Partial Pressure Calculator

In a mixture of gases that do not react, each gas exerts the pressure it would exert alone in the same container. That is its partial pressure, and Dalton's law says the total is their sum:

$P_{\text{total}} = P_1 + P_2 + \cdots + P_n$

The share each gas takes is set by its mole fraction:

$x_i = \frac{n_i}{n_{\text{total}}} \qquad\Longrightarrow\qquad P_i = x_i P_{\text{total}}$

Symbols and units:

• $P_i$ — partial pressure of component $i$, pascals (Pa) in SI; atm, kPa, bar and mmHg are all common
• $n_i$ — moles of component $i$, mol
• $x_i$ — mole fraction, dimensionless, and $\sum x_i = 1$

When it applies: ideal-gas behaviour — moderate pressures, temperatures well above condensation, no chemical reaction between components.

The assumption people forget: mole fractions use moles, not masses. $1$ g of hydrogen and $1$ g of oxygen are not equal shares — they are $0.50$ mol and $0.031$ mol.

If you know how much of one gas is in a container, you can compute its partial pressure directly, ignoring everything else present:

$P_i = \frac{n_i R T}{V}$

• $R$ — gas constant, $0.08206$ L·atm/(mol·K), or $8.314$ J/(mol·K) with $P$ in Pa and $V$ in m³
• $T$ — absolute temperature, kelvin (K)
• $V$ — volume of the container, litres (L) or m³ to match $R$

Because $V$, $R$ and $T$ are shared by every component, the ratio of partial pressures equals the ratio of moles — which is exactly why $P_i = x_i P_{\text{total}}$ works.

Gas collected over water: the sample is saturated with water vapour, so

$P_{\text{dry gas}} = P_{\text{total}} - P_{\text{H}_2\text{O}}$

where $P_{\text{H}_2\text{O}}$ is the tabulated vapour pressure at that temperature ($23.8$ mmHg at $25$ °C).

The assumption people forget: $T$ in kelvin, and $R$ chosen to match your pressure and volume units.

• Using mass fractions as mole fractions — divide each mass by its molar mass first.
• Using °C in $PV = nRT$ — add $273.15$ to get kelvin.
• Mismatching $R$ with the units — $0.08206$ goes with L and atm; $8.314$ goes with m³ and Pa.
• Forgetting the water vapour correction — a gas collected over water is wet, and skipping the subtraction overstates the amount collected.
• Letting the mole fractions miss $1$ — they must sum to exactly $1$; if they do not, a component has been dropped.
• Applying Dalton's law to reacting gases — if the components react, the mole counts change and the law no longer holds.
• Mixing pressure units mid-problem — $760$ mmHg $= 1$ atm $= 101.325$ kPa; convert once, at the start.