In a gas, the molecules are so far apart that they do not react with each other. The pressure of a gas is due to the different molecules colliding with other objects typically the walls of the container. When we have a mixture of gases, the pressure exerted by the molecules of an individual gas is known as partial pressure.
Dalton’s law states that “In a mixture of non-reacting gases the total pressure exerted by the mixture is equal to the sum total of the partial pressures exerted by the individual gases in the mixture’. It is also referred to as the Dalton’s law of partial pressure.
Dalton's law | Image source: image.slidesharecdn.com
Mathematically, the law can be represented as
Ptotal = P1 + P2 + P3 . . .
Where P1, P2, P3 are the partial pressures of the individual gases in the mixture and Ptotal is the total pressure exerted by the mixture.
Each gas is considered an ideal gas.
An ideal gas is the one that interacts with other gases without being attracted to their molecules. An ideal gas can be characterized by three state variables namely:
Absolute pressure (P),
Volume (V), and
Absolute temperature (T).
According to kinetic theory the relation can be written as
PV = nRT = NkT
Where n = number of moles
R = universal gas constant
N = number of molecules
k = Boltzmann constant
k = R/NA
NA = Avogadro's number
A mole of a pure substance is a mass of the material (in grams) that is numerically equal to the molecular mass of the substance in atomic mass units. A mole is also referred to as mol. Atomic mass unit is often abbreviated as amu.
The value of the universal gas constant R is 8.3145 J/mol K. The value of Boltzmann constant k is equal to 1.38066 x 10-23 J/K. k can be derived from the universal gas constant and Avogadro's number. This number has the value of 6.0221 x 1023 /mol.
Did you know: A mole of any material will contain Avogadro's number of molecules.
One mole of an ideal gas will occupy a total volume of 22.4 liters at Standard Temperature and Pressure. Standard temperature is considered to be 0°C and Standard pressure is considered to be one atmosphere pressure.
What is the partial pressures of hydrogen gas and oxygen gas in a mixture that contains 6.7 mol of hydrogen gas and 3.3 mol of oxygen gas? The mixture is kept in a 300 L container at 273 K. The total pressure of the gas mixture is 0.75 atm.
The pressure exerted by hydrogen gas is given by the formula
PHV = nRT
PH = nRT / V
= 6.7 * 08206 * 273 / 300
= 0.5 atm
P0 = PTotal - PH
= 0.75 - 0.5
= 0.25 atm
It must be noted that non ideal gases will deviate from this law due to non ideal conditions. The partial pressure of a gas is a measure of thermodynamic activity of the molecules in the gas.
Gases diffuse and react depending on their partial pressure. Henry’s Law states that gases will dissolve in liquids depending upon the equilibrium between the undissolved gas and the gas that has dissolved in the liquid.
There are many applications of the laws of gases such as in breathing and diving equipment.
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