A gaseous mixture contains 440.0 Torr of H2(g), 365.7 Torr of N2(g), and 88.7 Torr of Ar(g). Calculate the mole fraction, X, of each of these gases?

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Answer 1 · 2016-11-17T22:03:31

#chi_"H₂" = 0.4919; chi_"N₂" = 0.4089; chi_"Ar" = 0.0992#

We can express the mole fraction #chi_i# of an individual gas #i# in a mixture in terms of the component's partial pressure #P_i#:

#chi_i = P_i/P_"total"#

Then

#P_i = chi_iP_"total"#

#P_"H₂" = "440.0 Torr"#
#P_"N₂" = "365.7 Torr"#
#P_"Ar" = "88.7 Torr"#

#P_"total" = "(440.0 + 365.7 + 88.7) Torr" = "894.4 Torr"#

#chi_"H₂" = (440.0 color(red)(cancel(color(black)("Torr"))))/(894.4 color(red)(cancel(color(black)("Torr")))) = 0.4919#

#chi_"N₂" = (365.7 color(red)(cancel(color(black)("Torr"))))/(894.4 color(red)(cancel(color(black)("Torr")))) = 0.4089#

#chi_"Ar" = (88.7 color(red)(cancel(color(black)("Torr"))))/(894.4 color(red)(cancel(color(black)("Torr")))) = 0.0992#