Partial Pressure of Gas: Formula and Examples

The partial pressure of a gas is its share of the total pressure in a mixture. For an ideal gas mixture, use P_i = x_iP_total, where x_i is the gas’s mole fraction; enter the component amount and total pressure to calculate its partial pressure.

Formula

The partial pressure of component i is its mole fraction multiplied by the mixture’s total pressure:

P_i = x_iP_total = (n_i/n_total)P_total

• P_i is the partial pressure of gas i, in kPa in this calculator.
• x_i is its mole fraction, a dimensionless ratio.
• n_i is the amount of that gas, 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.

The calculator takes component and total amounts directly. If you already know the mole fraction, multiply it by total pressure instead. For example, a mole fraction of 0.20 in a mixture at 150 kPa gives a partial pressure of 30 kPa.

Worked Example

Using the calculator’s defaults—1 mol of the selected gas, 5 mol total, and a total pressure of 101.325 kPa—first find the mole fraction:

x = n / n_total = 1 mol / 5 mol = 0.2000

Then multiply by the total pressure:

P_i = xP_total = 0.2000 × 101.325 kPa = 20.265 kPa

Rounded to the calculator’s three decimal places, the partial pressure is 20.265 kPa.

Assumptions

• The gas mixture is treated as ideal, so Dalton’s law applies.
• The entered component amount is part of the total; it cannot exceed the total amount.
• All amounts refer to gases in the same mixture, and pressure is absolute pressure rather than gauge pressure.

Dalton’s Law and What Partial Pressure Means

Dalton’s law of partial pressures states that the total pressure of a mixture of nonreacting gases is the sum of the pressure contributions of its components:

P_total = P₁ + P₂ + P₃ + …

A partial pressure is not the pressure in a separate physical compartment. It is the pressure a gas would exert if it alone occupied the mixture’s volume at the same temperature, under the ideal-gas model. In a mixture, the molecules share the space and collide with the container walls; each gas contributes to the total pressure.

The mole fraction determines each gas’s share because, at the same temperature and volume, ideal-gas pressure is proportional to the number of moles. If a mixture contains 1 mol of one gas and 4 mol of another, their mole fractions are 0.20 and 0.80. At a total pressure of 101.325 kPa, their partial pressures are respectively 20.265 kPa and 81.060 kPa; together they equal 101.325 kPa.

Calculating from Gas Amount, Volume, or Composition

The mole-fraction formula is convenient when the amounts or composition are known. If instead the amount, temperature, and volume of one gas are known, the ideal gas law gives its partial pressure directly:

P_iV = n_iRT, so P_i = n_iRT/V.

Here, V is the mixture volume, T is absolute temperature in kelvin, and R is the gas constant in units consistent with pressure and volume. For pressure in pascals and volume in cubic metres, use R = 8.31446261815324 J/(mol·K). Temperature in Celsius must be converted to kelvin by adding 273.15.

For a gas mixture with a known volume percentage, that percentage can represent its mole fraction for an ideal gas mixture at a shared temperature and pressure. Convert the percentage to a decimal before multiplying by total pressure: 2.5% becomes 0.025, not 2.5. This equivalence is a gas-mixture relationship; it should not be assumed for arbitrary liquid solutions.

Units, Pressure Readings, and Common Errors

• Keep pressure units consistent. The result uses the unit entered for total pressure. If pressure is given in atm but the calculator expects kPa, convert with 1 atm = 101.325 kPa.
• Use absolute pressure. Gas-law equations and partial-pressure sums use pressure measured relative to a vacuum. A gauge reading is relative to the surrounding atmosphere and must be converted before use.
• Use the whole mixture as the denominator. The total amount includes every gas component, not just the component of interest.
• Check the composition. Mole fractions are between 0 and 1, and the fractions of all components in a mixture sum to 1, subject to rounding.
• Do not mix a dry-gas total with a wet-gas composition. Water vapor contributes to total pressure. If a gas is collected over water, its vapor pressure may need to be accounted for before finding the dry gas’s partial pressure.

When the Ideal-Gas Approximation Is Limited

Dalton’s law is a strong approximation for many gases at ordinary pressures and temperatures, but real gases can interact. At high pressure or near condensation, the relationship between composition and pressure may depart from the ideal prediction. More advanced treatments use fugacity or an equation of state, with parameters appropriate to the particular gases and conditions. Do not treat the ideal result as exact when those effects matter.

Partial pressure also depends on the specified mixture and its conditions. A gas can dissolve in a liquid or react, changing the gas-phase composition. The formula calculates the pressure contribution from the gas-phase amount; it does not predict chemical reaction, dissolution, or how much gas transfers between phases.

Frequently Asked Questions

What is the formula for partial pressure?
For an ideal gas mixture, P_i = x_iP_total, or P_i = (n_i/n_total)P_total. The partial pressures of all components add to the total pressure.

How do I calculate partial pressure from moles?
Divide the component’s moles by the mixture’s total moles to get its mole fraction, then multiply by total pressure. Make sure the component amount is included in the total.

Can partial pressure be greater than total pressure?
Not for a component in the same ideal-gas mixture: its mole fraction is at most 1, so its partial pressure cannot exceed the mixture’s total pressure.

Is partial pressure the same as concentration?
No. Partial pressure has pressure units, while concentration describes amount per volume. For an ideal gas, they are related by P_i = (n_i/V)RT.

How do I find the partial pressure of water vapor?
Use water vapor’s mole fraction times the total pressure when composition is known. For gas collected over liquid water at equilibrium, use the water-vapor pressure at the measured temperature; subtract it from the total pressure to find the pressure of the remaining dry gases.

Related

• Molar Volume Calculation: Ideal Gas Vm = RT ÷ P
• Van der Waals Gas Pressure Calculator: Real Gas Pressure
• The Ideal Gas Law Calculator: Pressure From PV = nRT

in n | Amount of gas | mol | 1 | 0
in nt | Total amount of gas mixture | mol | 5 | 0
in pt | Total pressure | kPa | 101.325 | 0
out pi | Partial pressure | kPa | (n / nt) * pt | 3
out x | Mole fraction | - | n / nt | 4