pH Value: formula
Enter a positive hydrogen-ion molarity as coefficient × 10^(−exponent). This dilute-solution model approximates activity by concentration: pH = −log10([H+]). Its pOH output uses pKw = 14, appropriate near 25°C, rather than a temperature-dependent water-ionization model.
pH Value: worked example
| Coefficient (a) | 3.2 |
|---|---|
| Exponent (n) | 4 |
| pH | 3.5 |
| pOH | 10.5 |
Zero or negative [H+] has no real logarithm and no valid pH here. pH can lie outside 0–14. Concentrated or nonideal solutions require activity corrections, and neutral pH changes with temperature; neutral pH 7 is the familiar 25°C approximation.
pH Value: changing Coefficient (a)
| Coefficient (a) | pH | pOH |
|---|---|---|
| 2.6 | 3.6 | 10.4 |
| 2.9 | 3.5 | 10.5 |
| 3.2 (example) | 3.5 | 10.5 |
| 3.5 | 3.5 | 10.5 |
| 3.8 | 3.4 | 10.6 |
pH Value: compare input ranges
| Input | Tested from | To | pH: low input | pH: high input | Swing |
|---|---|---|---|---|---|
| Exponent (n) | 3 | 5 | 2.5 | 4.5 | 2 (57%) |
| Coefficient (a) | 2.9 | 3.5 | 3.5 | 3.5 | 0.082 (2.3%) |
pH Value: individual input comparisons
| Input | Value | pH | pOH |
|---|---|---|---|
| Coefficient (a) | 2.6 | 3.6 | 10.4 |
| 2.9 | 3.5 | 10.5 | |
| 3.2 | 3.5 | 10.5 | |
| 3.5 | 3.5 | 10.5 | |
| 3.8 | 3.4 | 10.6 | |
| Exponent (n) | 2 | 1.5 | 12.5 |
| 3 | 2.5 | 11.5 | |
| 4 | 3.5 | 10.5 | |
| 5 | 4.5 | 9.5 | |
| 6 | 5.5 | 8.5 |
pH Value: combined input changes
| Coefficient (a) / Exponent (n) | 2 | 4 | 6 |
|---|---|---|---|
| 2.6 | 1.6 | 3.6 | 5.6 |
| 2.9 | 1.5 | 3.5 | 5.5 |
| 3.2 | 1.5 | 3.5 | 5.5 |
| 3.5 | 1.5 | 3.5 | 5.5 |
| 3.8 | 1.4 | 3.4 | 5.4 |
pH Value: which assumptions move the result?
pH Value: values and definitions
| Quantity and definition | Value used |
|---|---|
| Coefficient (a) — The number in front of the power of ten. | 3.2 |
| Exponent (n) — Enter 4 for 10⁻⁴. The concentration is a × 10⁻ⁿ mol/L. | 4 |
| pH | 3.5 |
| pOH | 10.5 |
pH Value: half and double Exponent (n)
| Exponent (n) | pH |
|---|---|
| 2 | 1.5 |
| 4 | 3.5 |
| 8 | 7.5 |
Common error: Reading pH as a linear scale. A drop of one pH unit is ten times the acidity, and a drop of two is a hundred times.
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The pH scale is a logarithm of hydrogen ion concentration, so each step is a tenfold change. A concentration of 3.2 times ten to the minus four gives a pH near 3.5, and pH 3 is ten times more acidic than pH 4. At room temperature pH and pOH add to 14, which is why the second output mirrors the first around 7.
Enter the concentration in moles per liter. A value in millimoles or micromoles needs converting first, or the pH lands several units off.
Prepare solutions on the molarity and dilution calculators, express low concentrations on the ppm page, and use the scientific notation calculator for the input. The percent yield and half-life pages cover other chemistry quantities, and the logarithm calculator explains the scale.
What does pH mean?
pH is defined in terms of hydrogen-ion activity. The simple classroom approximation −log₁₀[H⁺] uses molar concentration under conditions where activity effects are neglected. Solutions with substantial ionic-strength effects need a more appropriate treatment.
Why is the pH scale logarithmic?
A factor-of-ten change in hydrogen-ion activity changes pH by one unit. The familiar zero-to-fourteen range is not a universal mathematical bound. Temperature, activity conventions and concentrated solutions affect the interpretation; check the assumptions of the concentration approximation.
What is the pH of pure water?
About 7 at 25 degrees Celsius, which is neutral, with equal concentrations of hydrogen and hydroxide ions.