Question

What mass of sucrose (C12H22O11) should be combined with 485 g of water to make a solution with an osmotic pressure of 8.00 atm at 280 K ? (Assume the density of the solution to be equal to the density of the solvent.)

Answer 1

Osmotic pressure equation

V = nST

Where = osmotic pressure = 8atm

          V = volume of solution

         n = number of moles of solute = weight of solute / molecular weight of solute = w / 342 (M.W of sucrose)

        S = solution constant = 0.0821litre atm k^-1 mole^-1

           T = absolute temperature = 280K

n/V = /ST = 8/0.0821*280 = 0.348 moles /lit = Molarity of solution

Now relation between molarity and molality is

1/m = d/M - Molar mass of solute/1000

where m = molality,d=density of solution , M= molarity of solution

On solving m = 0.395molal

Now Molality = number moles of solute / Number kilograms of solvent

                      = (Weight of solute / Molecular weight of solute)/Number kilograms of solvent

weight of solute (sucrose) = 0.395x0.485x 342 = 65.5grams