Question

What mass of sucrose (C12H22O11) should be combined with 458 g of water to make a solution with an osmotic pressure of 8.70 atm at 300 K? (Assume the density of the solution to be equal to the density of the solvent.)

Answer 1

Use osmotic pressure equation

Osmotic pressure = CRT

Where C=concentration in mol/L

R= Universal gas constant=0.0821 L atm k^-1 mol^-1

T = temperature

T=300 k and osmotic pressure=8.70 atm

Putting the value in equation , we get

C = 8.70atm/(0.0821 L atm k^-1mol^-1 ×300 k)= 0.3532 mol/L

Amount of water =458g (given)

According to the question the density of solution assume to be density of water which is equal to 1g/ml ( taken from literature)

Use formula , density= mass/volume

Hence volume of solution= 458 g/1 g ml^-1=458 ml

Since 1000 ml of solution = 0.3532 mol of sucrose

Therefore 1 ml of solution = 0.3532 /1000 mol of sucrose

Therefore 458 ml of solution = (0.3532/ 1000)×458=0.1618 mol of sucrose

Now molar mass of sucrose = 342.2965 g/mol

Therefore mass of 0.1618 mol of sucrose = 0.1618×342.2965 = 55.38 g

Mass of sucrose combine = 55.38 g ( answer)