Easily calculate the pressure of any individual gas in a mixture using total pressure and mole fractions with Dalton's Law.
Dalton's Law of Partial Pressures states that in a mixture of non-reacting gases, the total pressure exerted is equal to the sum of the partial pressures of the individual gases. This principle is a cornerstone of gas behavior and is essential for understanding mixtures in various scientific fields.
The mathematical expression is:
Ptotal = P1 + P2 + P3 + ... + Pn
Where each partial pressure (Pi) can be calculated as:
Pi = Xi ร Ptotal
Xi is the mole fraction of gas i in the mixture.
Given a gas mixture with total pressure of 1 atm containing:
The partial pressures would be:
The sum is 0.78 + 0.21 + 0.01 = 1.00 atm, which matches the total pressure.
This calculator implements Dalton's Law of Partial Pressures (formulated by John Dalton in 1801), a fundamental principle in gas chemistry that applies to ideal gas mixtures. The law is based on the kinetic molecular theory assumption that gas particles are non-interacting and their individual pressures are independent.
Pi = Xi ร Ptotal
or equivalently: Pi = (ni / ntotal) ร Ptotal
| Symbol | Variable Name | Definition | SI Unit |
|---|---|---|---|
| Pi | Partial Pressure | Pressure that component i would exert if it alone occupied the container volume | Pa (Pascal) |
| Xi | Mole Fraction | Ratio of moles of component i to total moles: ni/ntotal | Dimensionless |
| Ptotal | Total Pressure | Sum of all partial pressures in the mixture | Pa (Pascal) |
| ni | Moles of component i | Amount of gas i in moles | mol |
The calculator supports three common pressure units with exact conversion factors:
Note: The calculator performs calculations in the selected unit without internal conversions, ensuring numerical stability and exact results as displayed.
The calculator performs these exact computational steps:
The calculator displays partial pressures to 4 decimal places and mole fractions to 4 decimal places. Due to floating-point arithmetic and rounding, the sum of displayed partial pressures may differ slightly from the displayed total pressure. This is normal numerical behavior and doesn't indicate calculation errors.
Mole fractions range from 0 to 1, not 0-100%. Entering 21% oxygen as 21 instead of 0.21 is a common error.
Dalton's Law assumes ideal gas behavior and non-reacting gases. It becomes less accurate at high pressures or with strongly interacting gases. For conditions where gas behavior deviates, a van der Waals equation calculator might be more appropriate.
This calculator assumes the following ideal conditions, which are standard for introductory chemistry applications:
Dalton's Law provides excellent accuracy for most gases at:
โข Temperatures well above their boiling points
โข Pressures below 10 atm
โข Non-polar gases with weak intermolecular forces
For high-precision work or extreme conditions, consider using real gas equations (van der Waals, etc.)
A gas mixture contains 2.5 moles of Nโ, 0.75 moles of Oโ, and 0.25 moles of COโ at a total pressure of 3.0 atm. Calculate the partial pressure of each component.
This exact calculation can be reproduced using the calculator by switching to "Use Moles" mode and entering the values above.
Think of partial pressure as the "contribution" each gas makes to the total pressure. Each gas behaves as if it alone occupies the entire container volume at its partial pressure.
Be prepared to: 1) Calculate partial pressures from mole fractions, 2) Determine mole fractions from partial pressures, 3) Apply Dalton's Law to gas collection over water problems. Remember that total pressure in these scenarios is often linked to principles from the combined gas law.
The calculations are based on standard physical chemistry principles as presented in authoritative textbooks:
Calculation Methodology: The algorithm uses exact arithmetic operations without approximations beyond standard floating-point precision. No empirical corrections or fitted parameters are applied.
Last Formula Review: October 2025 | Academic Review Cycle: Annual | Version: 2.1 (Dalton's Law Implementation)
This tool is designed for educational purposes and preliminary calculations. For publication-quality results or critical applications, verify calculations with primary literature sources and consider real-gas effects where appropriate.