The partial pressure depends on the number of moles, so our first task is to convert the mass percentages to moles.

Assume that you have 100 g of the gas.

Then you have 0.04 g of #"CO"_2#, 22.83 g of #"O"_2#, 75.33 g of #"N"_2#, and 1.8 g of #"H"_2"O"#.

#"Moles of CO"_2 = 0.04 color(red)(cancel(color(black)("g CO"_2))) × ("1 mol CO"_2)/(44.01 color(red)(cancel(color(black)("g CO"_2)))) = "0.000 91 mol CO"_2#

#"Moles of O"_2 = 22.83 color(red)(cancel(color(black)("g O"_2))) × ("1 mol O"_2)/(32.00 color(red)(cancel(color(black)("g O"_2)))) = "0.7134 mol O"_2#

#"Moles of N"_2 = 75.33 color(red)(cancel(color(black)("g N"_2))) × ("1 mol N"_2)/(28.01 color(red)(cancel(color(black)("g N"_2)))) = "2.689 mol N"_2#

#"Moles of H"_2"O" = 1.8 color(red)(cancel(color(black)("g H"_2"O"))) × ("1 mol H"_2"O")/(18.02 color(red)(cancel(color(black)("g H"_2"O")))) = "0.0999 mol H"_2"O"#

#"Total moles" = ("0.000 91 + 0.7134 + 2.689 + 0.0999) mol" = "3.503 mol"#

According to **Dalton's Law of Partial Pressures**,

#P_"CO₂" + P_"O₂" + P_"N₂" +P_"H₂O" = P_"Total" = "760 mmHg"#

Dalton's Law can also be expressed as

#color(blue)(bar(ul(|color(white)(a/a) P_i = chi_iP_"Total"color(white)(a/a)|)))" "#

where #i# represents a particular component and #chi_i# is its **mole fraction**.

For oxygen,

#chi_"O₂" = n_"O₂"/n_"Total"= (0.7134 color(red)(cancel(color(black)("mol"))))/(3.503 color(red)(cancel(color(black)("mol")))) = 0.2037#

#P_"O₂" = "0.2037 × 760 mmHg" = "155 mmHg"#