Find the mole fraction in the vapor phase.?

Your in Luck.

so first thing to note is that this is a two component raoult's law problem. Therefore we will need to use these equations.

Ya*P=Xa*Pa.sat

Yb*P=Xb*Pb.sat

Pa.sat and Pb.sat are saturated pressures (vapor partial pressures) which are given to you in the question

Ya and Yb are mole fractions in the liquid phase ( which we aren't given and will not need)

Xa and Xb are mole fraction in the vapor phase ( which we are trying to find)

let a be toluene and b benzene

We know that sum of mole fraction must equal one.

so Ya + Yb = 1

when we rewrite raoult's law using algebra, we see that:

P= Xa*Pa.sat + Xb*Pb.sat

Now there is a problem because we have 2 unknowns. This is really easy to deal with since its two component.

Here we can also say that summation of mole fraction for vapor phase must equal 1.

Xa +Xb=1

so

Xb=1-Xa

then we plug this back into main equation

P= Xa*Pa.sat + (1-Xa)*Pb.sat

solve for Xa then solve for Xb

can you post the work you have done so that it can be seen where you get stuck