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#