If a mixture of gases with a total pressure of 1.0 atm contains 2 mol #He#, 4 mol #Ne#, and 2 mol #O_2#, what is the partial pressure of the #He# in the mixture?
1 Answer
Explanation:
The partial pressure of a gas that's part of a gaseous mixture will depend on two things
- the mole fraction said gas has in the mixture
- the total pressure of the mixture
As you know, Dalton's Law of Partial Pressures allows you to calculate the partial pressure of gas that's part of a gaseous mixture by using the number of moles of that gas and the total number of moles present in the mixture - this is known as the mole fraction
#color(blue)(P_i - chi_i xx P_"total")" "# , where
In your case, you know that the mixture contains
#"2 moles"# of helium#"4 moles"# of neon#"2 moles"# of oxygen gas
The *total number of moles8 present in the mixture will thus be
#n_"total" = 2 + 4 + 2 = "8 moles"#
The mole fraction of helium will be
#chi_(He) = (2 color(red)(cancel(color(black)("moles "))))/(8color(red)(cancel(color(black)("moles")))) = 1/4 = 0.25#
Therefore, the partial pressure of helium will be
#P_(He) = chi_(He) xx P_"total"#
#P_(He) = 0.25 xx "1.0 atm" = color(green)("0.25 atm")#
I'll leave the answer rounded to two sig figs.
