Question

. Benzene and toluene form nearly ideal solutions. At 25.0°C the vapor pressure of pure benzene and pure toluene are 95.1 torr and 28.4 torr, respectively. What is the mole fraction of benzene in the vapor in equilibrium with a solution having mole fraction X benzene = 0.40 at 25.0°C?

(a) 0.77

(b) 0.69

(c) 0.60

(d) 0.40

(e) 0.30

Answer 1

Benzene and toluene form nearly ideal solutions. At 25.0°C the vapor pressure of pure benzene and pure toluene are 95.1 torr and 28.4 torr, respectively. What is the mole fraction of benzene in the vapor in equilibrium with a solution having mole fraction X benzene = 0.40 at 25.0°C?

mole fraction of Xbenzene = 0.40

Xtoulene = 0.60

Psolution = P_AX_A + P_BX_B

Psolution = Ptoulene x Xtolulene + Pbenzene x Xbenzene

              = 28.4 x 0.60 + 95.1 x 0.40

              = 55.08 torr

mole fraction of benzene in vapor = P_AX_A / Ptotal

                                                      = 38.04 / 55.08

mole fraction of benzene in vapor = 0.69

                                                      

Answer 2

Given:

• Vapor pressure of pure benzene ($P_{\text{benzene}}^{\ast }$) = 95.1 torr

• Vapor pressure of pure toluene ($P_{\text{toluene}}^{\ast }$) = 28.4 torr

• Mole fraction of benzene in the liquid ($X_{\text{benzene, liquid}}$) = 0.40

• Mole fraction of toluene in the liquid ($X_{\text{toluene, liquid}}$) = $1-0.40=0.60$

• $=0.60$

Step 1: Calculate the partial vapor pressures using Raoult's Law :

$$P_{\text{benzene}}=X_{\text{benzene, liquid}}\times P_{\text{benzene}}^{\ast }=0.40\times 95.1=38.04\text{ torr}$$$$P_{\text{toluene}}=X_{\text{toluene, liquid}}\times P_{\text{toluene}}^{\ast }=0.60\times 28.4=17.04\text{ torr}$$

Step 2: Find the total vapor pressure :

$$P_{\text{total}}=P_{\text{benzene}}+P_{\text{toluene}}=38.04+17.04=55.08\text{ torr}$$

Step 3: Calculate the mole fraction of benzene in the vapor phase ($Y_{\text{benzene}}$) :

$$Y_{\text{benzene}}=\frac{P_{\text{benzene}}}{P_{\text{total}}}=\frac{38.04}{55.08}\approx 0.69$$

 Answer is :

                       (b) 0.69