strong bases frequently occupy the pH 12 to 14 range. Your calculated value of 12.83 fits squarely into that strong-base region, which is exactly what chemistry theory predicts for NaOH at this concentration.
| Solution Type | Typical pH Range | Chemical Meaning | Instructional Use |
|---|---|---|---|
| Strong acid solutions | 0 to 3 | High [H+], very low [OH–] | Acid-base neutralization and safety training |
| Weakly acidic solutions | 4 to 6 | Moderate proton availability | Buffer examples and environmental chemistry |
| Neutral water at 25°C | 7.00 | [H+] = [OH–] = 1.0 × 10-7 M | Reference point for pH calculations |
| Weak base solutions | 8 to 11 | Moderately elevated [OH–] | Kb and equilibrium practice |
| Strong base solutions such as 0.0671 M NaOH | 12 to 13+ | High [OH–], complete dissociation assumption | Direct pOH and pH calculations |
Scientific Notation and Why It Matters Here
Chemistry relies heavily on scientific notation because concentrations span many orders of magnitude. The expression 6.71 × 10-2 M is simply a compact way to write 0.0671 M. Problems appear harder when written in scientific notation, but the chemistry is unchanged. In fact, the notation is often more precise and easier to compare across very large or very small values.
A useful mental shortcut is to move the decimal point two places to the left for 10-2. Thus, 6.71 becomes 0.0671. Once that conversion is clear, the pOH calculation becomes routine. This is one reason why chemistry teachers encourage students to practice both the scientific notation form and the decimal form before applying logarithms.
Is There Any Need for Kw or ICE Tables?
For this specific question, no ICE table is needed. You do not need to solve an equilibrium expression for a strong base like NaOH under standard assumptions. The ionic product of water, Kw, only appears indirectly through the relationship pH + pOH = 14.00 at 25°C. If the temperature changed substantially, then the value of Kw would change and the sum would no longer be exactly 14.00. However, most classroom problems explicitly or implicitly assume 25°C unless otherwise stated.
That is why this problem is often taught early in acid-base chemistry. It reinforces three foundational skills at once: interpreting strong electrolyte dissociation, using logarithms to compute pOH, and converting from pOH to pH. Once those skills are secure, students can move on to weaker acids and bases, polyprotic systems, and buffers.
Practical Interpretation of the Result
A pH of 12.83 indicates a highly alkaline solution. Such a solution can irritate or damage skin and eyes and can react with certain materials. In laboratory practice, sodium hydroxide is frequently used for neutralizations, cleaning applications, synthesis, and titrations. Even though this concentration is not the most concentrated NaOH solution encountered industrially, it is still very much a strong base and should be respected as such.
From an educational perspective, this value also demonstrates how the pH scale compresses large concentration differences into a manageable numeric range. A concentration of hydroxide ions of 0.0671 M may look moderate compared with 1.0 M NaOH, but its pH still lies deep in the basic region. That is the power of the logarithmic scale.
Quick Recap
- NaOH is a strong base and dissociates completely.
- [OH–] = 6.71 × 10-2 M = 0.0671 M.
- pOH = -log(0.0671) ≈ 1.17.
- pH = 14.00 – 1.17 ≈ 12.83.
- The solution is strongly basic.
Authoritative References for Acid-Base Chemistry
For additional verification and deeper study, consult these reliable academic and government resources:
- Chemistry LibreTexts for acid-base theory, pH, pOH, and strong base dissociation.
- U.S. Environmental Protection Agency for pH fundamentals and water chemistry context.
- National Institute of Standards and Technology for scientific measurement standards relevant to solution chemistry.
Bottom Line
If you are asked to calculate the pH of a 6.71 × 10-2 M NaOH solution, the correct result is 12.83 at 25°C. The reasoning is straightforward because NaOH is a strong base. Once you identify [OH–] as 0.0671 M, everything else follows from the standard pOH and pH formulas. Use the calculator above to verify the answer, explore the effect of changing the concentration, and visualize how hydroxide concentration, pOH, and pH relate to one another.