Partial Pressure (Dalton's Law) Calculator

Dalton's Law of Partial Pressures states that the total pressure of a non-reacting gas mixture equals the sum of the partial pressures of each component gas: P_total = P₁ + P₂ + P₃ + … The partial pressure of a gas component is the pressure that component would exert if it alone occupied the entire container volume at the same temperature.

For an ideal gas mixture, each component obeys the ideal gas law independently: Pᵢ = nᵢRT/V. Since the total pressure is the sum over all components, P_total = (n₁ + n₂ + …)RT/V = n_total RT/V, which is just the ideal gas law for the total amount. This means that in an ideal mixture, each gas behaves as if the others were absent.

The partial pressure of component i is also related to the total pressure by the mole fraction χᵢ: Pᵢ = χᵢ × P_total, where χᵢ = nᵢ/n_total. The mole fraction is dimensionless and always between 0 and 1. All mole fractions in a mixture sum to exactly 1.

John Dalton formulated this law in 1801 from experiments measuring the vapor pressure of water vapor mixed with air and other gases. He found that water vapor exerted the same pressure whether or not other gases were present — confirming that the components act independently.

Dalton's law is an ideal law and breaks down for mixtures of gases with strong intermolecular interactions (e.g., HCl and NH₃) or at very high pressures. For real mixtures, the fugacity of each component (its effective partial pressure corrected for non-ideality) is used instead.

Comprehensive understanding of the Partial Pressure (Dalton's Law) Calculator requires evaluating both standard baseline assumptions and dynamic real-world variables. In quantitative modeling, minor variances in input fidelity or rounding precision can compound across multi-step formulas.

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Step 1 — If mole fractions are known: Pᵢ = χᵢ × P_total. The mole fractions must sum to 1.

Step 2 — If individual moles and container conditions are known: Pᵢ = nᵢRT/V. Sum all Pᵢ to get P_total.

Step 3 — If partial pressures are known: P_total = ΣPᵢ. The mole fraction of each component is χᵢ = Pᵢ/P_total.

Step 4 — For gas collected over water at temperature T: P_dry gas = P_total − P_water(T). Look up the vapor pressure of water at T from a steam table.

Step 5 — Always verify that all mole fractions sum to 1 and that all partial pressures are positive.

Partial Pressure (Dalton's Law) Calculator Primary Governing Equation

Dalton's Law

Partial pressure from mole fraction

Partial pressure from ideal gas law

Mole fraction from partial pressure

A container holds 0.400 mol N₂, 0.150 mol O₂, and 0.050 mol Ar at 25 °C (298.15 K) in a 10.0 L vessel. Find the partial pressure of each gas and the total pressure.

Use Pᵢ = nᵢRT/V with R = 0.082057 L·atm/(mol·K), T = 298.15 K, V = 10.0 L.

P_N₂ = (0.400 × 0.082057 × 298.15) / 10.0 = 0.9786 atm.

P_O₂ = (0.150 × 0.082057 × 298.15) / 10.0 = 0.3670 atm.

P_Ar = (0.050 × 0.082057 × 298.15) / 10.0 = 0.1223 atm.

P_total = 0.9786 + 0.3670 + 0.1223 = 1.4679 atm. Verify with total moles: n_total = 0.600 mol; P_total = (0.600 × 0.082057 × 298.15)/10.0 = 1.4679 atm ✓

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Vapor pressure is the partial pressure exerted by a substance's vapor when in dynamic equilibrium with its liquid or solid phase at a given temperature. When collecting a gas over water, the gas is always saturated with water vapor, so the measured total pressure includes the vapor pressure of water (e.g., 23.8 mmHg at 25 °C).

Mole fraction (χ) is the ratio of moles of a component to total moles in the mixture. It is dimensionless and between 0 and 1. Mole fractions are useful in thermodynamics because they describe composition independently of total amount or pressure.

Henry's Law extends partial pressure concepts to solutions: the concentration of a dissolved gas is proportional to its partial pressure in the gas phase above the solution. This governs the solubility of O₂ in blood and CO₂ in beverages.

Key terms and core concepts associated with the Partial Pressure (Dalton's Law) Calculator include input parameter variance, unit normalization, margin of error, sensitivity analysis, and education principles.

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