Liquid A has vapor pressure x, and liquid B has vapor...

Liquid A has vapor pressure $x$, and liquid B has vapor pressure $y$. What is the mole fraction of the liquid mixture if the vapor above the solution is $30 . \%$ A by moles? $50 . \%$ A? $80 . \%$ A? (Calculate in terms of $x$ and $y .)$ Liquid A has vapor pressure $x$, liquid B has vapor pressure $y$. What is the mole fraction of the vapor above the solution if the liquid mixture is $30 . \%$ A by moles? $50 . \%$ A? $80 . \% \mathrm{~A}$ ? (Calculate in terms of $x$ and $y .$ )

Liquid A has vapor pressure $x$, and liquid B has vapor pressure $y$. What is the mole fraction of the liquid mixture if the vapor above the solution is $30 . \%$ A by moles? $50 . \%$ A? $80 . \%$ A? (Calculate in terms of $x$ and $y .)$

Liquid A has vapor pressure $x$, liquid B has vapor pressure
$y$. What is the mole fraction of the vapor above the solution if the liquid mixture is $30 . \%$ A by moles? $50 . \%$ A? $80 . \% \mathrm{~A}$ ? (Calculate in terms of $x$ and $y .$ )

Key Concepts

Mole Fraction and Phase Equilibrium

The concept of mole fraction is central in understanding both liquid and vapor compositions in phase equilibria. Mole fraction is defined as the ratio of the number of moles of one component to the total number of moles in the mixture. In vapor-liquid equilibrium, the mole fraction in the liquid phase, when combined with Raoult’s Law, permits the determination of the vapor pressures and consequently the vapor phase composition through the balance of chemical potentials across the phases.

Raoult’s Law

Raoult’s Law is a principle in physical chemistry stating that the partial vapor pressure of each component in an ideal liquid solution is directly proportional to its mole fraction in the solution and its pure component vapor pressure. This law is fundamental for relating the composition of the liquid phase to the contributions each component makes to the total vapor pressure above the solution.

Dalton’s Law of Partial Pressures

Dalton’s Law of Partial Pressures states that the total pressure of a gas mixture is the sum of the partial pressures of each individual component. In the context of vapor-liquid equilibrium, this law allows us to relate the partial pressures calculated using Raoult’s Law to the mole fractions in the vapor phase, with each component’s vapor mole fraction being the ratio of its partial pressure to the total vapor pressure.

Transcript

00:03 We're told that liquid a has a vapor pressure equal to x, and liquid b has a vapor pressure equal to y.

00:18 So what is the mole fraction of the liquid mixture if the vapor pressure above the solution is 30 % by moles? so the mole fraction of a plus the mole fraction of b is equal to 1, and then we can apply relative's law.

00:32 The partial pressure of a plus the partial pressure of a plus the partial pressure of b is equal to 1.

00:45 Not equal to 1, sorry, times 100 is equal to 30.

00:50 So that would be our 30%.

00:53 And now we can substitute these variables into this equation here.

01:00 Rearranging, i'll get 0 .30 is equal to the mole fraction of, a times x over the mole fraction of a times x plus the mole fraction of b times y and substituting mo fraction of a times x mole fraction of a times x plus one minus the mole fraction of a plus 0 .30y minus 0 .30 mole fraction of a is equal to the mole fraction of a times x and the mole fraction of a would be equal to 0 .30y over 0 .70x plus 0 .30y and here is our mole fraction of and this would be at 30 % a bimoles.

02:17 In a very similar way, if the vapor pressure is 50 % a, so 50 % a bimoles, the mole fraction of a is equal to y over x plus y and the mole fraction of b would be equal to 1 minus y over x plus y and if we have 80 % a bimals the mole fraction of a is equal to 0 .80y is equal to 0 .80 y over 0 .80x plus 1 .1 and the mole fraction of b is equal to 1 minus 0 .80y over 0 .20x plus 0 .80y.

03:44 If we in the second half we're looking at the mole fraction of the vapor above the solution, so the vapor above the solution, this would be, so the mole fraction of the vapor of the vapor above the solution.

04:12 Mor fraction a vapor is equal to p .a...

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