Answer: The mass of sucrose required is 69.08 g
Explanation:
To calculate the concentration of solute, we use the equation for osmotic pressure, which is:
[tex]\pi=iMRT[/tex]
Or,
[tex]\pi=i\times \frac{\text{Mass of solute}\times 1000}{\text{Molar mass of solute}\times \text{Volume of solution (in mL)}}\times RT[/tex]
where,
[tex]\pi[/tex] = osmotic pressure of the solution = 8.80 atm
i = Van't hoff factor = 1 (for non-electrolytes)
Mass of solute (sucrose) = ?
Molar mass of sucrose = 342.3 g/mol
Volume of solution = 564 mL (Density of water = 1 g/mL)
R = Gas constant = [tex]0.0821\text{ L.atm }mol^{-1}K^{-1}[/tex]
T = Temperature of the solution = 290 K
Putting values in above equation, we get:
[tex]8.80atm=1\times \frac{\text{Mass of sucrose}\times 1000}{342.3\times 546}\times 0.0821\text{ L.atm }mol^{-1}K^{-1}\times 290K\\\\\text{Mass of sucrose}=\frac{8.80\times 342.3\times 546}{1\times 1000\times 0.0821\times 290}=69.08g[/tex]
Hence, the mass of sucrose required is 69.08 g
