$$\pi = MRT$$
where:
- \(\pi\) is the osmotic pressure in atmospheres (atm)
- M is the molarity of the solution in moles per litre (mol/L)
- R is the ideal gas constant (0.08206 L atm/mol K)
- T is the absolute temperature in Kelvin (K)
We can use this equation to calculate the molarity of the sucrose solution required to achieve an osmotic pressure of 8.95 atm at 300 K.
$$M = \frac{\pi}{RT} = \frac{8.95 atm}{(0.08206 L atm/mol K)(300 K)}$$
$$M = 0.375 mol/L$$
We then need to calculate the mass of sucrose required to make 472 mL of a 0.375 mol/L solution.
$$mass = moles \times molar mass$$
The molar mass of sucrose is 342.3 g/mol.
$$mass = 0.375 mol/L \times 472 mL \times \frac{1 L}{1000 mL} \times 342.3 g/mol$$
$$mass = 59.8 g$$
Therefore, 59.8 g of sucrose should be combined with 472 mL of water to make a solution with an osmotic pressure of 8.95 atm at 300 K.
