Partial pressure Formula

Definition: The partial pressures is a way to calculate the pressure of each gas that is present in a mixture of gases. The total pressure of the system is defined by the sum of all these partial pressures. It is related to the Ideal Gas Equation and was discovered by John Dalton, this it is also known as Dalton's law of partial pressures.

General formula: The formula for defining the partial pressure comes from the gas ideal gas equation:

P V = nRT

In a system or mixture of gases, the pressure total is equal to the sum of all the individual pressure as:

P_t = P1 + P2 + . . .+ Pn

Then, P_Total = n₁(RT/V) + n₂(RT/V) + . . . + n_n(RT/V)

where, V, R, T are constants and the same for all the component, thus P is proportional to the mole of each gas. P_Total = (n₁ + n₂ + . . . + n_n ) RT/V or P_Total = (P ₁ + P₂ + . . . + P_n) (RT/V)

Use: It is used for a first approximation to the value of the individual pressures of the gases that are present in a mixture of gases; particularly, for pipes, equipments and in industry that uses gases for working.

Example: Having a cylinder that contains 7.12 g of Ne and 2.34 g of He, calculate the gas pressure of each gas and the total pressure on the cylinder, if the cylinder has a volume of 10.0 L and the temperature at the room is 25 ºC.

The first step for solving this problem is to calculate the mole of each gas:

mole Ne = 7.12 g (1 mol / 20.18 g) = 0.352 mol

mole He = 2.34 g (1 mol / 4.00 g) = 0.585 mol

P_Ne = 0.352 mol (8.314 J /mol K) (298 K) / 10.0 L = 87.21 atm

P_He = 0.585 mol (8.314 J /mol K) (298 K) / 10.0 L = 144.94 atm

P_Total = 87.21 atm + 144.94 atm = 232.15 atm

Considerations: The partial pressure formula always assumes that the gases have an ideal behaviors, it means that attractive or repulsive forces are not considered in the formula. In order to correct it and get a real behavior should be assumed some factors corrections as the van der Waals factor.