Calculate the composition of the vapor

Question

A solution is prepared by mixing 0.0400 mol CH2Cl2 and 0.0500 mol of CH2Br2 at 25°C. Assuming the solution is ideal, calculate the composition of the vapor (in terms of mole fractions) at 25°C. At 25°C, the vapor pressures of pure CH2Cl2 and pure CH2Br2 are 133 and 11.4 torr, respectively.

mole fraction of CH2Cl2 = ___

mole fraction of CH2Br2 = ___

Answer 1

Hi Abby! For this problem, we are going to need 2 equations: Raoults Law and the law of partial pressures. We are also going to assume that the solution and the vapor are ideal.

Raoults Law is that the vapor pressure above the liquid of a component of an ideal solution is given:

Pi = xi,soln P°i

That is, the vapor pressure of a component is equal to the mol fraction of that component IN THE SOLUTION multiplied by the PURE vapor pressure of that component. So for CH2Cl2 and for CH2Br2, we can find their mol fractions IN THE SOLUTION:

CH2Cl2: 0.0400/(0.0400+0.0500) = 0.444

CH2Br2: 0.0500/(0.0400+0.0500)= 0.556

Next, we can find the vapor pressure from Raoults Law and the given pure vapor pressures of each component:

CH2Cl2: P= (0.444)(133 torr) = 59.1 torr

CH2Br2: P = (0.556)(11.4 torr) = 6.34 torr

Now that we have the vapor pressure, we can use the law of partial pressures to determine the mol fraction of IN THE VAPOR:

Pi = xi,vap Ptotal

Notice that Ptotal is the sum of all the vapor pressures and the mol fraction is the vapor mol fraction of the component.

xi,vap = Pi/Ptotal

Ptotal = 59.1 torr + 6.34 torr = 65.4 torr

CH2Cl2: x,vap = 59.1 torr / 65.4 torr = 0.904

CH2Br2: x,vap = 6.34 torr/ 65.4 torr = 0.0969

Notice with these types of problems, it’s important to separate the numbers pertaining to the mixture from the numbers pertaining to the vapor. The equation that connects these two is Raoults law. I hope this helps!