#"Molality"# #=# #"Moles of solute"/"Kilograms of solvent"#
And here, #"molality"# #=# #((0.385*g)/(386.67*g*mol^-1))/(0.040*kg)=0.0249*mol*kg^-1#.
On the other hand, the mole fraction, #chi#, is dimensionless, and this is defined by the quotient.........
#chi_"solute"="Moles of solute"/"Total number of moles in solution"#
So here.........
#chi_"cholesterol"=("Moles of cholesterol")/("Moles of cholesterol+moles of chloroform")#
#=((0.385*g)/(386.67*g*mol^-1))/((0.385*g)/(386.67*g*mol^-1)+(40*g)/(119.38))=2.96xx10^-3#
And #"NECESSARILY"# #chi_"chloroform"=1-chi_"cholesterol"=0.997#
Why #"necessarily?"#