What mass of sucrose (C12H22O11) would you combine with 5.00 * 10^2 g of water to make a solution with an osmotic pressure of 8.55 atm at 298 K? (Assume a density of 1.0 g/mL for the solution.)

Verified step by step guidance

1. Identify the formula for osmotic pressure: \( \Pi = iMRT \), where \( \Pi \) is the osmotic pressure, \( i \) is the van't Hoff factor, \( M \) is the molarity, \( R \) is the ideal gas constant, and \( T \) is the temperature in Kelvin.
2. Since sucrose is a non-electrolyte, the van't Hoff factor \( i = 1 \). Rearrange the formula to solve for molarity \( M \): \( M = \frac{\Pi}{iRT} \).
3. Substitute the given values into the rearranged formula: \( \Pi = 8.55 \text{ atm} \), \( R = 0.0821 \text{ L atm/mol K} \), and \( T = 298 \text{ K} \). Calculate \( M \).
4. Use the definition of molarity \( M = \frac{\text{moles of solute}}{\text{liters of solution}} \) to find the moles of sucrose. Assume the volume of the solution is approximately the volume of water, which is \( 500 \text{ mL} = 0.500 \text{ L} \).
5. Calculate the mass of sucrose using its molar mass \( C_{12}H_{22}O_{11} \approx 342.3 \text{ g/mol} \) and the moles of sucrose found in the previous step.