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# Partial Pressure Formula

Dalton's law states that each gas in a mixture of gases exerts its own pressure, behaving as if it is the only gas present. The pressure exerted by the gas is known as partial pressure.

The partial pressure of a gas is a measure of its concentration and is expressed in kilo pascals (kPa). The Partial Pressure Formula of a gas in a mixture of gases is given by

Where PA is the partial pressure of gas A, nA is the number of moles of gas A, n is the total number of moles of gas in the mixture. fA is the mole fraction and PB is the barometric or total pressure of the mixture of gases.

The partial pressure of a gas is an idea (rather than something we can measure).  We think of the total pressure of a mixture as being composed of the pressure of each gas in the mixture. The diagram below illustrates this with three different gases (show as gases A, B, and C). When by itself in a container, each gas has a specific pressure. Those are at the top and labeled as such. Then those same amounts are all three pushed into the same container again, so now the total number of moles has increased and therefore the total pressure.

The pressure of the individual gases in the mixture is the partial pressure of that gas. The sum of the partial pressures is the total pressure.
Dalton's law of Partial Pressure Formula is mathematically expressed as

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## Partial Pressure Problems

Solved problems based on partial pressure are given below.

### Solved Examples

Question 1: To a tank containing N2 at 2.0atm and O2 at 1.0atm, we add an unknown quantity of CO2 until the total pressure within the tank is 4.6atm. What is the partial pressure of the CO2?
Solution:

Dalton's law tells us that the addition of CO2 does not affect the partial pressures of the N2 and O2 already present in the tank. The partial pressure of N2 and O2 remain at 2.0atm, respectively and their sum is 3.0atm. If the new pressure is 4.6atm, the partial pressure of the added CO2 must be 1.6atm. Thus when the final pressure is 4.6atm, the partial pressures are

4.6atm = 2.0atm + 1.0atm + 1.6atm

Question 2: A vessel under 2.015atm pressure contains nitrogen N2 and water vapor H2O. The partial pressure of N2 is 1.908atm. What is the partial pressure of the water vapor?
Solution:

Given
Total pressure = 2.015atm
Partial pressure of N2 = 1.908atm
Partial pressure of water vapor = ?

Now we use the equation

Ptotal = PN2 + Pwater vapor
2.015 = 1.908 + Pwater vapor
Pwater vapor = 0.107

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