Calculate the pH of a 6.71 × 10-2 M NaOH Solution
Use this interactive chemistry calculator to determine hydroxide concentration, pOH, and pH for a sodium hydroxide solution. The default setup is prefilled for 6.71 × 10-2 M NaOH, but you can also test related strong-base concentrations and temperature assumptions.
Strong Base pH Calculator
For a strong base like NaOH, we assume complete dissociation, so the hydroxide ion concentration equals the formal concentration of the base when one hydroxide is released per formula unit.
Enter or keep the default value for 6.71 × 10-2 M NaOH, then click Calculate pH to see the result and chart.
pH Profile Visualization
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, you begin by recognizing that NaOH is a strong base. In introductory and general chemistry, a strong base is assumed to dissociate completely in water. That means every mole of sodium hydroxide produces one mole of hydroxide ions, OH–. Because pH is based on hydrogen ion concentration and pOH is based on hydroxide ion concentration, strong base calculations usually proceed in a very direct order: find the hydroxide concentration, compute pOH, and then use the water ion-product relationship to determine pH.
For this specific problem, the concentration is written in scientific notation as 6.71 × 10-2 M. Converting that to standard decimal form gives 0.0671 M. Since NaOH contributes one hydroxide ion per formula unit, the hydroxide concentration is also 0.0671 M under the standard complete-dissociation assumption. The next step is to apply the formula pOH = -log[OH–]. Once pOH is known, you calculate pH by using pH + pOH = 14.00 at 25 degrees C. This is the standard classroom method and the one used in most chemistry homework, quizzes, and lab pre-calculations.
Step-by-Step Solution
- Write the dissociation equation: NaOH(aq) → Na+(aq) + OH–(aq)
- Determine hydroxide concentration: Because NaOH is a strong base, [OH–] = 6.71 × 10-2 M = 0.0671 M.
- Calculate pOH: pOH = -log(0.0671) ≈ 1.173.
- Calculate pH: pH = 14.00 – 1.173 = 12.827.
If your teacher requests a specific number of significant figures or decimal places, your final presentation may vary slightly. For many chemistry courses, reporting pH to three decimal places is acceptable when the concentration has three significant figures. In that case, a good final result is pH = 12.827. If rounded to two decimal places, the answer becomes 12.83.
Why NaOH Makes This Calculation Simpler
Sodium hydroxide is one of the classic examples of a strong Arrhenius base. Unlike weak bases such as ammonia, which require an equilibrium expression and a base dissociation constant, NaOH dissociates essentially completely in dilute aqueous solution. This simplifies the chemistry dramatically. You do not usually need an ICE table for a problem like this. Instead, the concentration of hydroxide ions comes directly from the stated molarity of the dissolved solute.
That complete-dissociation property matters because the logarithm in the pOH formula is sensitive to concentration. If the base were weak, only a fraction of the dissolved molecules would produce OH–, and your pH result would be much lower than the result for a comparably concentrated strong base. In the present problem, however, NaOH is strong enough that the direct approach is the correct one for standard chemistry coursework.
Common Formula Set for Strong Base Problems
- Strong base dissociation: M(OH)n → metal cation + nOH–
- Hydroxide concentration: [OH–] = n × base concentration
- pOH: pOH = -log[OH–]
- pH at 25 degrees C: pH = 14.00 – pOH
For NaOH specifically, n = 1. For calcium hydroxide, Ca(OH)2, n = 2. That distinction is why the calculator above includes a base selection menu. The chemistry principle is the same, but the hydroxide stoichiometry changes. For NaOH at 6.71 × 10-2 M, there is no multiplier beyond 1, so [OH–] remains 0.0671 M.
Detailed Numerical Check
Let us verify the math carefully. The concentration in decimal form is 0.0671. Taking the negative common logarithm:
pOH = -log(0.0671) ≈ 1.17309
Now subtract this from 14.00:
pH = 14.00 – 1.17309 = 12.82691
Rounded appropriately, the final pH is 12.827. This value is strongly basic, which is consistent with a sodium hydroxide solution having a concentration in the 10-2 M range.
Comparison Table: Strong Base Concentration vs pH at 25 degrees C
| NaOH Concentration (M) | [OH-] (M) | pOH | pH | Interpretation |
|---|---|---|---|---|
| 1.00 × 10-4 | 0.0001 | 4.000 | 10.000 | Mildly basic relative to concentrated laboratory bases |
| 1.00 × 10-3 | 0.0010 | 3.000 | 11.000 | Clearly basic, often used in simple classroom examples |
| 6.71 × 10-2 | 0.0671 | 1.173 | 12.827 | Your target calculation, strongly basic |
| 1.00 × 10-1 | 0.1000 | 1.000 | 13.000 | Typical textbook strong-base benchmark |
| 1.00 | 1.0000 | 0.000 | 14.000 | Idealized upper-end classroom value at 25 degrees C |
The progression in the table shows how rapidly pH rises as hydroxide concentration increases. Because the pH scale is logarithmic, a tenfold change in hydroxide concentration changes pOH by 1 unit. That is why moving from 0.0010 M to 0.0100 M NaOH produces a measurable but not linear change in pH. For students, this is one of the most important conceptual points in acid-base chemistry: pH values do not scale arithmetically with concentration.
Temperature and the Meaning of pH + pOH = 14
Many students memorize pH + pOH = 14, but the more exact statement is that pH + pOH = pKw, where pKw depends on temperature. At 25 degrees C, pKw is commonly taken as 14.00, which is why chemistry problems at room temperature use that value. However, as temperature changes, the ionization constant of water changes too. The calculator on this page lets you compare common pKw assumptions for different temperatures to see how the final pH shifts slightly.
This distinction becomes especially important in more advanced analytical chemistry, environmental chemistry, and chemical engineering. In those fields, high precision and temperature control matter. In general chemistry homework, though, if no temperature is mentioned, assume 25 degrees C and use 14.00.
Comparison Table: Approximate pKw by Temperature
| Temperature | Approximate pKw | pOH for 0.0671 M OH- | Calculated pH | Comment |
|---|---|---|---|---|
| 10 degrees C | 14.17 | 1.173 | 12.997 | Colder water has a slightly larger pKw |
| 25 degrees C | 14.00 | 1.173 | 12.827 | Standard textbook condition |
| 50 degrees C | 13.60 | 1.173 | 12.427 | Warmer water has a lower pKw |
The numerical values in the temperature table illustrate a subtle but important point: pH values are not universal without context. A neutral pH is not always 7.00 unless the system is at 25 degrees C. As the ionization of water changes with temperature, the reference point changes too. For educational calculations, always check whether the problem specifies a temperature before applying the standard 14.00 shortcut.
Frequent Mistakes Students Make
- Forgetting dissociation: Some students calculate pH directly from 0.0671 M, but for a base you should first calculate pOH from [OH–].
- Using the wrong logarithm sign: pOH is -log[OH-], not log[OH-].
- Misreading scientific notation: 6.71 × 10-2 is 0.0671, not 0.00671.
- Mixing up strong and weak bases: NaOH is strong, so no Kb setup is needed.
- Over-rounding too early: Keep extra digits during intermediate steps to avoid final rounding errors.
Real-World Context for Sodium Hydroxide
Sodium hydroxide is widely used in industry, education, and chemical processing. It appears in drain cleaners, soap production, paper pulping, pH adjustment systems, and laboratory titrations. Because it is strongly caustic, even moderately concentrated solutions can cause skin and eye injury. A pH above 12, such as the pH of this 6.71 × 10-2 M solution, indicates a highly basic solution that should be handled with proper safety procedures, including gloves and eye protection.
Laboratory calculations like this one are not just academic exercises. They help predict reactivity, corrosiveness, and neutralization behavior. If you know the pH of a NaOH solution, you can estimate how much acid would be required to neutralize it, evaluate whether a solution is safe for a given process stream, and interpret sensor readings or titration curves more confidently.
Authoritative References for Acid-Base Chemistry
- LibreTexts Chemistry for university-level explanations of pH, pOH, and strong base calculations.
- U.S. Environmental Protection Agency for water chemistry and pH background in environmental systems.
- NIST Chemistry WebBook for authoritative chemistry data resources.
Best Short Answer
If you need the concise homework response, write it like this:
NaOH is a strong base, so [OH–] = 6.71 × 10-2 M. Therefore, pOH = -log(6.71 × 10-2) = 1.173. Then pH = 14.00 – 1.173 = 12.827. The pH of the solution is 12.83.
Summary
To calculate the pH of a 6.71 × 10-2 M NaOH solution, first use the fact that sodium hydroxide is a strong base and fully dissociates in water. That gives [OH–] = 0.0671 M. Next, compute pOH with the negative logarithm: pOH ≈ 1.173. Finally, subtract from 14.00 at 25 degrees C to obtain pH ≈ 12.827. This is a standard strong-base calculation and a classic example of how logarithmic concentration scales work in acid-base chemistry.