Question

What mass of sucrose (C12H22O11) should be combined with 4.60×10² g of water to make a solution with an osmotic pressure of 9.00 bar at 310 K ? (Assume a density of 1.0 gmL−1 for the solution.?

Answer 1

The expression for osmotic pressure can be written as follows:

Π = iMRT

Where,

Π = osmotic pressure = 9.00bar = (9.00 x 0.9869) atm = 8.8821atm

i = van’t Hoff factor = 1 for sucrose

M = molar concentration (mol/L)

R = universal gas constant = 0.08206 L·atm/mol·K

T = absolute temperature = 310K

Thus, molar concentration of sucrose can be calculated as follows:

8.8821atm = 1 x M x (0.08206 L·atm/mol·K) x 310K

M = (8.8821atm) / [(0.08206 L·atm/mol·K) x 310K]

M = (8.8821atm) / [(0.08206 L·atm/mol·K) x 310K]

M = 0.3492 mol/L

Therefore, amount of sucrose required to make 0.3492 mol/L aqueous solution by using 4.60×10² g of water can be calculated as follows:

(Since, density of water is 1 g/mL, therefore, 4.60×10² g of water is equal to 4.60×10² mL)

Moles of sucrose = 0.3492 mol/L x 4.60×10² x 10^-3 L

Moles of sucrose = 0.1606 mol

Therefore, weight of 0.1606 moles of sucrose in grams can be calculated as follows:

(Molar mass of sucrose is 342g/mol)

Weight of sucrose = 0.1606 mol x 342g/mol

Weight of sucrose = 55g

Therefore, 55g of sucrose should be combined with 4.60×10² g of water to make a solution with an osmotic pressure of 9.00 bar at 310 K