Partial Pressure and Total Pressure Formula

The total pressure of a mixture of nonreacting gases is the sum of their partial pressures: P_total = ΣP_i. For an ideal gas, a component’s partial pressure is P_i = x_iP_total = n_iRT/V; this calculator uses the mole fractions and total pressure you enter to return each gas’s partial pressure and the total.

Formula

For a mixture of ideal gases, Dalton’s law states that total pressure is the sum of the partial pressures:

P_total = P₁ + P₂ + … + P_i = ΣP_i

For each gas, its partial pressure can be calculated from its mole fraction:

P_i = x_iP_total, where x_i = n_i/n_total.

• P_i is the partial pressure of component i, in kPa here.
• P_total is the mixture’s total pressure, in kPa.
• x_i is the component’s mole fraction, a unitless ratio between 0 and 1.
• n_i is the amount of that gas in moles; n_total is the total amount of gas in moles.

The mole fractions of all components add to 1 for a mixture containing only those components: Σx_i = 1. The equivalent ideal-gas expression is P_i = n_iRT/V, using R = 8.31446261815324 J/(mol·K), absolute temperature T in kelvin, volume V in m³, and pressure in pascals. The calculator uses the mole-fraction form, so it does not require temperature or volume as inputs.

Worked Example

Use the calculator’s default values: total pressure = 101.325 kPa, x₁ = 0.700, and x₂ = 0.300.

1. Gas 1 partial pressure: P₁ = 101.325 kPa × 0.700 = 70.9275 kPa, or 70.928 kPa to three decimal places.
2. Gas 2 partial pressure: P₂ = 101.325 kPa × 0.300 = 30.3975 kPa, or 30.398 kPa to three decimal places.
3. Sum: 70.9275 kPa + 30.3975 kPa = 101.325 kPa.

The partial pressures sum to the entered total pressure because the two fractions add to 1. If fractions do not add to 1, the calculator still multiplies each fraction by total pressure, but the displayed sum will not equal that total.

Assumptions

• The gas mixture is treated as ideal, and the components are nonreacting.
• The entered fractions are mole fractions for the same gas mixture and pressure conditions.
• The example is a two-component mixture; add the partial pressures of any additional components when applying the general formula.

How Partial Pressure Works

A partial pressure is the pressure a gas component contributes within a mixture under the ideal-gas model. It is not a separate layer of pressure or a claim that gases occupy separate parts of the container. Gas molecules move throughout the available volume; the partial-pressure idea assigns each component a share of the pressure based on its amount.

For ideal gases, the mole fraction and volume fraction are equal when the gases share the same temperature and pressure. Thus, if a component makes up 21% of the gas molecules, its partial pressure is 21% of the mixture’s total pressure. This is why a gas’s partial pressure can be found without separately knowing the container’s volume, provided the total pressure and mole fraction are known.

Using the Calculator and Checking Inputs

Enter a total pressure in kPa and a mole fraction for each of the two components. Fractions are decimal proportions, not percentages: enter 0.21 for 21%, rather than 21. The calculator reports the two partial pressures and their sum. To use another pressure unit, convert all pressures consistently; for example, 1 atm = 101.325 kPa. Do not add pressures expressed in different units without converting them first.

For a mixture with more than two gases, calculate each P_i = x_iP_total and add the results, or group components whose combined mole fraction is known. Round only at the end when possible. Small differences between a rounded sum and the stated total may result from rounding displayed values.

• Check that each mole fraction is from 0 to 1.
• Check that the fractions for all gases in the mixture add to approximately 1.
• Use absolute pressure, not gauge pressure, when applying the ideal-gas relationships. Gauge pressure is measured relative to the surrounding atmosphere.
• Use the same pressure unit for the total and every partial pressure.

Dalton’s Law and Its Limits

Dalton’s law is a useful approximation for many gas mixtures at ordinary pressures, especially when gases are sufficiently dilute that interactions between molecules have little effect. Real gases can depart from ideal behavior at high pressure or near condensation, where intermolecular forces and molecular volume matter. Under those conditions, partial pressure may need a more advanced treatment using fugacity or other non-ideal gas corrections rather than the simple mole-fraction formula.

Be careful when a gas is collected over liquid water. The measured total pressure includes water vapor as well as the gas of interest. If the water-vapor pressure is known at the relevant temperature, the dry gas pressure is P_dry = P_total − P_{water vapor}. This is a related use of partial pressures, not a reason to treat the wet total pressure as the dry gas’s pressure.

Common Misconceptions

Partial pressure is not the same as concentration, although the two are related for an ideal gas at a specified temperature. Pressure has units such as kPa or atm; mole fraction has no units. Also, a gas’s partial pressure is not necessarily the pressure it would have after being isolated and compressed into a different volume. The formula P_i = x_iP_total refers to that component’s share in the original mixture at the same temperature and volume.

Another frequent error is using percent composition as though it were a fraction. Convert percentages by dividing by 100: 35% becomes 0.35. If the composition is given by mass rather than moles, it cannot be used directly as x_i; first convert each component’s mass to moles using its molar mass, then divide by the total moles.

Frequently Asked Questions

What is the formula for total pressure?
Total pressure is the sum of all component partial pressures: P_total = P₁ + P₂ + … . This is Dalton’s law for an ideal gas mixture.

How do I calculate partial pressure from mole fraction?
Multiply the component’s mole fraction by the total pressure: P_i = x_iP_total. Use a decimal fraction and keep pressure units consistent.

Do mole fractions have to add up to 1?
Yes, when the listed components account for the entire mixture. If they do not, a component may be missing or the percentages may not have been converted or normalized correctly.

Can partial pressure be greater than total pressure?
Not for a component in an ideal mixture with a valid mole fraction between 0 and 1. Its partial pressure is a share of the total and cannot exceed it.

Does the formula work for gases collected over water?
Yes, but the measured total includes water vapor. Subtract the water-vapor pressure at the relevant temperature to find the dry gas pressure when that is the quantity needed.

Related

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

in pt | Total pressure | kPa | 101.325 | 0
in x1 | Mole fraction of gas 1 | - | 0.700 | 0
in x2 | Mole fraction of gas 2 | - | 0.300 | 0
out p1 | Partial pressure of gas 1 | kPa | pt * x1 | 3
out p2 | Partial pressure of gas 2 | kPa | pt * x2 | 3
out ps | Sum of partial pressures | kPa | p1 + p2 | 3