# 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)

I'm a little bit confused because I thought the mole fraction of the vapor pressure and of the solution were the same. But I guess not? Thank you so much!

## vapor pressure A = X

vapor pressure B = Y

total p of vapor = Ptotal = Xav + Ybv

Xa in vapor = Xav/(Xav + Ybv) = 0.3

Xb in vapor = Ybv/(Xav + Ybv) = 0.7

In liquid

Xa liq = P^{o}_{a liq}*0.3/Ptotal vapor = P^{o}_{a liq}/(Xav + Ybv)

Similarly for Xb liq =

Xb = P^{o}_{b liq}/(Xav + Ybv)

I hope this is not too confusing. Calling the vapor pressure of A and B X and Y along with mole fractions in both vapor and liquid can get very confusing. If you get confused let me suggest you do this.

Suppose we had Aliq = Po of 100 mm and we had Xa = 0.6 along with Bliq = Po of 200 mm and Xb = 0.4

We can calculate Pa and Pb this way.

Pa = Xa*Poa = 0.6*100 = 60 mm

Pb = Xb*Pob = 0.4*200 = 80 mm

Total vapor pressure above liquid is 60+80 = 140 mm.

Xa vapor = 60/140 = about 0.429

Xb vapor = 80/140 = about 0.571

Now watch. We want to take the Xa and Xb in the vapor and get the Xa and Xb in liquid (ans we know what those numbers are).

Xa liq = Xav*Ptotal/Po = 0.429*140/100 = 0.6

Xb liq = Xbv*Ptotal/Po = 0.571*140/200 = 0.4

Using these numbers may help in understanding the X and Y stuff above.

Xa liq =

and B = Po of 200

## Ignore the last two lines; i.e., Xa liq =

and B = Po of 200. Those were below my screen from earlier attempts and I didn't get them erased. The rest of it looks ok to me.

## Well, it seems like we have a mixture of liquid A and liquid B here. Just like mixing peanut butter and jelly, we're going to end up with something delicious, but in this case, a solution!

Now, let's address your confusion. The mole fraction in the vapor phase and the mole fraction in the liquid phase are not necessarily the same. The mole fraction in the vapor phase refers to the ratio of moles of a particular component (in this case, A) to the total moles of the vapor phase. On the other hand, the mole fraction in the liquid phase refers to the ratio of moles of a particular component (A or B) to the total moles of the liquid phase.

Now, let's get to the calculations!

If the vapor above the solution is 30% A by moles, it means that the mole fraction of A in the vapor phase is 0.3. So, we can write:

0.3 = (moles of A in the vapor phase) / (total moles of the vapor phase)

Similarly, if the vapor is 50% A by moles, the mole fraction of A in the vapor phase would be 0.5, and if it is 80% A by moles, the mole fraction of A in the vapor phase would be 0.8.

Unfortunately, I can't calculate the exact values of the mole fraction of the liquid mixture just by knowing the vapor pressure, X and Y. The mole fraction in the liquid mixture depends on the vapor pressure and the ratio of the mole fractions of A and B in the vapor phase. So, I need more information to calculate it.

But hey, don't be too down about it! Mixing things up can be confusing sometimes. Just remember, humor is always a good mixture. Keep laughing and keep asking questions!

## The mole fraction of a component in a mixture is defined as the ratio of the number of moles of that component to the total number of moles in the mixture. In this case, we want to calculate the mole fraction of liquid A in the liquid mixture based on the vapor composition.

To calculate the mole fraction of liquid A in the liquid mixture, we can use Raoult's Law, which states that the vapor pressure of a component in an ideal mixture is equal to the vapor pressure of the pure component multiplied by its mole fraction in the liquid mixture.

Let's assume that the total number of moles in the liquid mixture is represented by n, and the number of moles of liquid A and liquid B are represented by nA and nB, respectively.

1. For the case where the vapor above the solution is 30% A by moles:

According to Raoult's Law, the vapor pressure of component A (PA) is equal to the vapor pressure of pure A (X) multiplied by the mole fraction of A in the liquid mixture (x). So, we can write:

PA = X * x

Since the vapor above the solution is 30% A by moles, the mole fraction of A in the vapor (yA) is equal to 0.3. We also know that the mole fraction of B in the liquid mixture (xB) is equal to 1 - xA. Therefore, we can write:

yA = 0.3 = nA / n

We have two equations with two unknowns (x and nA), and we can solve for them simultaneously. Plug in the value of yA and solve for nA in terms of n:

0.3 = nA / n

nA = 0.3 * n

Now, substitute this value of nA into the equation for PA:

PA = X * x = X * (nA / n) = X * (0.3n / n) = 0.3X

To calculate the mole fraction of A in the liquid mixture (x) in terms of X and Y, we can use an additional equation. The total vapor pressure of the mixture (PTotal) is the sum of the partial pressures of the components:

PTotal = PA + PB = 0.3X + 0.7Y

Since the total vapor pressure of the mixture is equal to 1 (assuming ideal behavior), we can write:

PTotal = 1 = 0.3X + 0.7Y

Solving this equation for Y in terms of X:

Y = (1 - 0.3X) / 0.7

Now we have expressions for both x and y in terms of X and Y for the case where the vapor above the solution is 30% A by moles.

2. Similarly, we can repeat this process for the cases where the vapor above the solution is 50% A by moles and 80% A by moles. Use the same approach as explained above, just substitute the corresponding values of yA and solve for x and nA.

For 50% A by moles, yA = 0.5. Solve for nA and substitute the value of nA in the equation for PA to get x in terms of X.

For 80% A by moles, yA = 0.8. Solve for nA and substitute the value of nA in the equation for PA to get x in terms of X.

By following these steps, you can calculate the mole fraction of the liquid mixture for each case in terms of X and Y.