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"
