Calculate pH and pOH Given [H+] = 4.02 × 10-8 M
Use this premium acid-base calculator to convert hydrogen ion concentration into pH, pOH, and hydroxide concentration with a clear worked solution and interactive chart.
pH / pOH Calculator
Default example is set to [H+] = 4.02 × 10^-8 M at 25°C.
What this tool returns
Expert Guide: How to Calculate pH and pOH Given H = 4.02 × 10-8 M
If you need to calculate pH and pOH given H = 4.02 × 10-8 M, the process is straightforward once you know the core logarithmic relationships used in acid-base chemistry. The hydrogen ion concentration, written as [H+], tells you how acidic or basic a solution is. From that single value, you can determine both pH and pOH, which are two of the most common quantitative measures in general chemistry, analytical chemistry, environmental science, and biology.
For the specific value [H+] = 4.02 × 10-8 M, the standard textbook method at 25°C uses the formulas pH = -log[H+] and pOH = 14.00 – pH. Because the hydrogen ion concentration is slightly lower than 1.0 × 10-7 M, the pH will turn out to be slightly above 7, meaning the solution is slightly basic under the idealized classroom interpretation. That result surprises many students because they associate any listed [H+] value with acidity, but acidity and basicity depend on the magnitude of that concentration, not just the presence of H+.
Step 1: Start with the pH formula
The definition of pH is:
Substitute the given hydrogen ion concentration into the expression:
To evaluate this, you can split the logarithm into two pieces:
Since log(10-8) = -8 and log(4.02) ≈ 0.6042:
Now apply the negative sign from the pH formula:
Rounded to the correct number of decimal places based on the significant figures in 4.02, the pH is:
Step 2: Calculate pOH from pH
At 25°C, the relationship between pH and pOH is:
Substitute the pH you just calculated:
Rounded appropriately:
So the final textbook answer is:
- pH = 7.40
- pOH = 6.60
Why the pH is greater than 7
At 25°C, neutral water has [H+] = 1.0 × 10-7 M and pH = 7.00. In this problem, the hydrogen ion concentration is 4.02 × 10-8 M, which is smaller than 1.0 × 10-7 M. A lower hydrogen ion concentration means the solution is less acidic and therefore more basic. That is why the pH is above 7.
This is a key concept: pH and concentration move in opposite directions because pH is a negative logarithm. As [H+] decreases, pH rises. As [H+] increases, pH falls.
How significant figures affect the final answer
In logarithmic calculations, the number of decimal places in the pH is determined by the number of significant figures in the concentration. The value 4.02 has three significant figures, so the pH should usually be reported with three digits after the decimal in intermediate work and two decimal places if your instructor or textbook rounds to reflect the precision clearly. Many chemistry instructors would accept pH = 7.396 and pOH = 6.604, while a neatly rounded classroom answer is pH = 7.40 and pOH = 6.60.
Worked solution in a simple exam format
- Write the formula: pH = -log[H+]
- Substitute the value: pH = -log(4.02 × 10-8)
- Calculate: pH = 7.3958 ≈ 7.40
- Use pH + pOH = 14.00
- Find pOH: pOH = 14.00 – 7.40 = 6.60
Comparison table: [H+] and pH at 25°C
| Hydrogen ion concentration [H+] | pH | Interpretation |
|---|---|---|
| 1.0 × 10^-1 M | 1.00 | Strongly acidic |
| 1.0 × 10^-3 M | 3.00 | Acidic |
| 1.0 × 10^-7 M | 7.00 | Neutral at 25°C |
| 4.02 × 10^-8 M | 7.40 | Slightly basic |
| 1.0 × 10^-10 M | 10.00 | Basic |
| 1.0 × 10^-13 M | 13.00 | Strongly basic |
Real-world comparison table: common pH ranges
The following values are useful contextual benchmarks. These ranges are commonly taught in chemistry and environmental science to help students interpret whether a pH result is reasonable.
| System or substance | Typical pH range | What it tells you |
|---|---|---|
| Pure water at 25°C | 7.0 | Neutral reference point |
| Human blood | 7.35 to 7.45 | Tightly regulated, slightly basic |
| Drinking water standard guidance | 6.5 to 8.5 | Often cited operational range for water systems |
| Seawater | About 8.1 | Naturally slightly basic |
| Black coffee | About 5.0 | Mildly acidic |
| Household bleach | 11 to 13 | Strongly basic |
Important nuance: when [H+] is below 1 × 10-7 M
There is an advanced point worth noting. In introductory problems, if the concentration of H+ is explicitly given, you normally use that number directly in the pH equation. That is exactly what we did here. However, in more advanced equilibrium chemistry, when acid concentrations become extremely small, the autoionization of water can no longer be ignored. Water itself contributes H+ and OH–, and that matters near the neutral region.
So if a problem says a solution has an analytical acid concentration around 10-8 M, the true equilibrium pH may require a more complete treatment using Kw and charge balance. But if the problem specifically states that [H+] = 4.02 × 10-8 M, then the standard direct calculation gives pH = 7.40 and pOH = 6.60.
How to verify the answer with pOH and [OH–]
After finding pOH, you can compute hydroxide ion concentration:
For pOH = 6.6042:
This is larger than the hydrogen ion concentration of 4.02 × 10-8 M, which is consistent with the idea that the solution is basic under the standard 25°C model.
Common mistakes students make
- Forgetting the negative sign in pH = -log[H+]
- Typing the exponent incorrectly into a calculator
- Using natural log instead of base-10 log
- Subtracting from 7 instead of 14 when finding pOH at 25°C
- Confusing the coefficient 4.02 with the final pH value
- Assuming every H+ concentration means the solution must be acidic
Calculator shortcut for scientific notation
On most scientific calculators, you can enter the concentration as 4.02 EXP -8 or 4.02 EE -8. Then use the base-10 logarithm button. The correct sequence is typically:
- Enter 4.02 EXP -8
- Press log
- Change the sign or multiply by -1
- Record pH
- Subtract from 14.00 to get pOH
Why this topic matters in chemistry, biology, and environmental science
pH calculations are not just classroom exercises. They are used in laboratory titrations, industrial quality control, medical diagnostics, water treatment, soil analysis, food science, and environmental monitoring. For example, blood pH is closely controlled around 7.4, natural waters are routinely monitored for acceptable pH ranges, and chemical manufacturing often depends on accurate pH adjustment for reaction efficiency and product stability.
If your computed pH for [H+] = 4.02 × 10-8 M is about 7.40, that result is numerically close to the normal pH of human blood, which gives a nice practical reference point. It also reinforces the larger idea that pH values near 7 represent relatively low hydrogen ion concentrations compared with strongly acidic systems.
Authoritative references for deeper study
For additional reading on pH, water chemistry, and acid-base fundamentals, consult these authoritative sources:
- U.S. Environmental Protection Agency: pH overview
- U.S. Geological Survey: pH and water
- Chemistry educational resources used by university instructors
Final answer summary
To calculate pH and pOH given H = 4.02 × 10-8 M, use the standard formulas at 25°C:
- pH = -log(4.02 × 10-8) = 7.40
- pOH = 14.00 – 7.40 = 6.60
That means the solution is slightly basic in the standard classroom interpretation. If you are studying for a quiz, exam, AP Chemistry unit, or first-semester college chemistry course, this is the exact workflow you should practice until it becomes automatic.