Partial Pressure: Formula and Calculation Example

Partial pressure is the pressure a single gas in a mixture would exert if it occupied the same volume alone at the same temperature. Calculate it by multiplying the total pressure by that gas’s mole fraction; this calculator takes total pressure and gas composition as inputs and returns the gas’s partial pressure.

Formula

Partial pressure = total pressure × mole fraction, or pᵢ = xᵢP.

• pᵢ is the partial pressure of gas i, in the same pressure unit as the total pressure.
• xᵢ is the mole fraction of gas i, a unitless value from 0 to 1.
• P is the total pressure of the gas mixture, in kPa here. Other consistent pressure units, such as atmospheres, pascals, bar, or psi, can also be used.

The mole fraction is the amount of the selected gas divided by the total amount of gas, with both amounts measured in the same units: xᵢ = nᵢ/nₜₒₜₐₗ. For an ideal gas mixture, a gas’s mole fraction equals its volume fraction when the gases are compared at the same temperature and pressure.

Worked Example

Using the calculator’s default values, the total pressure is 101.325 kPa and the gas mole fraction is 0.21.

1. Use pᵢ = xᵢP.
2. Substitute the values: pᵢ = 0.21 × 101.325 kPa.
3. Calculate: pᵢ = 21.27825 kPa.
4. Round to two decimal places: 21.28 kPa.

The result is the pressure contribution associated with the selected gas under the ideal-mixture model. The 0.21 fraction is an example input, not a claim that every gas mixture contains that proportion.

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 component partial pressures: P = p₁ + p₂ + … + pₙ. Each component’s partial pressure represents its contribution to the mixture’s total pressure. It is not a separate pressure physically measured in a sealed mixture by removing the other gases; it is a useful quantity defined by the gas-mixture relationship.

For example, if two ideal gases have mole fractions of 0.70 and 0.30 at a total pressure of 200 kPa, their partial pressures are 140 kPa and 60 kPa. Together they add back to 200 kPa. For a complete composition, the mole fractions add to 1 and the component partial pressures add to the total pressure.

How to Calculate It from Composition

When composition is given as amounts rather than a mole fraction, first find the fraction for the gas of interest. Divide its amount by the sum of the amounts, then multiply that fraction by total pressure. For instance, a mixture containing 2 moles of one gas and 8 moles of another has 10 total moles. The first gas’s mole fraction is 2/10 = 0.20, so its partial pressure is 0.20 times the total pressure.

Use these steps to avoid confusing a percentage with a fraction:

1. Identify the total pressure and make sure it is an absolute pressure, not a gauge pressure.
2. Find the gas’s mole fraction. Convert a percentage to a decimal by dividing by 100: 21% becomes 0.21.
3. Multiply the fraction by the total pressure.
4. Report the answer in the same pressure unit as the input, with sensible rounding.

If the composition is specified by mass, mass percentages are not mole fractions. Convert each gas’s mass to moles using its molar mass, add the moles, and then calculate the selected gas’s mole fraction.

Units, Gauge Pressure, and Humidity

Pressure units can be converted before or after the calculation, provided they are used consistently. One atmosphere is 101.325 kPa, while 1 psi is approximately 6.895 kPa. The partial pressure uses the same unit as the total pressure: a calculation in atmospheres gives an answer in atmospheres; one in psi gives psi. Do not enter a pressure in one unit and interpret the number as another.

Dalton’s law uses absolute pressure, measured relative to a vacuum. A gauge-pressure reading is measured relative to local atmospheric pressure, so convert it before calculating: absolute pressure = gauge pressure + local atmospheric pressure. This distinction matters whenever the pressure instrument reports gauge pressure.

Water vapor also contributes to the total pressure of a gas mixture. For a moist gas, the dry-gas partial pressure is often calculated as total pressure minus water-vapor pressure. If a dry-gas composition is then used, apply its mole fraction to the dry-gas pressure rather than accidentally treating the full moist pressure as dry gas. The appropriate water-vapor pressure depends on the conditions, including temperature.

Assumptions and Common Mistakes

The simple relationship pᵢ = xᵢP is the standard ideal-gas mixture calculation. It works well for many ordinary gas-mixture calculations, but real gases can deviate from ideal behavior, especially at high pressures or near condensation. In those cases, more detailed thermodynamic models may be needed; the basic calculator does not correct for non-ideal behavior.

• Using a percent as a decimal: enter 21% as 0.21, not 21.
• Mixing pressure units: all pressure values in a calculation must use the same unit.
• Using gauge instead of absolute pressure: add local atmospheric pressure to gauge pressure first.
• Confusing mass fraction and mole fraction: convert mass amounts to moles before applying Dalton’s law.
• Rounding too early: keep extra digits during intermediate steps and round only the reported answer.

Frequently Asked Questions

What is the formula for partial pressure?
For an ideal gas mixture, pᵢ = xᵢP: multiply the gas’s mole fraction by the mixture’s total absolute pressure.

How do I find partial pressure from a percentage?
Divide the percentage by 100 to get a mole fraction, then multiply by total pressure. For example, a 25% mole fraction is 0.25.

Do partial pressures add up to total pressure?
Yes. Under Dalton’s law, the partial pressures of all gas components sum to the mixture’s total pressure.

Can I use volume percent instead of mole fraction?
For an ideal gas mixture, volume fraction at the same temperature and pressure equals mole fraction. This equivalence may not be sufficiently accurate for non-ideal conditions.

Can partial pressure be greater than total pressure?
Not for a component with a mole fraction between 0 and 1 in the ideal-mixture calculation: pᵢ = xᵢP, so its partial pressure is no greater than the total pressure.

Related

• Calculate Specific Heat Capacity
• Natural Frequency: Formula and Calculation
• Calculating Energy: Formula, Units, and Examples

in P | Total pressure | kPa | 101.325 | 0
in x | Gas mole fraction | - | 0.21 | 0
out p | Partial pressure | kPa | P * x | 2