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Partial Pressure

The molecules of air constantly collide with the walls of the container. These collisions apply a force on the walls of the container which is nothing but called as pressure.

Pressure is force per unit area applied by the gas. However as we know, air is not a single compound but mixture of gases like nitrogen, oxygen etc.

"Partial pressure of a particular component of a gaseous mixture is equal to the mole fraction of that component times the total pressure."

The pressure contribution of each gas is called its partial pressure. Partial pressure can thus be defined as pressure exerted if that gas alone had occupied the volume. Thus the total pressure of air would be sum of partial pressures of nitrogen, oxygen etc.

The total pressure is thus sum of partial pressures of the ideal gases. This is defined by Dalton's law of partial pressures.

P Air = P N2 + PO2 + P misc.

where P Air is total pressure of air, P N2, P O2 are partial pressures of nitrogen, oxygen etc.

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Henry's Law

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It states that in a gas-gas solution, the concentration of the solute gas is directly variable to the partial pressure of the solute gas.

Partial pressures have been very useful in diving profession to measure breathing gases. Even when the diver comes out after diving, he is not immediately exposed to normal air pressure but is progressively put through different pressure chambers.

Partial pressure = total absolute pressure x volume fraction of gas component

The equilibrium constant can also be expressed as ratio of partial pressures of products to partial pressures of reactants.

Partial Pressure Equation

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Ideal gas equation of the gas relates the pressure, volume, number of moles and temperature.

PV = nRT
Where
  • P is the pressure of the gas in atm
  • V is the volume of the gas in Liter
  • n is the number of moles
  • R is the universal gas constant and
  • T is the temperature of the gas in Kelvin.
  • n in the equation may also represent the total number of moles when mixture of gas is present at a particular temperature. For example consider a mixture containing hydrogen and helium.
  • Let na be the moles of the hydrogen and Pa is the partial pressure of the hydrogen.
  • Let nb be the moles of the Helium gas and Pb is pressure of the Helium.
The total number of the moles is represented by n. n is given by

n = na + nb

The ideal gas equation for the mixture of gases can be written as

PV = (na + nb)RT

We can also represent the ideal gas equation for the individual gases in the mixture as

Pa V = naRT

Pb V = nbRT

Here the volume of the gases would be same. For both Hydrogen and Helium there would be equal space for the gases to occupy. As per the kinetic theory of gases, the volume occupied by the molecule of the gas is negligible compared to the volume of the container. Hence both hydrogen and Helium can occupy the entire volume.

So volume of the container is V for both Hydrogen and Helium. Temperature is also kept constant on the whole vessel and hence T is also same for both the gases.
Pa and Pb represent the partial pressure of Hydrogen and Helium.

P = $\frac{{[na + nb]}RT}{V}$

P = $\frac{na RT}{V}$ + P = $\frac{nbRT}{V}$

Pa = $\frac{naRT}{V}$

and

Pb = $\frac{nbRT}{V}$

Therefore,

P = Pa + Pb

Mole Fraction and Partial Pressures

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Ideal gas equation of the gas relates the pressure, volume, number of moles and temperature. The ideal gas equation is combination of Boyle’s Law, Charles Law, Guy Lusaac law and Avogadro’s Law.

Ideal as equation is given by the formula


PV = nRT
Where

P is the pressure of the gas in atm
V is the volume of the gas in Liter
n is the number of moles
R is the universal gas constant and
T is the temperature of the gas in Kelvin.
n in the equation may also represent the total number of moles when mixture of gas is present at a particular temperature.

For example consider a mixture containing hydrogen and helium.
Let na be the moles of the hydrogen and Pa is the partial pressure of the hydrogen. Let nb be the moles of the Helium gas and Pb is pressure of the Helium.
The total number of the moles is represented by n.
n is given by n = na + nb

The ideal gas equation for the mixture of gases can be written as

PV = (na + nb)RT -------(1)

We can also represent the ideal gas equation for the individual gases in the mixture as

Pa V = naRT ------ (2)
Pb V = nbRT
------ (3)

Here the volume of the gases would be same. For both Hydrogen and Helium there would be equal space for the gases to occupy. As per the kinetic theory of gases, the volume occupied by the molecule of the gas is negligible compared to the volume of the container. Hence both hydrogen and Helium can occupy the entire volume. So volume of the container is V for both Hydrogen and Helium.

Temperature is also kept constant on the whole vessel and hence T is also same for both the gases. Pa and Pb represent the partial pressure of Hydrogen and Helium.

Equation (1) can be written as

P = $\frac{{[na + nb]}RT}{V}$ ------ (4)

Equation (4) can be split up into

P = $\frac{naRT}{V}$ + P = $\frac{nbRT}{V}$ ------(5)

Equation (2) can be written as

Pa = $\frac{naRT}{V}$

Equation (3) can be rewritten as

Pb = $\frac{nbRT}{V}$

So equation (5) becomes

P = Pa + Pb

So the total pressure of the mixture of the gas is the sum of the partial pressure of Hydrogen and Helium. Dalton’s Law of partial pressure statement Dalton Law of partial pressure can be stated as “The Total pressure of the mixture of gas is equal to the sum of the Pressure of the individual gases. The pressure of the individual gas can be taken as the pressure exerted by the gas when no other gas is present.”
Dalton’s Law of partial pressure can be expressed mathematically as

Total pressure = Pressure-A + Pressure-B + Pressure-C ………. Pressure-n

Where

Pressure-A is the pressure exerted by the gas A and
Pressure-B is the pressure exerted by the gas B and
Pressure-n is the pressure exerted by the nth gas.
The most important application of the Dalton’s Law of partial pressure is finding out the volume of the gas when it is collected over water. The molar volume at STP can be used to find the mole of the gas collected at the particular temperature. But the main problem in determining the moles of the gas is that, the water vapor would be contaminated with the gas because the gas is collected over water. So the pressure exerted in the vessel would be due to the dry gas collected over water and also the water vapor.

According to Dalton's Law ,
Total pressure = Pressure of the dry gas + pressure of the water vapor
The pressure of the water vapor at particular temperature is constant and is called as aqueous tension, so the above equation can be rewritten as

Total pressure = pressure of the dry gas + Aqueous tension
Pressure of the dry gas = Total pressure – Aqueous tension Dalton's law of partial pressure examples.

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