The mole fraction of liquid A in a binary liquid solution of ApA∗=300 Torr and BpB∗=800 Torr  is 0.6. The pressure at which last droplet of liquid is vapouried and the mole fraction of A in this last droplet, respectively, are

# The mole fraction of liquid A in a binary liquid solution of and  is 0.6. The pressure at which last droplet of liquid is vapouried and the mole fraction of A in this last droplet, respectively, are

1. A

400 Torr and 0.80

2. B

400 Torr and 0.20

3. C

500 Torr and 0.75

4. D

500 Torr and 0.45

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### Solution:

When the last droplet of liquid is vapourized, the composition of vapour formed will be ${y}_{\mathrm{A}}=0.60$ (given composition of the liquid solution).

Hence, ${y}_{\mathrm{A}}=\frac{{p}_{\mathrm{A}}}{p}=\frac{{x}_{\mathrm{A}}{p}_{\mathrm{A}}^{\ast }}{{x}_{\mathrm{A}}{p}_{\mathrm{A}}^{\ast }+{x}_{\mathrm{B}}{p}_{\mathrm{B}}^{\ast }}=\frac{{x}_{\mathrm{A}}{p}_{\mathrm{A}}^{\ast }}{{p}_{\mathrm{B}}^{\ast }+\left({p}_{\mathrm{A}}^{\ast }-{p}_{\mathrm{B}}^{\ast }\right){x}_{\mathrm{A}}}$

i.e.

Solving for ${x}_{\mathrm{A}}$, we get ${x}_{\mathrm{A}}=0.80$.

The pressure of the vapour will be