The vapor above a mixture of pentane and hexane at room...

The vapor above a mixture of pentane and hexane at room temperature contains $35.5 \%$ pentane by mass. What is the mass percent composition of the solution? Pure pentane and hexane have vapor pressures of 425 torr and 151 torr, respectively, at room temperature.

Key Concepts

Raoult's Law

Raoult's Law relates the partial vapor pressure of each component in a liquid mixture to the mole fraction of that component and the vapor pressure of the pure substance. It is fundamental in predicting how each component contributes to the overall vapor pressure in ideal mixtures.

Vapor Pressure

Vapor pressure is the pressure exerted by a vapor in equilibrium with its liquid phase at a given temperature. It quantifies a substance's tendency to evaporate and is a key property in determining the behavior of mixtures in vapor-liquid equilibrium.

Liquid-Vapor Equilibrium

Liquid-vapor equilibrium describes a state where the rate of evaporation of a liquid equals the rate of condensation from its vapor, resulting in a stable composition. Understanding this equilibrium is crucial for relating the compositions of the vapor and the liquid phases.

Composition Conversions

Converting between mole fraction and mass percent is essential when dealing with mixtures, especially because experimental measures may be reported in one form while theoretical models use another. This conversion is important for accurately determining the composition of the original solution from the equilibrium vapor composition.

Transcript

00:01 Problem 126.

00:03 The vapor above a mixture of painting and hexing at a rotten temperature contained 35 .5 % of painting by mass.

00:14 What is the mass percent composition of the solution? so the pure paint and hexing have vapor pressure of 425 and 151 tour.

00:27 So for this question, the mole fraction of a component in vapor.

00:47 Why? this small fraction of a component in vapor, the letter y, is the ratio of partial pressure of each component in the vapor above the solution, p -i, to the total vapor pressure of the solution, p -total.

01:49 All right, so this means that yi is equal to p i divided by p total, and p i is equal to p -0 of i times the more fraction of i divided by p total.

02:16 So here the p -0 is the vapor pressure of the pure component i at the same temperature, and the more fraction.

02:26 So the vapor pressure of p -0 of p -0 is equal to 425 tor.

02:40 And p -0 of hexing is equal to 151 tor.

02:50 So with the known values obtained the equation for more fraction, painting, and hexane, we have y -painain.

03:04 Equal to p of painting, 0 times small fraction of painting divided by p total.

03:14 So we have 0 .396 equal to 425 times small fraction of painting divided by p total.

03:35 And the same for hexing, we have y of hexing equal to p0 of hexing times small fraction of hexing divided by p total.

03:47 So that is 0 .604 is equal to p total 151 times 1 minus small fraction of painting.

04:02 So now equate the expression for p total.

04:08 From the first one, we have p total equal to 425 times small fraction of p.

04:24 Divided by 0 .396.

04:28 And from this one we get 151 times 1 minus mole fraction divided by 0 .604.

04:44 So now we'll multiply these two numbers to both side of the equation.

04:52 We get 1073 .232 equal to 250 times 1 minus more fraction of painting.

05:09 And we solve for the more fraction, we get the value equal to 1073 .232 plus 250.

05:22 That's equal to 0 .189...

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