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.

Key Concepts

Osmotic Pressure

Osmotic pressure is the pressure required to prevent the flow of solvent into a solution through a semipermeable membrane. It is directly proportional to the molarity of the solute and can be calculated using the formula π = iCRT, where π is the osmotic pressure, i is the van 't Hoff factor, C is the molarity, R is the ideal gas constant, and T is the temperature in Kelvin.

Molarity

Molarity is a measure of concentration defined as the number of moles of solute per liter of solution. It is crucial for calculating osmotic pressure, as the osmotic pressure is dependent on the concentration of solute particles in the solution. To find molarity, you can use the formula M = moles of solute / volume of solution in liters.

Van 't Hoff Factor

The van 't Hoff factor (i) represents the number of particles into which a solute dissociates in solution. For sucrose, which does not dissociate in solution, i equals 1. This factor is important in osmotic pressure calculations, as it affects the total number of solute particles contributing to the pressure exerted by the solution.