Equilibrium Partial Pressure Equation Calculator

This calculator finds the equilibrium partial pressure of a gas in a mixture from its mole fraction and the mixture’s total pressure. Enter the gas mole fraction and total pressure; the result is the gas’s partial pressure, with the other input shown for context.

Formula

For a gas mixture at equilibrium, the partial pressure of component i is its mole fraction multiplied by the mixture’s total pressure:

p_i = y_iP

• p_i is the partial pressure of gas i, in kPa in this calculator.
• y_i is the gas’s mole fraction, a dimensionless ratio equal to the amount of that gas divided by the total amount of gas.
• P is the total pressure of the gas mixture, in kPa.

Pressure units must match: multiplying a mole fraction by pressure in kPa gives partial pressure in kPa. The mole fraction must be between 0 and 1. This calculation uses Dalton’s law for a gas mixture and does not independently determine chemical equilibrium composition; the mole fraction must already be known or calculated from an equilibrium model or measurement.

Worked Example

Using the calculator’s defaults, the gas mole fraction is 0.25 and total pressure is 101.325 kPa.

1. Apply the equation: p_i = y_iP.
2. Substitute the values: p_i = 0.25 × 101.325 kPa.
3. Calculate: p_i = 25.33125 kPa, which rounds to 25.331 kPa at three decimal places.

The corresponding mole fraction check is 25.33125 / 101.325 = 0.25, displayed as 0.250.

Assumptions

• The mixture is treated as an ideal gas mixture, so Dalton’s law applies.
• The entered mole fraction describes the gas composition at the same equilibrium state as the entered total pressure.
• All pressures use the same reference and unit. The calculation does not account for non-ideal gas behavior or a liquid’s vapor-pressure correction.

What Partial Pressure Means

A gas mixture exerts a total pressure. Each component contributes a share of that pressure, called its partial pressure. In the ideal-gas model, the partial pressure is the pressure that component would exert if it alone occupied the same volume at the same temperature. Dalton’s law says the total pressure equals the sum of the partial pressures:

P = p₁ + p₂ + …

The mole fraction gives the component’s share of the total number of gas molecules. For component i, y_i = n_i/n_total, where n is amount of substance in moles. For an ideal mixture, this amount fraction is also the component’s fraction of total pressure. Mole fractions across all gas components sum to 1, and their partial pressures sum to the total pressure.

“Equilibrium” can mean that the gas composition has settled under specified conditions, such as equilibrium between a vapor and its liquid. The equation p_i = y_iP relates that composition to pressure; it does not by itself tell you what the equilibrium composition will be. That generally requires additional information, such as an equilibrium constant, temperature, and starting amounts.

Using the Equation Correctly

First identify the total pressure of the mixture and the mole fraction of the gas of interest. Then multiply. If composition is given as a percentage, divide by 100 to convert it to a mole fraction before using the equation. For example, 25% corresponds to y = 0.25, not 25.

• If the gas fraction is given as a percentage, convert it to a decimal fraction.
• Use absolute pressure, not gauge pressure. If a pressure instrument reports gauge pressure, add the local atmospheric pressure to obtain absolute pressure before applying the equation.
• Keep pressure units consistent throughout. Convert the final result if a different unit is required.
• Check that each gas fraction is between 0 and 1 and that all mixture fractions together total approximately 1.

For example, a gas at 25% mole fraction in a mixture at 101.325 kPa has a partial pressure of 25.331 kPa. If the same composition is at a total pressure of 200 kPa, its partial pressure is 50 kPa. The pressure changes with total pressure even though the mole fraction stays the same.

Equilibrium, Vapor Pressure, and Limitations

A common related case is a gas in equilibrium with a liquid. The vapor’s partial pressure is still part of the total gas pressure, but its equilibrium value may be determined by vapor–liquid equilibrium rather than by the pressure equation alone. For an ideal liquid mixture, Raoult’s law is often written p_i = x_ip_i^*, where x_i is the liquid-phase mole fraction and p_i^* is the pure component’s vapor pressure at that temperature. Real mixtures may require activity coefficients or other non-ideal models. Do not substitute a liquid-phase mole fraction for a gas-phase mole fraction in Dalton’s law.

At sufficiently high pressures or for strongly interacting gases, real-gas effects can make partial pressure an imperfect representation of a component’s thermodynamic contribution. Fugacity is then used in equilibrium calculations; it is an adjusted, effective pressure rather than simply yP. Also, if the gas is collected over a liquid, the measured total pressure can include the liquid’s vapor. In that situation, subtract the vapor contribution when the relevant calculation requires the dry gas pressure.

This calculator is therefore useful when total pressure and gas-phase composition are known and ideal-mixture behavior is a reasonable approximation. It is not a chemical-equilibrium solver, a vapor-pressure calculator, or a substitute for an appropriate real-gas model.

Frequently Asked Questions

What is the equation for equilibrium partial pressure?
For an ideal gas mixture, p_i = y_iP: multiply the component’s gas-phase mole fraction by the total pressure.

How do I calculate partial pressure from percentage?
Divide the percentage by 100 to obtain the mole fraction, then multiply by total pressure. For example, 10% at 100 kPa gives 0.10 × 100 = 10 kPa.

Is partial pressure the same as vapor pressure?
No. Partial pressure is one gas component’s share of a mixture’s pressure. Vapor pressure is the pressure of a vapor in equilibrium with its condensed phase at a specified temperature; it may equal that component’s partial pressure under the stated equilibrium conditions.

Do partial pressures add up to total pressure?
Yes, for an ideal gas mixture, the sum of the components’ partial pressures equals the total pressure.

Can I use gauge pressure in this equation?
Not directly. Convert gauge pressure to absolute pressure by adding atmospheric pressure, then use that absolute pressure with the gas mole fraction.

Related

• Ideal Gas Equation Volume Calculator and Formula
• Partial Pressure Chemistry: Calculate Gas Mixture Pressures
• Molar Gas Volume at RTP: Equation and Calculator

in y | Gas mole fraction | - | 0.25 | 0 | 1
in pt | Total pressure | kPa | 101.325 | 0
out pp | Equilibrium partial pressure | kPa | y * pt | 3
out ycheck | Gas mole fraction | - | pp / pt | 3