Carbon tetrachloride (CCl4) and benzene (C6 H6) form ideal solutions. Consider an equimolar solu

Carbon tetrachloride (CCl4) and benzene (C6 H6) form ideal...

Carbon tetrachloride $\left(\mathrm{CCl}_{4}\right)$ and benzene $\left(\mathrm{C}_{6} \mathrm{H}_{6}\right)$ form ideal solutions. Consider an equimolar solution of $\mathrm{CCl}_{4}$ and $\mathrm{C}_{6} \mathrm{H}_{6}$ at $25^{\circ} \mathrm{C}$. The vapor above the solution is collected and condensed. Using the following data, determine the composition in mole fraction of the condensed vapor.

Key Concepts

Mole Fraction

Mole fraction is a dimensionless quantity representing the ratio of the number of moles of a particular component to the total number of moles in the mixture. It is used to express composition in both the liquid and vapor phases, especially when applying Raoult's law and in analysis of vapor-liquid equilibria.

Dalton's Law of Partial Pressures

Dalton's Law of Partial Pressures asserts that the total pressure exerted by a mixture of gases is equal to the sum of the partial pressures of each individual gas. This principle complements Raoult’s law in evaluating the overall pressure of the vapor phase in equilibrium with an ideal solution.

Vapor-Liquid Equilibrium (VLE)

Vapor-liquid equilibrium refers to the condition where a liquid and its vapor are in dynamic equilibrium, meaning that the rates of evaporation and condensation are equal. In the context of ideal solutions, VLE is determined by the balance of partial pressures as described by Raoult's law and is essential for predicting the compositions of both the liquid and vapor phases.

Ideal Solutions

An ideal solution is one in which the interactions between unlike molecules are exactly the same as those between like molecules, leading to no enthalpy of mixing. This assumption allows the solution to follow Raoult's law exactly, meaning that the vapor pressure of each component in the mixture is directly proportional to its mole fraction in the liquid phase.

Raoult's Law

Raoult's law states that in an ideal solution, the partial pressure of each volatile component in the vapor phase is equal to the product of the mole fraction of the component in the liquid phase and the vapor pressure of the pure component. This law is fundamental for calculating the vapor composition in equilibrium with its corresponding liquid phase.

Transcript

00:01 Let's use the data provided to calculate the mole fraction of the condensed vapor, and we have carbon tetrachlorite and benzene.

00:11 So first of all, from the problem, we're going to have to calculate the pure vapor pressure values.

00:22 So c6h6 liquid to c6h6 gas.

00:32 Equilibrium constant here is equal to the partial pressure of c6h6 which is equal to the initial pressure of c6h6 and our delta g knot's reaction would be equal to the delta g knot formation of c6 h6 in the gas phase minus the delta g knot formation c6 h6 in the liquid phase.

01:17 Putting these values in, this is a 129 .66 kilojoules per mole minus 124 .50 kilojoules per mole and the delta the g knot for the reaction works out to 5 .16 kilojoules per mole and then our delta g knot is equal to negative r t lawn k so we can rearrange here and find that the lawn of k is equal to delta g not over minus r t delta g is 5 .16 times 10 to the 3 joules per mole minus 8 .3145 joules per mole kelvin.

02:28 Temperature in kelvin is 298 kelvin, and this is equal to minus 2 .08.

02:34 And then the equilibrium constant here, which is equal to the initial pressure of c6h6, is equal to the e to the minus 2 .08, and we find that this is equal to 0 .125 atmospheres.

02:57 And now let's look at for ccl4.

03:05 And so we have ccl4, liquid.

03:09 Liquid to ccl4 gas and the equilibrium constant here is going to be equal to the partial pressure of ccl4 which is equal to the initial pressure of ccl4 and so delta g not reaction is equal to delta g not formation c.

03:48 Cl4 in the gas phase minus delta g not formation ccl4 in the liquid phase substitute these numbers in here.

03:58 This is negative 60 .59 kilojoules per mole minus minus 65 .21 kilojoules per mole and we find that this is equal to to 4 .62 kilojoules per mole...

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