The formula for mole fraction χ of a component in a mixture is
color(blue)(bar(ul(|color(white)(a/a)χ = "moles of component"/"total moles"color(white)(a/a)|)))" "
"Moles of Ne" = 11.94 color(red)(cancel(color(black)("g Ne"))) × "1 mol Ne"/(20.18 color(red)(cancel(color(black)("g Ne")))) = "0.591 67 mol Ne"
"Moles of Ar" = 9.56 color(red)(cancel(color(black)("g Ar"))) × "1 mol Ne"/(39.95 color(red)(cancel(color(black)("g Ar")))) = "0.2393 mol Ar"
"Total moles" = "(0.591 67 + 0.2393) mol" = "0.830 97 mol"
χ_text(Ar) = (0.2393 color(red)(cancel(color(black)("mol"))))/("0.830 97" color(red)(cancel(color(black)("mol")))) = 0.288
