# 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?

Nov 17, 2016

${\chi}_{\text{H₂" = 0.4919; chi_"N₂" = 0.4089; chi_"Ar}} = 0.0992$

#### Explanation:

We can express the mole fraction ${\chi}_{i}$ of an individual gas $i$ in a mixture in terms of the component's partial pressure ${P}_{i}$:

${\chi}_{i} = {P}_{i} / {P}_{\text{total}}$

Then

${P}_{i} = {\chi}_{i} {P}_{\text{total}}$

${P}_{\text{H₂" = "440.0 Torr}}$
${P}_{\text{N₂" = "365.7 Torr}}$
${P}_{\text{Ar" = "88.7 Torr}}$

${P}_{\text{total" = "(440.0 + 365.7 + 88.7) Torr" = "894.4 Torr}}$

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