A solution contains naphthalene (C10H8) dissolved in hexane (C6H14) at a concentration of 12.35% naphthalene by mass. Calculate the vapor pressure of hexane above the solution at 25 °C. The vapor pressure of pure hexane at 25 °C is 151 torr.

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Determine the mass of naphthalene and hexane in the solution. Assume a total mass of 100 g for simplicity, which means 12.35 g of naphthalene and 87.65 g of hexane.

Calculate the number of moles of naphthalene (C_{10}H_{8}) using its molar mass (128.17 g/mol).

Calculate the number of moles of hexane (C_{6}H_{14}) using its molar mass (86.18 g/mol).

Find the mole fraction of hexane in the solution using the formula: \( \text{Mole fraction of hexane} = \frac{\text{moles of hexane}}{\text{moles of hexane} + \text{moles of naphthalene}} \).

Apply Raoult's Law to find the vapor pressure of hexane above the solution: \( P_{\text{solution}} = \chi_{\text{hexane}} \times P^0_{\text{hexane}} \), where \( P^0_{\text{hexane}} \) is the vapor pressure of pure hexane (151 torr).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Raoult's Law

Raoult's Law states that the vapor pressure of a solvent in a solution is directly proportional to the mole fraction of the solvent in the solution. This principle is essential for calculating the vapor pressure of hexane above the naphthalene solution, as it allows us to determine how the presence of naphthalene affects the vapor pressure of hexane.

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture, defined as the number of moles of that component divided by the total number of moles of all components in the mixture. In this case, calculating the mole fraction of hexane is crucial for applying Raoult's Law to find the vapor pressure of hexane above the solution.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid or solid phase at a given temperature. Understanding vapor pressure is vital for this problem, as it provides the baseline (pure hexane vapor pressure) needed to calculate the altered vapor pressure when naphthalene is present in the solution.

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Raoult's Law and Vapor Pressure

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