Question

What mass of sucrose (C12H22O11) should be combined with 461g of water to make a solution with an osmotic pressure of 8.20atm at 305K ? (Assume the density of the solution to be equal to the density of the solvent.)

Answer 1

What mass of sucrose (C12H22O11) should be combined with 461g of water to make a solution with an osmotic pressure of 8.20atm at 305K ? (Assume the density of the solution to be equal to the density of the solvent.)

Given:

Mass of water = 461 g

Osmotic pressure = 8.20 atm

T = 305 K

Solution:

Osmotic pressure( ? )= MRT

Here M is molar concentration, R is gas constant = 0.08206 L atm/ mol K

T = temperature in K

Lets plug all the value in above equation to get Concentration of sucrose.

M = ? / RT

= 8.20 atm /(( 0.08206 L atm per K per mol ) *305 K)

= 0.3276 mol/L

From the concentration of sucrose we find its moles.

We calculate volume of solution by using density of water.

         ( density of water = density of solution assumed in the problem )

Density of water = 1.00 g/mL

Density = mass / volume

Volume = Mass / density

So the volume of water = volume of solution = 461 g water/ 1.00 g per mL

= 461 mL =0.461 L

We know Moarity = #moles / Volume in L

# moles = Molarity * volume in L

We know molarity and volume in L

Lets plug these in above equation to get # moles of sucrose

= (0.3276 mol / L )* 0.461 L

= 0.151 mol sucrose

Mass in g of sucrose = # moles * molar mass of sucrose

Molar mass of sucrose = 342.29 g/mol

Mass of sucrose in g = 0.151 mol * 342.29 g/mol

= 51.7 g sucrose

So we have to combine 51.7 g of sucrose with 461 g of water.