pH Calculator
This professional-grade pH calculator helps students, lab technicians, and water-quality professionals compute pH, pOH, hydrogen-ion and hydroxide-ion concentrations across multiple scenarios: direct input, strong/weak acids and bases, and buffers. It optionally adjusts for temperature via pKw so you can trust results in real-world conditions.
Results
Data Source and Methodology
Authoritative data sources:
- IUPAC Gold Book — “pH”, 2019 update. URL: https://goldbook.iupac.org/terms/view/P04524
- Bandura, A. V.; Lvov, S. N. “The Ionization Constant of Water over Wide Ranges of Temperature and Density”, Journal of Physical and Chemical Reference Data 35, 2006. DOI: 10.1063/1.1928231. Tabulated pKw values (0–60 °C) are used with linear interpolation.
All calculations are strictly based on the formulas and data provided by this source.
The Formula Explained
Primary definitions:
Inline: \( \mathrm{pH} = -\log_{10}(a_{\mathrm{H}^+}) \approx -\log_{10}([\mathrm{H}^+]) \)
Inline: \( \mathrm{pOH} = -\log_{10}([\mathrm{OH}^-]) \), and \( \mathrm{pH} + \mathrm{pOH} = \mathrm{p}K_w(T) \)
Weak acid (HA) exact solution:
\( K_a = \dfrac{[\mathrm{H}^+][\mathrm{A}^-]}{[\mathrm{HA}]}, \quad \text{with } [\mathrm{H}^+] = x \text{ satisfying } K_a = \dfrac{x^2}{C - x} \)
\( x = \dfrac{-K_a + \sqrt{K_a^2 + 4K_a C}}{2} \), \( \mathrm{pH} = -\log_{10}(x) \)
Weak base (B) exact solution:
\( K_b = \dfrac{[\mathrm{BH}^+][\mathrm{OH}^-]}{[\mathrm{B}]}, \quad x = \dfrac{-K_b + \sqrt{K_b^2 + 4K_b C}}{2} = [\mathrm{OH}^-] \), \( \mathrm{pH} = \mathrm{p}K_w - \mathrm{pOH} \)
Buffer (Henderson–Hasselbalch): \( \mathrm{pH} = \mathrm{p}K_a + \log_{10}\!\left(\dfrac{[\mathrm{A}^-]}{[\mathrm{HA}]}\right) \)
Glossary of Variables
- [H⁺], [OH⁻]: Molar concentrations (mol/L) of hydrogen and hydroxide ions.
- pH, pOH: Negative base-10 logarithms of [H⁺] and [OH⁻], respectively.
- Ka, Kb: Acid and base dissociation constants for weak electrolytes.
- pKa, pKb: Negative base-10 logarithms of Ka and Kb.
- C: Formal concentration (initial molarity) of the acid/base before dissociation.
- Kw: Ion product of water; pKw = −log10(Kw), temperature-dependent.
How it Works: A Step-by-Step Example
Task: Find the pH of 0.10 M acetic acid at 25 °C. Given pKa = 4.76.
- Convert constant: \(K_a = 10^{-4.76} \approx 1.74 \times 10^{-5}\).
- Apply the exact weak-acid solution: \( x = \dfrac{-K_a + \sqrt{K_a^2 + 4K_a C}}{2} \).
- Compute x: \( x \approx \dfrac{-1.74\times10^{-5} + \sqrt{(1.74\times10^{-5})^2 + 4\cdot 1.74\times10^{-5}\cdot 0.10}}{2} \approx 1.32\times10^{-3}\) mol/L.
- pH: \( \mathrm{pH} = -\log_{10}(1.32\times10^{-3}) \approx 2.88 \).
- At 25 °C, pKw ≈ 14.00, so \( \mathrm{pOH} = 14.00 - 2.88 = 11.12 \).
Frequently Asked Questions (FAQ)
What’s the difference between concentration and activity?
pH is defined via activity. In dilute solutions, activity is often approximated by concentration. For accurate work at higher ionic strengths, use activity coefficients (e.g., Debye–Hückel or Pitzer models).
Why can pH be less than 0 or greater than 14?
At very high acid or base concentrations or at temperatures where pKw differs from 14, pH can extend outside the 0–14 range. This calculator does not impose an artificial cap.
How precise are weak acid/base results?
We solve the exact quadratic, avoiding small-x approximations. However, real systems may deviate due to activity effects or secondary equilibria.
Does this handle polyprotic species?
The current version assumes monoprotic acids/bases in “strong” and “weak” modes. Buffer mode accepts any pKa relevant to the buffering pair.
Can I change the number of significant figures?
Results are displayed with sensible defaults for readability. You can copy the raw numbers and format them as needed.
Is temperature correction required?
For many room-temperature lab problems, assuming 25 °C (pKw ≈ 14) is fine. For environmental or process conditions, enable temperature correction.