Which of the following will have the lowest total vapor...

Which of the following will have the lowest total vapor pressure at $25^{\circ} \mathrm{C}$ ? a. pure water (vapor pressure $=23.8$ torr at $25^{\circ} \mathrm{C}$ ) b. a solution of glucose in water with $\chi_{\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}}=0.01$ c. a solution of sodium chloride in water with $\chi_{\mathrm{NaCl}}=0.01$ d. a solution of methanol in water with $\chi_{\mathrm{CH}_{3} \mathrm{OH}}=0.2$ (Consider the vapor pressure of both methanol [ 143 torr at $\left.25^{\circ} \mathrm{C}\right]$ and water. $)$

Which of the following will have the lowest total vapor pressure at $25^{\circ} \mathrm{C}$ ?
a. pure water (vapor pressure $=23.8$ torr at $25^{\circ} \mathrm{C}$ )
b. a solution of glucose in water with $\chi_{\mathrm{C}_{6} \mathrm{H}_{12} \mathrm{O}_{6}}=0.01$
c. a solution of sodium chloride in water with $\chi_{\mathrm{NaCl}}=0.01$
d. a solution of methanol in water with $\chi_{\mathrm{CH}_{3} \mathrm{OH}}=0.2$ (Consider the vapor pressure of both methanol [ 143 torr at $\left.25^{\circ} \mathrm{C}\right]$ and water. $)$

Key Concepts

Vapor Pressure in Binary Mixtures

In solutions containing two volatile components, the total vapor pressure is a combination of the partial pressures of each component, determined by both their mole fractions and pure component vapor pressures. This requires considering the contributions of each volatile component to understand the overall vapor pressure behavior, especially when one component has a significantly different vapor pressure than the other.

Electrolyte vs Non-electrolyte Behavior

The distinction between electrolytes and non-electrolytes is crucial because electrolytes dissociate into multiple ions in solution, effectively increasing the number of solute particles compared to non-electrolytes at the same molar concentration. This dissociation amplifies colligative effects such as vapor pressure lowering, making the solution's properties more sensitive to the presence of electrolytes.

Colligative Properties

Colligative properties are characteristics of solutions that depend only on the number of solute particles present rather than their identity. Vapor pressure lowering is one such property, where the addition of a nonvolatile solute decreases the mole fraction of the solvent, thereby reducing its vapor pressure according to the principle that the behavior of the solvent molecules is affected by the presence of solute particles.

Raoult's Law

Raoult's Law states that the partial vapor pressure of a component in a solution is equal to the vapor pressure of the pure component multiplied by its mole fraction in the solution. This law is fundamental in understanding how solutes alter the vapor pressure of solvents in ideal solutions, predicting linear relationships between vapor pressure lowering and solute concentration.

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