Which of the following solutions will give rise to a greater...

Which of the following solutions will give rise to a greater osmotic pressure at equilibrium: $5.00 \mathrm{~g}$ of $\mathrm{NaCl}$ in $350.0 \mathrm{~mL}$ water or $35.0 \mathrm{~g}$ of glucose in $400.0 \mathrm{~mL}$ water? For $\mathrm{NaCl}$, molecular mass $=58.5$ amu; for glucose, molecular mass $=180$ amu.

Key Concepts

Osmotic Pressure

Osmotic pressure is a colligative property that depends on the number of solute particles in a solution. It reflects the tendency of a solvent to move across a semipermeable membrane from a region of lower solute concentration to one of higher concentration. The quantitative relationship is given by ? = iMRT, where ? is the osmotic pressure, i is the van't Hoff factor, M is the molarity, R is the gas constant, and T is the absolute temperature.

Colligative Properties

Colligative properties are physical properties of solutions that depend primarily on the number of solute particles present and not on their specific identities. Examples include osmotic pressure, boiling point elevation, freezing point depression, and vapor pressure lowering. They allow comparison of solutions based on the effective particle concentration regardless of the chemical nature of the solute.

Solute Concentration and Molarity

Solute concentration, often expressed as molarity, is crucial in determining the magnitude of colligative properties. It is defined as the number of moles of solute per liter of solution. Higher molarity indicates more solute particles in a given volume, thereby potentially increasing the osmotic pressure.

van't Hoff Factor

The van't Hoff factor (i) measures the number of particles into which a solute dissociates in solution. For ionic compounds, this factor is greater than one due to ionization, while for non-electrolytes like most organic compounds, it is typically equal to one. This concept is key in understanding differences in osmotic pressure for different types of solutes even at identical molar concentrations.

Molar Mass and Moles Conversion

Understanding the conversion from mass to moles using molar mass is fundamental in calculating the concentration of a solution. The number of moles is obtained by dividing the mass of the solute by its molar mass, enabling the determination of molarity when combined with the volume of the solution. This step is essential in comparing the osmotic pressure of different solutions.

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