Question

How is the partial pressure of a gas in a mixture related to the total pressure of the gaseous mixture?

Answer 1

The pressure that is exerted by one of the molecules in a mixture of gasses is known as Partial pressure. It is a measure of the thermodynamic activity of the gas. The total pressure of the gas is the sum of the pressure of the individual gases. The relation between the two is given by Dalton.

Complete answer: The question above is asking the relation between the partial pressure of the gas and the total pressure of the gas. Before reaching the answer let us know what both the terms mean.
Partial pressure: suppose there is a mixture of gases. The mixture contains individual gas molecules and every molecule will be exerting certain pressure provided they all have the same volume and same temperature. so the pressure exerted by a particular gas in a mixture is known as partial pressure.
Total pressure: it is the sum of all the partial pressures of individual gases in a mixture.
Both the terms are related by the equation given by John Dalton. The equation is:
Partial pressure of the individual gas = mole fraction of that gas $\times$ total pressure of the mixture
For coming to this particular equation john Dalton gave another law known as Dalton’s law of partial pressure which states that the total pressure of a mixture of gases in a container equals to the sum of the pressures of each gas:
${P_{total}} = {P_1} + {P_2} + {P_3} + ......$ Where ${P_{total}}$ is the total pressure in a mixture and ${P_1} + {P_2} + {P_3} + ......$are the partial pressure of individual gases.
So the partial pressure of individual gas for e.g. first component ${P_1}$ is equal to mole fraction of this component multiplied by total pressure of the mixture
${P_1} = {X_1} \times {P_{total}}$
Therefore the partial pressure of the individual gas is:
${P_n} = {X_n} \times {P_{total}}$ (${P_n} =$Partial pressure of individual gas ‘n’ and ${X_n} =$mole fraction of that component)

Note:
Both the above forms of partial pressure are very important in solving the problems. If two quantities are known then the third one can be found out. Like if partial pressures are known then mole fraction can be calculated and vice-versa. The partial pressures are important in predicting the movement of individual gases.