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Raoult's law plays a pivotal role in describing the vapor pressure of a solvent in a solution as a function of its concentration. It asserts that the partial vapor pressure of each component in an ideal mixture is directly proportional to its mole fraction in the solution.

For a solution with multiple components, Raoult's law can be expressed as:\( p_i = x_i \times P_i^\text{sat} \), where:\( p_i \) is the partial pressure of component \( i \) in the gas phase, \( x_i \) is the mole fraction of \( i \) in the liquid phase, and \( P_i^\text{sat} \) is the saturation pressure of component \( i \). Understanding this concept is crucial when dealing with the major component in a mixture, like water in the example provided.

To apply Raoult's law, one must determine the mole fraction of the component, which can be calculated from the mole percentage, as shown in the given exercise for water. Once known, this fraction is multiplied by the established saturation pressure of the component at a given temperature to find its partial pressure in the overall system.

On the other end of the spectrum, Henry's law explains the behavior of gases that are sparingly soluble in a liquid. The partial pressure of the gas above the solution is proportionate to the concentration of the gas dissolved in the liquid. A practical equation for Henry’s law is:\( p_i = x_i \times H_i \), where:\( p_i \) denotes the partial pressure of the gas, \( x_i \) is the mole fraction of the gas in the liquid, and \( H_i \) is Henry's law constant for the gas at a given temperature.

In the application for the less abundant component, such as nitrogen in the exercise, Henry’s law is used due to nitrogen's relatively low concentration. Its mole fraction, when multiplied by its temperature-dependent Henry’s constant, yields the partial pressure of nitrogen in the system. It's imperative to note that Henry's law constants vary with temperature and must be gathered from reliable data sources for precise calculations.

• Mole fractions are simply the ratio of the number of moles of a particular substance to the total number of moles in a mixture. They are dimensionless numbers that represent the concentration of constituents in a mixture.


• Mathematically, for a substance \( i \) in a mixture of \( n \) components, the mole fraction \( x_i \) is calculated as:\( x_i = \frac{n_i}{\text{sum of all moles in the mixture}} = \frac{n_i}{\text{sum of} \text{ } n_1 + n_2 + ... + n_n} \).


• The mole fractions must add up to 1 when combined for all the components in a mixture.


• Within the context of chemical equilibrium calculations, knowing the mole fractions assists with the application of Raoult's law for the major component and Henry’s law for the minor components, thus determining the partial pressures and hence the composition of the vapor phase.

In the example given, we first convert mole percentages to mole fractions to assess the composition of nitrogen (\( N_2 \)) and water (\( H_2O \)) before applying the appropriate law to calculate the pressure and mole fractions in the gas phase.