To determine the mole fraction of substance B when the vapor pressure of the mixture is 80 torr, the key equation that applies is Raoult's Law for an ideal solution:
Ptotal=xAPA+xBPBP_{\text{total}}=x_AP_A+x_BP_BPtotal=xAPA+xBPB
where:
- PtotalP_{\text{total}}Ptotal is the vapor pressure of the mixture (80 torr),
- xAx_AxA and xBx_BxB are the mole fractions of substances A and B,
- PAP_APA and PBP_BPB are the vapor pressures of pure substances A and B.
To solve for xBx_BxB, one needs the vapor pressures PAP_APA and PBP_BPB of the pure substances at the given temperature. The mole fractions satisfy xA+xB=1x_A+x_B=1xA+xB=1. Because the query references a diagram that was not provided, the vapor pressures of the pure substances A and B are not explicitly given here. However, with those vapor pressures known or obtained from the diagram, rearranging Raoult's law yields:
xB=Ptotal−xAPAPBx_B=\frac{P_{\text{total}}-x_AP_A}{P_B}xB=PBPtotal−xAPA
or using xA=1−xBx_A=1-x_BxA=1−xB:
Ptotal=(1−xB)PA+xBPBP_{\text{total}}=(1-x_B)P_A+x_BP_BPtotal=(1−xB)PA+xBPB
xB=Ptotal−PAPB−PAx_B=\frac{P_{\text{total}}-P_A}{P_B- P_A}xB=PB−PAPtotal−PA
Thus, once the vapor pressures PAP_APA and PBP_BPB are known from the diagram or data, the mole fraction of B can be calculated directly for the given total vapor pressure of 80 torr. If the user provides the vapor pressures for the pure substances or the diagram, the calculation can be completed exactly. This explanation is based on Raoult's law and common practice for mildly volatile solvent mixtures.
