Partial Pressure Equation: Formula and Examples

The partial pressure equation is P_i = x_iP_total: a gas’s partial pressure equals its mole fraction multiplied by the total pressure. This calculator uses the amount of one gas and the total amount of gas to find its mole fraction, then returns that gas’s partial pressure in the same pressure units you enter.

Formula

The calculator applies Dalton’s law of partial pressures:

P_i = x_iP_total = (n_i/n_total)P_total

P_i is the partial pressure of gas i, in kPa here.
x_i is the mole fraction of gas i, with no units.
n_i is the amount of gas i, in mol.
n_total is the total amount of all gases in the mixture, in mol.
P_total is the mixture’s total pressure, in kPa here.

Mole fraction is the amount of a component divided by the total amount of all components. The pressure units do not have to be kPa: use atm, bar, or another consistent unit for total pressure, and the calculated partial pressure will be in that same unit. The calculator’s displayed unit is kPa.

Worked Example

With the calculator’s default values, gas i has 1 mol, the mixture contains 4 mol total, and the total pressure is 101.325 kPa.

Find the mole fraction: x_i = n_i/n_total = 1 mol / 4 mol = 0.25.
Multiply the mole fraction by total pressure: P_i = 0.25 × 101.325 kPa = 25.33125 kPa.
Rounded to three decimal places, the partial pressure is 25.331 kPa.

The result represents the pressure contribution associated with that gas under the mixture conditions. For an ideal-gas mixture, the partial pressures of all components add up to the total pressure.

Assumptions

The mixture is treated as an ideal gas, so Dalton’s law applies.
The amount of gas i is part of the stated total amount: n_i cannot exceed n_total.
All amounts refer to the same gas mixture and conditions.

How Partial Pressure Works

Dalton’s law says that, for a mixture of nonreacting gases behaving ideally, total pressure is the sum of the individual partial pressures: P_total = P₁ + P₂ + … . A partial pressure is not a separate pressure that can be measured by removing one gas while leaving everything else unchanged. It is the pressure each component would exert if it alone occupied the mixture’s volume at the same temperature.

The mole fraction gives the proportion of gas particles belonging to a component. For an ideal mixture, that proportion is also the component’s proportion of total pressure. If a gas makes up 25% of the mixture by moles, its partial pressure is 25% of the total pressure.

The same relationship can be expressed with the ideal gas law. For gas i, P_iV = n_iRT, so P_i = n_iRT/V. For the whole mixture, P_total = n_totalRT/V. Dividing these equations gives P_i/P_total = n_i/n_total. This makes clear that the mole-fraction equation follows from the ideal gas law when the gases share a volume and temperature.

When to Use Each Form

Use P_i = x_iP_total when the composition is known as a mole fraction or percentage. Use P_i = (n_i/n_total)P_total when amounts in moles are known. If the gas amount, volume, and temperature are known instead, the ideal gas form P_i = n_iRT/V can be useful; temperature must be in kelvins and the gas constant R must match the pressure and volume units.

For example, if a mixture is 20% gas A by mole and has a total pressure of 150 kPa, then P_A = 0.20 × 150 kPa = 30 kPa. If the composition is supplied as a percentage, divide it by 100 before using it as a mole fraction. A 20% composition is 0.20, not 20.

Common Mistakes and Limits

Using the wrong total: The denominator must include all gases in the mixture, not just the components of interest.
Mixing units: The partial pressure has the same unit as total pressure. Do not combine a pressure in atm with a total pressure in kPa without converting one of them.
Confusing mole fraction and mass fraction: A component’s share by mass is not generally its share by moles. Convert masses to moles using molar masses before using this equation.
Counting vapor above a liquid: In a gas mixture containing vapor, the vapor contributes to total pressure. For a gas collected over water, the dry-gas pressure is total pressure minus water-vapor pressure at the relevant temperature.

Dalton’s law is an ideal-gas approximation. Real gases can depart from ideal behavior, particularly at high pressures or near condensation, because molecules interact and occupy volume. In those cases, partial-pressure calculations may need a real-gas model or measured data. Also, if the mixture reacts, condenses, or changes composition, the amounts used must describe the mixture at the conditions of interest.

Frequently Asked Questions

What is the equation for partial pressure?
P_i = x_iP_total, where x_i is the gas’s mole fraction. Equivalently, P_i = (n_i/n_total)P_total.

How do I calculate partial pressure from a percentage?
Convert the percentage to a decimal by dividing by 100, then multiply by total pressure. For example, 35% becomes 0.35; at 200 kPa, the partial pressure is 70 kPa.

Can partial pressure be greater than total pressure?
Not for a component in a conventional ideal-gas mixture with a mole fraction from 0 to 1. Its partial pressure is between zero and total pressure; the sum of all component partial pressures equals the total.

Does partial pressure depend on the gas identity?
For an ideal mixture, it depends on the component’s mole fraction and total pressure, not directly on its chemical identity. Gas identity matters indirectly when determining composition or when real-gas effects are significant.

How do you find oxygen’s partial pressure in air?
Multiply the oxygen mole fraction by the total pressure. Dry air contains about 0.2095 oxygen by mole, so at a total pressure of 101.325 kPa its ideal partial pressure is about 21.2 kPa. Water vapor or other changes to the gas mixture affect the applicable fraction and pressure.

Formula used

in ni | Amount of gas i | mol | 1 | 0
in nt | Total amount of gas | mol | 4 | 0
in pt | Total pressure | kPa | 101.325 | 0
out pi | Partial pressure of gas i | kPa | (ni / nt) * pt | 3
out xi | Mole fraction of gas i | - | ni / nt | 4

Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work

Method: the standard formula for this calculation with the constants and conversion factors written on the page, rounded as each result states. See method and constants, the disclaimer or report an error.