Question #e49bd

The osmotic pressure is the pressure that needs to be applied in a U-shaped tube from the side of a semi-permeable membrane with less concentration to prevent solvent from flowing to the side with more concentration.

The osmotic pressure relation is similar to the ideal gas law:

#Pi = icdotcRT#

where:

• #Pi# is the osmotic pressure in #"atm"#.
• #i# is the van't Hoff factor, i.e. the effective number of solute particles in solution per solute particle. #i >= 1# for electrolytes, and for glucose, #i = 1#.
• #c# is the concentration in #"mol/L"# of the solution.
• #R = "0.082057 L"cdot"atm/mol"cdot"K"# is the universal gas constant.
• #T# is the temperature in #"K"#.

So, you just have to find the concentration in #"mol/L"#. A #5%# solution is presumably #5% "w/w"#, or #5%# by mass (but you should have specified that).

So in #"100.00 g solution"# you would have #"5.00 g glucose"#. You also have not specified what the solvent was, so I will assume it is water... In that case, this is dilute enough that the density is approximately that of water at #18^@ "C"#.

#rho_(H_2O) = "0.998599 g/mL"# at #18^@ "C"#

#(5.00 cancel"g glucose")/(100.0 cancel"g solution") xx (998.599 cancel"g soln")/"1 L soln" xx "1 mol glucose"/(180.1559 cancel"g glucose")#

#=# #"0.277 M glucose"#

As a result, the osmotic pressure is:

#color(blue)(Pi) = (1) cdot ("0.277 mol/L") cdot ("0.082057 L"cdot"atm/mol"cdot"K") cdot (18 + "273.15 K")#

#=# #color(blue)("6.62 atm")#