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1‑Propanol (𝑃∘1=20.9 Torr at 25 ∘C) and2‑propanol (𝑃∘2=45.2 Torr at 25 ∘C) formideal solutions in all proportions....

Question

1‑Propanol (𝑃∘1=20.9 Torr at 25 ∘C) and2‑propanol (𝑃∘2=45.2 Torr at 25 ∘C) formideal solutions in all proportions. Let 𝑥1 and 𝑥2 represent the mole fractionsof 1‑propanol and 2‑propanol in a liquid mixture, respectively,and 𝑦1 and 𝑦2represent the mole fractions of each inthe vapor phase.For a solution of these liquidswith 𝑥1=0.640, calculate the composition of the vaporphase at 25 ∘C.𝑦1=_______𝑦2=_______

1‑Propanol (𝑃∘1=20.9 Torr at 25 ∘C) and 2‑propanol (𝑃∘2=45.2 Torr at 25 ∘C) form ideal solutions in all proportions. Let 𝑥1 and 𝑥2 represent the mole fractions of 1‑propanol and 2‑propanol in a liquid mixture, respectively, and 𝑦1 and 𝑦2represent the mole fractions of each in the vapor phase. For a solution of these liquids with 𝑥1=0.640, calculate the composition of the vapor phase at 25 ∘C. 𝑦1=_______ 𝑦2=_______



Answers

A solution is prepared by mixing 1.000 mole of methanol $\left(\mathrm{CH}_{3} \mathrm{OH}\right)$ and 3.18 moles of propanol $\left(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{CH}_{2} \mathrm{OH}\right)$ What is the composition of the vapor (in mole fractions) at $40^{\circ} \mathrm{C} ? \mathrm{At} 40^{\circ} \mathrm{C},$ the vapor pressure of pure methanol is 303 torr, and the vapor pressure of pure propanol is 44.6 torr.

Solution. For the above question we have Ideal pressure is eggs. A is equal to X B and we have two compounds here benzene and to lean. A preparation is equal to 0.500 in 2 95 plus bind 500 in 2 28. Also here, benzene is equal to 95 door and Tallinn is equal to 28 Tour. So here, 67.5 door is it weird to $97.5 plus 14 tall. So here X is equal to one and X for benzene is equal to point 500 And export Olene is equal 2.500 So here we have for benzene 0.500 into $95. Divided by 61.5 is equal to 0.77 Multiply 0.77 my eggs off benzene. And next to behave for a Tolin 0.500 into 28 or divided by 61.5. Is it too? 0.23 eggs tolling? Uh huh.

Dune from 66 Chapter 11 bandying tell you informed ideas issue consider solution bending, talking prepared, 25 degrees Celsius Zooming the mole fractions of benzene. Tell you we end the vapor phase or equal Calculate the competition solution. And I tried hundreds Celsius, The vapor pressure, the benzene, uh, benzene and tall Ewing are 95 28 tour, respectively. So we're gonna use and the total pressure together, that's gonna be 124. So we're gonna use the formula. So in the vapor phase, they are equal. That's not necessarily what they're gonna be in solution. It means the formula, the more fractions gonna equal the partial pressure over Petey P Big. So the the mole fraction for benzene is going to equal 95 over 1 23 And that's going to be E 0.7 seven. And the more fraction for valuing it's going to be 28 over 1 23 is gonna be 0.23 ready? So that's the competition ever solution. It's composed of the fraction of benzene is 0.77

Let's calculate the composition of a mixture of Tom, human and benzene. The pressure of tone Ewing is equal to the more fraction of the tall. You mean partial pressure of the tall Ewing and the, um, pressure of the benzene is equal to more fraction of the benzene, partial pressure of the benzene and because the mole fractions air equals. So because, uh, directions are equal, we're told that in the question the, um, pressure of tall Ewing is equal to the pressure of the benzene. Therefore, more fraction of tell you in for the pressure of the timing, even to the mole fraction of the benzene or for pressure, the benzene you can substitute in here. We don't know the more fraction of the tall, you mean, uh, or the benzene. So let's assign a variable here and let's assign, um, let's assign this to be sorry 28 98 Benzene tall Ewing. Let's seem that this is X. So the mole fraction uh, let's the mole fraction of the toy going to stick with the axe There. For the mole fraction, the benzene would be one minus x, the to half the equal one. So substituting in here The mole fraction of the tall. You mean we use X partial pressure of the tell. You mean the pressure eyes 28. It should be one minus X and vapor. Pressure for the benzene is 95 tour. Let's leave out the units here. This would be 28 x is equal to in 95 minus 95 pets. Add 95 acceptable sides and you would get 1 23 x with 95 a lot of 1 23 from both sides. We find that X is equal to point. Let's do you, um too sick Figs 0.77 Therefore, let's take that back up here. The mole fraction of the tall You mean people 2.77 And the more fraction of the benzene is one minus X, which will be equal 2.23 and there is a composition of the solution at 25 degrees Celsius.

So what we know is that moral fraction Which is X. Ch 3? Which meeting all is equal to a number of moles of eternal over a number of most of meat in oil. Class eight And on. Okay, so this is the formula. And if this is C. H. 30 H. Is equal to given moss over more little Irma's Okay. No molecular mass of the H. three or H will be 12.01 Carbon three into 1. 16 plus one. Right? So this is equal to 32.05 g. Berman therefore, Number of moles of Ch three, which is equal to Given Masses. 50 g divided by 32.05 g for mold. So this is equal to 1.56 moore's. Right? Moving on, we'll do the same calculation for eternal C. two H 5 voyage divided by moller maas 12 89. Now, muller myself, eternal is 12 points. You don't want multiplying by 2-plus 5. The 16 last one. So this is equal to 46.08 g Permal. So the number of moles of 18 all will be equal to 50 grams divided by 46.08 grounds One more, which is equal to 1.08 Moon's. Okay? So now we have all the data and we'll substitute CH three, which is equal to 1.56 moules Divided by 1.56 Plus 1.08 moles is equal to 15 9.1 percent. Right? So Now we'll do the same thing for 18 hour. This will be a number of moles of eternal, divided by a number of moles off Lieutenant. All plus number of moves off eternal. So this is 1.0 way to Mars Divided by 1.08 Plus 1.56 moles. Which is equal to 40.9 plus sent. So now we have this next part is we have to calculate the vapor pressure of the eternal and eating. All right. So we know pressure off CH three witch solution Is equal to pressure off CH three wet into X. Ch three words. OK So pressure off Ch three witch Solution is 94. You're into Little .591. This is 55.55 door. Okay so we do the same for eating all. Now this will be equal to Let's see to it. five which? 44 door In 20.409. This is equal to 17.99. Okay. Moving on to the next part. We have to calculate the Mueller factions in paper. So moller faction button. They performed so pleasure of CH three oh itch solution divided by pressure of solution plus pressure of eternal solution. So this will be 55.55 Divided by 55.55 plus 17.99. This is equal to 75.5 seen. So we do the similarly for eating all divided by solution plus eternal right? So this will be 17.99, divided by 55.55 and plus like what? 17 point 99. So this gives it on Sunday 24.5 percent. Okay?


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