Question

Benzene has a formula of C6H6 and a vapor pressure of 96.4 torr at 298 K. Toluene has a formula of C7H8 and a vapor pressure of 28.9 torr at 298 K. If a solution is made of 299 g of toluene and 391 g of benzene, what is the vapor pressure of the solution?

Answer 1

Answer: The vapor pressure of the solution is 55.2 torr

Explanation:

$p_1=x_1p_1^0$ and $p_2=x_2P_2^0$

where, x = mole fraction in solution

$p^0$ = pressure in the pure state

According to Dalton's law, the total pressure is the sum of individual pressures.

$p_{total}=p_1+p_2$$p_{total}=x_Ap_A^0+x_BP_B^0$

x = mole fraction = $\frac{\text {moles}}{\text {total moles}}$

Given : 299 g of toluene and 391 g of benzene.

moles of toluene = $\frac{\text{Given mass}}{\text {Molar mass}}=\frac{299g}{92g/mol}=3.25moles$

moles of benzene= $\frac{\text{Given mass}}{\text {Molar mass}}=\frac{391g}{78g/mol}=5.01moles$

Total moles = moles of solute (toluene)  + moles of solvent (benzene) = 3.25 + 5.01 = 8.26

$x_{benzene}$ = mole fraction of benzene =$\frac{3.25}{8.26}=0.39$

$x_{toluene}$ =mole fraction of toluene = (1-0.39) = 0.61

$p_{benzene}^0=96.4torr$

$p_{toluene}^0=28.9torr$

$p_{total}=0.39\times 96.4+0.61\times 28.9=55.2torr$

Thus the vapor pressure of the solution is 55.5 torr