Calculate the pH of 5.0 × 10-6 M
Use this premium calculator to find pH, pOH, hydrogen ion concentration, and hydroxide ion concentration for dilute acidic or basic solutions. The default example is 5.0 × 10-6 M, a classic chemistry problem.
Default example: determine the pH of a solution with concentration 5.0 × 10-6 M treated as [H+].
How to calculate the pH of 5.0 × 10-6 M
When students search for how to calculate the pH of 5.0 × 10-6 M, they are usually working through a general chemistry problem involving hydrogen ion concentration. In most introductory problems, the concentration given in molarity is interpreted as the hydrogen ion concentration, written as [H+]. Once you know [H+], you use the pH equation:
pH = -log10[H+]
For the specific value 5.0 × 10-6 M, the calculation is straightforward:
pH = -log10(5.0 × 10-6) = 5.3010
Rounded to the correct number of decimal places, the pH is typically reported as 5.30. This tells you the solution is acidic because its pH is below 7. At the same time, it is only mildly acidic compared with strong acid solutions such as 0.1 M hydrochloric acid, which has a pH near 1.
Step by step solution
- Identify the concentration provided: 5.0 × 10-6 M.
- Assume it represents hydrogen ion concentration, so [H+] = 5.0 × 10-6 M.
- Apply the definition of pH: pH = -log10[H+].
- Substitute the value: pH = -log10(5.0 × 10-6).
- Evaluate the logarithm to obtain 5.3010.
- Round appropriately and report the final answer as pH = 5.30.
Why the answer is not simply 6
A very common mistake is to look at the exponent -6 and assume the pH must be 6. That would only be true if the concentration were exactly 1.0 × 10-6 M. The coefficient matters. Because the concentration is 5.0 × 10-6 M, the hydrogen ion concentration is five times larger than 1.0 × 10-6 M, so the pH is lower than 6. Specifically, log10(5.0) is about 0.699, which shifts the pH down to 5.301.
Scientific notation and logarithms in pH calculations
Scientific notation is ideal for acid-base chemistry because ion concentrations often span many orders of magnitude. A concentration such as 5.0 × 10-6 M can be separated into two parts:
- The coefficient: 5.0
- The power of ten: 10-6
Using logarithm rules, you can write:
log(5.0 × 10-6) = log(5.0) + log(10-6)
= 0.6990 – 6 = -5.3010
Then take the negative of that quantity for pH:
pH = -(-5.3010) = 5.3010
This is one of the most reliable ways to check your calculator work, especially during exams. If you understand the exponent and coefficient separately, you are much less likely to make a sign mistake.
What pOH would this solution have?
At 25°C, pH and pOH are related by the equation:
pH + pOH = 14.00
So if pH = 5.30, then:
pOH = 14.00 – 5.30 = 8.70
You can also determine hydroxide ion concentration using:
[OH-] = 10-pOH = 10-8.70 ≈ 2.0 × 10-9 M
This confirms that hydroxide is present at a lower concentration than hydrogen ion, which is exactly what you would expect in an acidic solution.
Comparison table: common hydrogen ion concentrations and pH values
| [H+] concentration (M) | Calculated pH | Interpretation | Relative acidity vs 1.0 × 10-7 M |
|---|---|---|---|
| 1.0 × 10-1 | 1.00 | Strongly acidic | 1,000,000 times more acidic |
| 1.0 × 10-3 | 3.00 | Acidic | 10,000 times more acidic |
| 5.0 × 10-6 | 5.30 | Mildly acidic | 50 times more acidic |
| 1.0 × 10-7 | 7.00 | Neutral at 25°C | Baseline |
| 1.0 × 10-9 | 9.00 | Basic | 100 times less acidic |
How significant figures affect your pH answer
In chemistry, pH reporting follows a special rule. The number of decimal places in the pH should match the number of significant figures in the concentration. The concentration 5.0 × 10-6 M has two significant figures, because the coefficient 5.0 contains two significant digits. Therefore, your pH should be reported with two digits after the decimal place: 5.30. If the concentration had been 5.00 × 10-6 M instead, the pH could be reported as 5.301.
Does water autoionization matter for 5.0 × 10-6 M?
This is a smart question because pure water itself contributes hydrogen ions and hydroxide ions through autoionization. At 25°C, pure water has [H+] = 1.0 × 10-7 M and [OH-] = 1.0 × 10-7 M. If a problem gives a concentration that is much larger than 1.0 × 10-7 M, the water contribution is often small enough to ignore in introductory work.
Here, 5.0 × 10-6 M is 50 times larger than 1.0 × 10-7 M. That means the supplied hydrogen ion concentration dominates the equilibrium, and the standard pH formula gives a very good classroom answer. In more advanced analytical chemistry, you may solve a quadratic relation to include water exactly, but that level of precision is usually unnecessary for this type of exercise.
Data table: benchmark acid-base values used in introductory chemistry
| Quantity | Value at 25°C | Why it matters | Source context |
|---|---|---|---|
| Ion-product constant of water, Kw | 1.0 × 10-14 | Connects [H+] and [OH-] through Kw = [H+][OH-] | Standard general chemistry constant |
| Neutral [H+] in pure water | 1.0 × 10-7 M | Defines pH 7.00 at 25°C | Used as the neutral benchmark |
| Neutral pH at 25°C | 7.00 | Divides acidic and basic conditions in many basic calculations | Introductory chemistry convention |
| Relationship between pH and pOH | pH + pOH = 14.00 | Allows fast conversion between acid and base scales | Derived from Kw |
| Given problem concentration | 5.0 × 10-6 M | Produces pH 5.30 if treated as [H+] | Target example on this page |
Practical interpretation of pH 5.30
A pH of 5.30 is acidic, but not extremely acidic. On the logarithmic pH scale, every one-unit change corresponds to a tenfold change in hydrogen ion concentration. That means a solution at pH 5.30 is about 50 times more acidic than neutral water at pH 7.00, because:
107.00 – 5.30 = 101.70 ≈ 50
This logarithmic behavior is what makes pH so useful. Very large differences in chemical behavior can be expressed using a compact scale. It is also why pH values should never be interpreted linearly. A pH 4 solution is not just “a little more acidic” than pH 5; it is ten times more acidic.
Common mistakes when solving pH from molarity
- Ignoring the coefficient. For 5.0 × 10-6 M, the coefficient 5.0 shifts the pH from 6.00 to 5.30.
- Dropping the negative sign. The pH formula contains a negative sign in front of the logarithm.
- Confusing [H+] with [OH-]. If the given concentration is hydroxide, you must calculate pOH first and then convert to pH.
- Rounding too aggressively. Keep enough digits during the calculation and round only at the end.
- Forgetting temperature assumptions. The familiar neutral pH of 7.00 strictly applies at 25°C.
When the concentration represents hydroxide instead
If a problem gives 5.0 × 10-6 M as [OH-] rather than [H+], the path changes:
- Calculate pOH = -log(5.0 × 10-6) = 5.30.
- Use pH + pOH = 14.00.
- Compute pH = 14.00 – 5.30 = 8.70.
This would describe a mildly basic solution. The calculator above lets you switch between these two interpretations instantly so you can compare outcomes and verify your homework process.
Recommended authoritative references
- LibreTexts Chemistry for university-level explanations of logarithms, pH, pOH, and acid-base equilibria.
- U.S. Environmental Protection Agency for real-world guidance on pH in environmental systems and water quality.
- U.S. Geological Survey for practical context on pH measurement and natural water chemistry.
Final answer for the target problem
If the value 5.0 × 10-6 M is the hydrogen ion concentration, then the correct pH is:
pH = 5.30
That answer comes directly from the logarithmic definition of pH and is the expected result in standard general chemistry coursework. You can use the calculator on this page to reproduce the answer, explore how changing the exponent affects acidity, and compare pH with pOH visually using the chart.