What mass of sucrose (C12 H22 O11) would you combine with 5.00 ×10^2 g of water to make a soluti

step 1 Question 84, what mass of sucrose would you combine with 5 times 10 to 2 grams of water to make

What mass of sucrose (C12 H22 O11) would you combine with...

What mass of sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ would you combine with $5.00 \times 10^{2} \mathrm{g}$ of water to make a solution with an osmotic pres- sure of 8.55 atm at 298 $\mathrm{K}$ ? (Assume a density of 1.0 $\mathrm{g} / \mathrm{mL}$ for the solution.)

What mass of sucrose $\left(\mathrm{C}_{12} \mathrm{H}_{22} \mathrm{O}_{11}\right)$ would you combine with $5.00 \times 10^{2} \mathrm{g}$ of water to make a solution with an osmotic pres-
sure of 8.55 atm at 298 $\mathrm{K}$ ? (Assume a density of 1.0 $\mathrm{g} / \mathrm{mL}$ for the
solution.)

Key Concepts

Osmotic Pressure

Osmotic pressure is a colligative property that arises when a solvent moves across a semipermeable membrane to balance the solute concentrations on either side. It is quantitatively described by the equation ? = iMRT, where ? is the osmotic pressure, i is the van’t Hoff factor representing the number of particles into which a solute dissociates, M is the molarity of the solution, R is the gas constant, and T is the temperature in Kelvin.

Molarity

Molarity is a measure of the concentration of a solution, defined as the number of moles of solute per liter of solution. It is a fundamental concept in solution chemistry that links the amount of solute with the solvent volume, allowing for the calculation of various colligative properties, including osmotic pressure.

Colligative Properties

Colligative properties are characteristics of solutions that depend solely on the ratio of solute particles to solvent molecules, rather than the identity of the solute. These properties include osmotic pressure, boiling point elevation, freezing point depression, and vapor pressure lowering, and they are key to understanding how the addition of a solute can alter the physical properties of a solvent.

Molar Mass

Molar mass is the mass of one mole of a substance, expressed in grams per mole, and it is essential for converting between the mass of a solute and the number of moles. This conversion is crucial in preparing solutions with desired concentrations and for quantitative analyses involving colligative properties.

Van't Hoff Factor

The van’t Hoff factor is a numerical representation of the number of particles a solute produces when dissolved in a solvent. It plays an important role in colligative properties; for non-electrolytes, which do not dissociate in solution, the factor is typically 1, simplifying calculations related to osmotic pressure and other related phenomena.

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