#P_"CO₂" = "0.2 atm"# and #P_"N₂" = "0.3 atm"#.
The partial pressure of a gas A in a mixture is proportional to its mole fraction #chi#:
#P_"A" = chi_"A"P_"tot"#
where
#chi_"A" = n_"A"/n_"tot"#
#chi_"CO₂" = n_"CO₂"/(n_"CO₂" + n_"N₂") = "4 mol"/"4 mol + 6 mol" = (4 color(red)(cancel(color(black)("mol"))))/(10 color(red)(cancel(color(black)("mol")))) = 0.4#
#chi_"N₂" = n_"N₂"/(n_"CO₂" + n_"N₂") = (6 color(red)(cancel(color(black)("mol"))))/(10 color(red)(cancel(color(black)("mol")))) = 0.6#
#P_"tot" = 380 color(red)(cancel(color(black)("Torr"))) × "1 atm"/(760 color(red)(cancel(color(black)("Torr")))) = "0.500 atm"#
#P_"CO₂" = chi_"CO₂"P_"tot" = "0.4 × 0.500 atm" = "0.2 atm"#
#P_"N₂" = chi_"N₂"P_"tot" = "0.6 × 0.500 atm" = "0.3 atm"#
