Question

A mixture of gases exists in a sealed container with the following percentages each: helium $40\% $ , neon $50\% $ and argon $10\% $ . If the total pressure of the gases is $1100torr$ , then which is the following is true about these gases?
A. The partial pressure of the argon gas is $21.56torr$ .
B. The partial pressure of the neon gas is $21.56torr$.
C. The partial pressure of the neon gas is $550torr$.
D. The partial pressure of the argon gas is $100torr$.
E. The partial pressure of the gases cannot be calculated with the given information.

Answer 1

Hint: In a mixture of gases, each constituent gas has a partial pressure which is the notional pressure of that constituent gas if it alone occupied the entire volume of the original mixture at the same temperature. The total pressure of an ideal gas mixture is the sum of the partial pressures of the gases in the mixture.

Complete step by step answer:
According to Dalton's law of partial pressure, we can state that the partial pressure of a constituent gas in a mixture of gases is equal to the product of the total pressure of the gaseous mixture and the mole fraction of that constituent in the gaseous mixture.
Let the total mass of the gaseous mixture be $100g$ .
Number of moles of $40\% He$ = $\dfrac{{\dfrac{{40}}{{100}} \times 100}}{4} = 10mol$
Number of moles of $50\% Ne$ = $\dfrac{{\dfrac{{50}}{{100}} \times 100}}{{20}} = 2.5mol$
Number of moles of $10\% Ar$ = $\dfrac{{\dfrac{{10}}{{100}} \times 100}}{{40}} = 0.25mol$
Mathematically, Dalton’s law of partial pressure can be written as:
${P_A} = {P_{total}} \times {x_A}$
Where, ${P_A} = $ partial vapor pressure of A
${P_{total}} = $ Total vapor pressure of the gaseous mixture
${x_A} = \dfrac{{n{ _A}}}{{{n_{total}}}} = $ mole fraction of A
${n_A} = $ number of moles of A
${n_{total}} = $ total number of moles
Partial pressure of A = ${P_A} = \dfrac{{{n_A}}}{{{n_{total}}}} \times {P_{total}}$
Applying the above equation for helium, neon and argon, we have:
Partial pressure of Helium = ${P_{He}} = \dfrac{{10}}{{10 + 2.5 + 0.25}} \times 1100 = 862.75torr$
Partial pressure of Neon= ${P_{Ne}} = \dfrac{{2.5}}{{10 + 2.5 + 0.25}} \times 1100 = 215.7torr$
Partial pressure of Helium = ${P_{Ar}} = \dfrac{{0.25}}{{10 + 2.5 + 0.25}} \times 1100 = 21.56torr$
Thus, the correct option is A. The partial pressure of the argon gas is $21.56torr$ .

Note:
Dalton's law is not strictly followed by real gases, with the deviation increasing with pressure. Under such conditions the volume occupied by the molecules becomes significant compared to the free space between them. In particular, the short average distances between molecules increases intermolecular forces between gas molecules enough to substantially change the pressure exerted by them, an effect not included in the ideal gas model.