Gas Mixture Partial Pressure

Physics Thermodynamics • Advanced Applications and Extensions in Thermodynamics

Written by STEM Calculators Team Published January 8, 2026 Updated February 24, 2026

3. Gas Mixture Partial Pressure

Apply Dalton’s law for ideal gas mixtures: $P_{\text{tot}}=\sum_i P_i$ and $P_i=y_i\,P_{\text{tot}}$ . Optional “humid air” mode adds water vapor using $P_{H_2O}=\phi\,P_{\text{sat}}(T)$ and splits the remaining dry-gas pressure. Includes an Amagat-style volume fraction view and a pie chart of composition.

Inputs support: pi, e, sqrt(), sin, cos, exp, log, and *. Pressure can be entered in atm, kPa, or bar.

Mixture setup

Total pressure $P_{tot}$: Pressure unit: Mole-fraction handling: Show Amagat volumes: Humid air mode: Temperature $T$ (°C): Relative humidity $\phi$ (%):

Tip: In humid mode, your entered gas fractions are treated as dry-gas fractions. The tool computes $P_{H_2O}$ and uses $P_{dry}=P_{tot}-P_{H_2O}$ for the remaining gases.

Components (mole fractions)

Gas	Mole fraction $y_i$
Sum	—

3 gases

Ready

Steps

Enter values and click Solve.

Composition pie chart

Mole fractions (includes $H_2O$ if humid mode)

Hover: —

Results table

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Theory: Gas Mixture Partial Pressure (Dalton + humid air)

1) Dalton’s law (ideal gas mixtures)

For an ideal gas mixture at a common temperature and volume, the total pressure equals the sum of the partial pressures:

\[ P_{\text{tot}}=\sum_i P_i. \]

The partial pressure of species $i$ is proportional to its mole fraction $y_i$:

\[ P_i=y_i\,P_{\text{tot}},\qquad y_i=\frac{n_i}{n_{\text{tot}}}. \]

Intuition: each component “acts like” it alone occupied the same container at the same $T$.

2) Example (dry air at 1 atm)

Given: $P_{\text{tot}}=1\ \text{atm}$ and composition $y_{N_2}=0.78$, $y_{O_2}=0.21$, $y_{Ar}=0.01$.

\[ P_{N_2}=0.78\cdot 1=0.78\ \text{atm},\quad P_{O_2}=0.21\cdot 1=0.21\ \text{atm},\quad P_{Ar}=0.01\cdot 1=0.01\ \text{atm}. \]

Check:

\[ P_{N_2}+P_{O_2}+P_{Ar}=0.78+0.21+0.01=1\ \text{atm}=P_{\text{tot}}. \]

3) Humid air mode (water vapor)

When water vapor is present, its partial pressure is commonly modeled using relative humidity $\phi$:

\[ P_{H_2O}=\phi\,P_{\text{sat}}(T), \]

where $P_{\text{sat}}(T)$ is the saturation vapor pressure at temperature $T$.

A convenient way to treat the remaining gases is to define the dry-gas pressure:

\[ P_{\text{dry}}=P_{\text{tot}}-P_{H_2O}. \]

If your entered composition $\{y_i\}$ is the dry-gas composition, then:

\[ P_i=y_i\,P_{\text{dry}}. \]

The calculator reports both: (i) your dry fractions $y_i$, and (ii) the total mole fractions including water, which satisfy $\sum y_i=1$.

4) Amagat’s law (volume fractions)

Amagat’s law of additive volumes (for ideal mixtures) says that at the same $T$ and $P$, the total volume is the sum of “partial volumes.”

Under ideal-gas assumptions, the volume fraction equals the mole fraction:

\[ \frac{V_i}{V_{\text{tot}}}=y_i. \]

In the calculator, the Amagat column is shown as $V_i/V_{tot}$, using total mole fractions (including water if humid mode is on).

5) Notes on “real mixtures” (advanced)

Dalton’s law is exact for ideal gases. For real mixtures at high pressure or strong interactions, partial pressures can be corrected using fugacity:

\[ f_i = \phi_i\,y_i\,P_{\text{tot}}, \]

where $\phi_i$ is a fugacity coefficient from an equation of state or activity model. In that case, “effective” partial pressures depart from $y_iP_{\text{tot}}$.

Steps

Composition pie chart

Results table

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