Let #x = "mass of NaCl"#
Then #(10.2 - x) = "mass of sucrose"#.
The formula for osmotic pressure #Pi# is
#color(blue)(bar(ul(|color(white)(a/a)Pi = icRTcolor(white)(a/a)|)))" "#
where
#i =# the van't Hoff #i# factor
#c =# the molar concentration of a component
#R =# the universal gas constant
#T =# the kelvin temperature
We have two solutes, #"NaCl"# and sucrose.
For #"NaCl"#:
#i = 2#
#"Moles of NaCl" = x/58.44color(white)(l) "mol" = "0.017 11"x color(white)(l)"mol"#
#c = ("0.017 11"color(white)(l) "mol")/"0.250 L" = "0.068 45"x color(white)(l)"mol/L"#
#T = "(23 + 273.15) K = 296.15 K"#
#Pi_text(NaCl) = 2 × "0.068 45"x color(red)(cancel(color(black)("mol·L"^"-1"))) × "0.082 06" color(red)(cancel(color(black)("L")))·"atm"·color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 296.15 color(red)(cancel(color(black)("K"))) = 3.327xcolor(white)(l) "atm"#
For sucrose:
#i = 1#
#"Moles of sucrose" = (10.2-x)/342.30 "mol" = ("0.029 80 - 0.002 921"x) color(white)(l)"mol"#
#c = (("0.029 80 - 0.002 921"x) color(white)(l)"mol")/"0.250 L" = ("0.1192 - 0.011 69"x) color(white)(l)"mol/L"#
#Pi_text(sucrose) = 1 × ("0.1192 - 0.011 69"x) color(red)(cancel(color(black)("mol·L"^"-1"))) × "0.082 06" color(red)(cancel(color(black)("L")))·"atm"·color(red)(cancel(color(black)("K"^"-1""mol"^"-1"))) × 296.15 color(red)(cancel(color(black)("K"))) = 24.30("0.1192 - 0.011 69"x) color(white)(l)"atm" = (2.897 - 0.2841x) color(white)(l)"atm"#
#Pi_text(NaCl) + Pi_text(sucrose) = Pi_text(total)#
#3.327x color(red)(cancel(color(black)("atm"))) + (2.897 - 0.2841x) color(red)(cancel(color(black)("atm"))) = 6.55 color(red)(cancel(color(black)("atm")))#
#3.327x + 2.897 - 0.2841x = 6.55#
#3.043x = 3.653#
#x = 3.653/3.043 = 1.20#
Mass of #"NaCl"# = 1.20 g.
#"Mass % NaCl" = (1.20 color(red)(cancel(color(black)("g"))))/(10.2 color(red)(cancel(color(black)("g")))) × 100 % = 11.8 %#
