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# How is the partial pressure of a gas in a mixture calculated?

Last updated date: 17th Jun 2024
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Hint: To solve this question Dalton’s law of partial pressure is the key term. The law states that the total partial pressure of the mixture is the sum of the individual partial pressure exerted by the gases present in the mixture.

The pressure exerted by the individual gas present in the mixture of gases is termed as partial pressure.
The total pressure exerted by the mixture of the gases is determined with the help of Dalton’s law of partial pressure.
The Dalton’s Law of partial pressure states the total pressure exerted by the mixture of gases is the sum of the partial pressure of the individual gas present in the mixture.
The total partial pressure of the gas is represented as shown below.
${P_{total}} = {P_1} + {P_2} + {P_3}.......$
The partial pressure of the individual gas can also be determined by using the Dalton’s Law of partial pressure and mole fraction.
The formula is shown below.
${P_i} = {x_i} \times {P_{total}}$
Where,
${P_i}$ is the partial pressure of the individual gas
${x_i}$ fraction of the individual gas
${P_{total}}$is the total partial pressure exerted by the mixture.
Here, the mole fraction is calculated by dividing the number of moles of gas by the total moles of the gases present in the mixture.
The formula is shown below.
${X_i} = \dfrac{{{n_i}}}{{{n_{total}}}}$
Where,
${X_i}$ is the mole fraction of individual gas
${n_i}$ is the number of moles of individual gas
${n_{total}}$ is the total moles

Note: When ideal gas is present, the partial pressure can also be calculated by using the ideal gas equation.
The ideal gas equation is given as shown below.
$pV = nRT$
Where,
p is the pressure of the ideal gas
V is the volume
n is the number of moles
R is the rate constant
T is the temperature.