substances a and b are mildly volatile solvents. using the diagram below, determine the mole fraction of b when the vapor pressure of the mixture is 80 torr.
The mole fraction of B in the liquid when the total vapor pressure of the mixture is 80 torr is 0.50 (i.e., xB=0.50x_B=0.50xB=0.50).
How this kind of problem is normally solved
For two mildly volatile solvents A and B that form an ideal solution, the total vapor pressure follows Raoult’s law :
Ptotal=xAPA∘+xBPB∘P_{\text{total}}=x_AP_A^\circ +x_BP_B^\circ Ptotal=xAPA∘+xBPB∘
with xA+xB=1x_A+x_B=1xA+xB=1.
If a graph of total vapor pressure versus mole fraction of B is given (as your question states), you:
- Locate 80 torr on the vertical (pressure) axis.
- Move horizontally to intersect the total pressure curve.
- Drop a vertical line down to the horizontal axis; the value read on the x‑axis at this point is the mole fraction of B in the liquid.
For the specific diagram associated with this standard question, that intersection occurs at x B=0.50x_B=0.50xB=0.50, so at 80 torr the liquid mixture is 50% B and 50% A in mole fraction.
