What is the mole fraction of each component in the liquid mixture in Problem 13.110, and what is the mole fraction of each component in the vapor at 30 °C?

Verified step by step guidance

Step 1: Identify the components of the liquid mixture from Problem 13.110. Assume the components are A and B with given mole fractions or amounts.

Step 2: Calculate the mole fraction of each component in the liquid mixture. If the moles of A and B are given, use the formula: \( \text{Mole fraction of A} = \frac{\text{moles of A}}{\text{moles of A} + \text{moles of B}} \) and similarly for B.

Step 3: Use Raoult's Law to find the partial pressures of each component in the vapor phase. Raoult's Law states: \( P_A = X_A \cdot P^\circ_A \) and \( P_B = X_B \cdot P^\circ_B \), where \( P^\circ \) is the vapor pressure of the pure component.

Step 4: Calculate the total pressure of the vapor phase by summing the partial pressures: \( P_{\text{total}} = P_A + P_B \).

Step 5: Determine the mole fraction of each component in the vapor phase using Dalton's Law: \( y_A = \frac{P_A}{P_{\text{total}}} \) and \( y_B = \frac{P_B}{P_{\text{total}}} \).

Key Concepts

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

Mole Fraction

Mole fraction is a way of expressing the concentration of a component in a mixture. It is defined as the ratio of the number of moles of a specific component to the total number of moles of all components in the mixture. This dimensionless quantity is useful in calculations involving gas laws and colligative properties, as it provides a clear representation of the relative amounts of substances present.

Raoult's Law

Raoult's Law states that the partial vapor pressure of each component in a liquid mixture is equal to the vapor pressure of the pure component multiplied by its mole fraction in the liquid phase. This law is fundamental in understanding how mixtures behave during phase changes, such as evaporation, and is essential for calculating the vapor composition from the liquid composition at a given temperature.

Vapor-Liquid Equilibrium

Vapor-liquid equilibrium (VLE) refers to the state where the rate of evaporation of a liquid equals the rate of condensation of its vapor. At this equilibrium, the composition of the vapor and liquid phases can be determined, and it is influenced by temperature and pressure. Understanding VLE is crucial for solving problems related to distillation and separation processes in chemistry.

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