Partial Pressure Formula: Calculate a Gas’s Share

The partial pressure formula is P_i = x_iP_total: multiply a gas’s mole fraction by the total pressure of the gas mixture. This calculator works out the partial pressure from a gas’s amount and the mixture’s total pressure, and also reports the mole fraction.

Formula

For an ideal gas mixture, the partial pressure of component i is its mole fraction multiplied by the total pressure:

P_i = x_iP_total = (n_i/n_total)P_total

• P_i is the partial pressure of component i, in kPa in this calculator.
• x_i is its mole fraction, a unitless ratio.
• n_i is the amount of that component, 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 total pressure is the sum of the component partial pressures: P_total = ΣP_i. If a pressure is supplied in another unit, convert it before using the calculator. For example, 1 atm = 101.325 kPa; do not combine a pressure in atm with one in kPa without conversion.

Worked Example

Using the calculator’s default values, the mixture contains 1 mol of gas i within 3 mol total, at 101.325 kPa.

x_i = n_i/n_total = 1 mol / 3 mol = 0.33333

P_i = x_iP_total = 0.33333… × 101.325 kPa = 33.775 kPa

The component’s partial pressure is 33.775 kPa. The mole fraction is 0.3333 when rounded to four decimal places. The repeating fraction is used before rounding the final pressure.

Assumptions

• The mixture behaves as an ideal gas, so the partial-pressure form of Dalton’s law applies.
• The inputs describe the same gas mixture, and n_total includes every gas component.
• Amounts are nonnegative and the total amount is positive; the component amount cannot exceed the total.
• This calculator is for study and lab-planning arithmetic, not a substitute for a measurement or a validated method.

How Partial Pressure Works

In the ideal-gas model, gas particles move independently and share the volume available to the mixture. Each component contributes to the pressure as if it alone occupied that volume at the mixture’s temperature. The pressure associated with that contribution is its partial pressure. Dalton’s law states that the total pressure is the sum of those contributions.

Because the ideal-gas equation is P V = n R T, gases in the same mixture share V and T. Their pressure contributions are therefore proportional to their mole amounts: P_i/P_total = n_i/n_total. This ratio is the mole fraction. The relationship explains why a gas’s partial pressure depends on its share of the mixture, not merely on whether it is present.

For example, if a two-component ideal mixture has mole fractions 0.20 and 0.80 and a total pressure of 100 kPa, their partial pressures are 20 kPa and 80 kPa. Adding them gives the total, 100 kPa. A component’s partial pressure cannot exceed the total pressure when all amounts are nonnegative.

When to Use the Formula

Use this relationship when you know a mixture’s total pressure and the proportion of a gas in it. Mole fractions can come from measured or specified amounts in moles. For an ideal gas mixture, they can also be calculated from volume fractions when the gases are compared at the same temperature and pressure. A percentage composition must be divided by 100 to obtain a fraction: 25% becomes 0.25.

• Known amounts: divide the target component’s moles by the total moles, then multiply by total pressure.
• Known mole fraction: multiply that fraction directly by total pressure.
• Known partial pressure and total pressure: divide the partial pressure by total pressure to find the mole fraction.
• Known all-but-one components: subtract their partial pressures from the total to find the remaining component’s pressure, provided the values describe the same mixture and conditions.

The result is useful in gas-law calculations and in interpreting gas composition. It is a pressure contribution, not a separate pressure chamber or a claim that components occupy separate regions of the container.

Common Mistakes and Limits

A frequent error is using the component’s amount as a fraction without dividing by the total amount. If the component is 1 mol in a 3 mol mixture, its mole fraction is one third, not 1. Another is using a percentage as if it were already a decimal fraction: 30% must be entered as 0.30.

• Include every gaseous component in n_total, including gases that seem minor.
• Keep pressure units consistent. The calculator uses kPa and does not automatically convert an entered value in atm, bar, or mmHg.
• Do not confuse partial pressure with gas concentration. The former has pressure units; mole fraction has no units.
• A result should satisfy 0 ≤ P_i ≤ P_total, and all component partial pressures should sum to the total, subject to rounding.

Dalton’s law is exact for the ideal-gas model and often a useful approximation for real gases at relatively low pressures. At high pressures or under conditions where intermolecular interactions matter, real gases can depart from ideal behavior. More advanced treatments use fugacity or other non-ideal corrections; this simple calculator does not.

Frequently Asked Questions

What is the formula for partial pressure?
P_i = x_iP_total, where x_i = n_i/n_total. In words, multiply the gas’s mole fraction by the total pressure.

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

Does partial pressure equal the gas’s pressure if it were alone?
For an ideal mixture, it is the pressure that component would exert alone in the mixture’s volume at the same temperature. It is not a separate pressure physically isolated from the other gases.

Can partial pressure be greater than total pressure?
Not for a component in an ordinary mixture with nonnegative amounts: its mole fraction is at most 1, so its partial pressure is at most the total. A larger calculated value usually indicates inconsistent units or inputs.

How do I find total pressure from partial pressures?
Add the partial pressures of all gas components in the mixture. Convert them to the same pressure unit first.

Is partial pressure the same as vapor pressure?
No. Partial pressure describes one component’s contribution in a gas mixture. Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid at a particular temperature.

Related

• Partial Pressure and Total Pressure Formula
• Partial Pressure Equation: Formula and Examples
• Volume of Gas Equation: Formula and Calculator

in ni | Amount of gas i | mol | 1 | 0
in nt | Total amount of gas mixture | mol | 3 | 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