A benzene-toluene solution with xbenz =0.300 has a normal...

A benzene-toluene solution with $x_{\text {benz }}=0.300$ has a normal boiling point of $98.6^{\circ} \mathrm{C} .$ The vapor pressure of pure toluene at $98.6^{\circ} \mathrm{C}$ is $533 \mathrm{mm} \mathrm{Hg}$. What must be the vapor pressure of pure benzene at $98.6^{\circ} \mathrm{C} ?$ (Assume ideal solution behavior.)

Key Concepts

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the ratio of moles of that component to the total moles of all components. It is a fundamental concept in solution thermodynamics and is used directly in applying Raoult's Law.

Normal Boiling Point

The normal boiling point is the temperature at which the vapor pressure of the liquid equals the external atmospheric pressure (typically 1 atm or 760 mm Hg). It is used as a reference temperature to analyze the thermodynamic behavior of pure substances and solutions.

Raoult's Law

Raoult's Law states that the partial vapor pressure of a component in an ideal solution is equal to the product of its mole fraction in the liquid phase and its pure component vapor pressure. This concept is essential in relating the composition of a solution to the overall vapor pressure at a given temperature.

Ideal Solution Behavior

In an ideal solution, the interactions between unlike molecules are similar to the interactions between like molecules, allowing the use of simple mixing laws such as Raoult's Law to predict thermodynamic properties, including vapor pressures.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. It is a measure of the tendency of a substance to vaporize and is a key parameter when determining boiling points and phase equilibria.

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