What is the osmotic pressure of #"2 mols"# of sucrose dissolved in #"1 kg"# of water at #25^@ "C"#? At this concentration, the density of the solution is about #"1.4 kg/L soln"#.

I got #"67.50 atm"# using a #"1.971 molal"# solution, which is quite large. If I use #"2 molal"# I get #"68.50 atm"#.

Well, with the density of the solution, you can then go from molality to molarity. This assumes, however, that the solution is sufficiently dilute that the density of the solution is approximately the density of the solvent.

But since we would have #"1 kg"# of water, or over #"55 mols"# of water, #"2 mols"# of sucrose is probably nothing in comparison.

The osmotic pressure #Pi# is given in a form reminiscent of the ideal gas law:

#Pi = icRT#

where #i# is the van't Hoff factor, #c# is the molar concentration, and #R# and #T# are from the ideal gas law. For sucrose, a nonelectrolyte, #i = 1#.

As a result, once we find the molar concentration, we are done. However, the maximum solubility of sucrose in water at #25^@ "C"# is around #"1.971 mol/kg"# (#67.47% "w/w"#), so I'm using that instead.

#"1.971 mol solute"/cancel"kg solvent" xx (cancel"1.4 kg")/"L solution" ~~ "2.760 mol solute"/"L solution"#

Thus,

#color(blue)(Pi) = 1 cdot 2.760 cancel"mol"//cancel"L" xx 0.082057cancel"L"cdot"atm/"cancel"mol"cdotcancel"K" cdot 298.15 cancel"K"#

#=# #color(blue)("68 atm")# to two sig figs (but you only get one!)

of osmotic pressure is needed to prevent solvent flow across a semi-permeable membrane towards the side of a U-tube with more solute.