Partial Pressure Equation and How to Use It

Use Dalton’s law to find a gas’s partial pressure: P_i = x_iP_total, where x_i is the gas’s mole fraction and P_total is the total pressure. Enter the amount of the gas, the total amount of gas, and the total pressure to calculate its partial pressure in the same pressure unit.

Formula

For a component of an ideal gas mixture, Dalton’s law is P_i = x_iP_total = (n_i/n_total)P_total. Here, P_i is the component’s partial pressure in kPa, x_i is its mole fraction (a dimensionless ratio), n_i is the amount of that component in mol, n_total is the total amount of gas in the mixture in mol, and P_total is the mixture’s total pressure in kPa. The mole fraction is the component’s moles divided by the sum of moles of every gas component.

Because mole fraction is dimensionless, the partial pressure has the same unit as total pressure. You can use Pa, kPa, bar, or atm, for example, as long as the total pressure is supplied in that unit. This calculator uses kPa. To convert the result, 1 atm = 101.325 kPa exactly, so divide a pressure in kPa by 101.325 to express it in atm.

Worked Example

With the calculator’s default values, the gas of interest has n_i = 1 mol, the mixture has n_total = 4 mol, and P_total = 101.325 kPa.

1. Find the mole fraction: x_i = n_i/n_total = 1 mol/4 mol = 0.25.
2. Multiply by the total pressure: P_i = x_iP_total = 0.25 × 101.325 kPa = 25.33125 kPa.
3. Rounded to the calculator’s three decimal places, the partial pressure is 25.331 kPa. The mole fraction output is 0.2500.

Assumptions

• The gas mixture behaves ideally, so Dalton’s law applies to the mixture.
• The gas amounts describe all components in the mixture, and the total amount is their sum. The component amount cannot exceed the total amount.
• The supplied pressure is the total pressure of the gas mixture, not the pressure of one component.

How Partial Pressure Works

In an ideal gas mixture, each gas component contributes to the pressure as if it alone occupied the mixture’s volume at the same temperature. The partial pressure is that component’s contribution; the pressures of all components add to the total:

P_total = P₁ + P₂ + P₃ + …

This relationship links pressure to composition. If a component makes up 20% of the gas particles by amount, its mole fraction is 0.20 and its partial pressure is 20% of the total pressure under the ideal-mixture model. The composition percentage must refer to the gas mixture, not to the pressure unit or to a liquid volume.

For a specified mixture composition and total pressure, the partial pressure does not require the container volume or temperature as separate inputs. Those conditions matter when finding the total pressure from other information, or when real-gas behavior is significant.

Using Other Information to Find It

You may not always know the mole amounts directly. Several equivalent approaches can supply the needed mole fraction or partial pressure:

• Gas composition: If composition is given as a fraction of total moles, use that fraction as x_i. For example, a 0.30 mole fraction at 200 kPa gives P_i = 0.30 × 200 kPa = 60 kPa.
• Ideal gas law: For one component, P_iV = n_iRT, so P_i = n_iRT/V. Use absolute temperature in kelvin and units consistent with the gas constant R. This form is useful when that component’s amount, mixture volume, and temperature are known.
• Pressure difference: If the total pressure and all other component partial pressures are known, subtract their sum: P_i = P_total − ΣP_other. A negative result signals inconsistent measurements or inputs, since a partial pressure cannot be negative in an ordinary gas mixture.

These methods describe the same ideal-gas relationship when the measurements refer to the same mixture, temperature, and volume. The calculator uses the mole-fraction form because it directly shows how composition divides total pressure.

Common Mistakes and Limits

• Using the wrong total: The denominator must include all gas components, including gases that are easy to overlook. A mole fraction calculated from only some components will be too large.
• Mixing units: Keep pressure units consistent when adding component pressures or applying Dalton’s law. The calculator returns kPa because its pressure input is in kPa.
• Confusing percent and fraction: Convert a percentage to a decimal before multiplying. For example, 25% means 0.25, not 25.
• Using wet and dry gas values interchangeably: Gas collected over liquid may include vapor from that liquid. The measured total pressure then includes the vapor’s partial pressure; subtract it when the required value is the dry-gas pressure.
• Rounding too early: Carry extra digits through the mole-fraction calculation and round only the final answer. Otherwise small errors can accumulate, especially in mixtures with several components.

Dalton’s law is an ideal-gas approximation. At high pressure or near conditions where a gas condenses, intermolecular interactions can make real gases depart from the simple sum of ideal partial pressures. In those cases, a more detailed thermodynamic treatment may be required. Also, partial pressure is not the same as a gas’s volume fraction in every situation; the direct equivalence follows for ideal gas mixtures at the same temperature and pressure.

Frequently Asked Questions

What is the equation for partial pressure?
For a gas in a mixture, P_i = x_iP_total. If amounts are known, use P_i = (n_i/n_total)P_total.

How do I calculate partial pressure from mole fraction?
Multiply the mole fraction by the mixture’s total pressure. A mole fraction of 0.40 in a mixture at 150 kPa gives a partial pressure of 60 kPa.

How do I find partial pressure without mole fraction?
If you know the component’s moles, total moles, and total pressure, calculate x_i = n_i/n_total first. Alternatively, use P_i = n_iRT/V when the amount, volume, and temperature are known and units match R.

Do partial pressures add up to total pressure?
Yes, for an ideal gas mixture, the partial pressures of all components sum to the total pressure. Real gases can depart from this idealized relationship, especially at high pressure.

Does temperature affect partial pressure?
At fixed mole fraction and fixed total pressure, Dalton’s law gives the same partial pressure regardless of temperature. If volume and amount are fixed instead, changing temperature changes pressure according to the ideal gas law.

What is the partial pressure of water vapor in a gas collected over water?
The measured total pressure includes water vapor. If the vapor pressure of water at the measurement temperature is known, subtract it from the total pressure to find the dry-gas pressure. The vapor pressure depends on temperature.

Related

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

in ni | Moles of gas i | mol | 1 | 0
in nt | Total moles of gas | mol | 4 | 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 | mol/mol | ni / nt | 4