Question

Benzene and toluene form nearly ideal solutions. At 20°C, the vapour pressure of benzene is 75 torr and
that of toluene is 22 torr. The parial vapour pressure of benzene at 20°C for a solution containing 78g of
benzene and 46g of toluene in torr is
(A) 50
(B) 25
(C) 37.5
(D) 53.5
​

Answer 1

Given:

• Vapour pressure of benzene(Pₐ°) = 75 torr
• Vapour pressure of toulene(P꜀) = 22 torr
• Mass of benzene = 78 g
• Mass of toulene = 46 g
• Molar mass of benzene = 78 g/mol
• Molar mass of toulene = 92 g/mol

To find:

• Partial vapour pressure of benzene(Pₐ)

Explanation:

Relation to be used

Pₐ =  Xₐ. Pₐ° ( By using Raoult's law)

Here, Xₐ represents the mole fraction of benzene.

In order to find the mole fraction first, we need to find the moles of benzene and toluene.

a)Moles of benzene:

$\to\sf{ n_a=\dfrac{m_a}{M_a}}$

$\to\sf{ n_a=\dfrac{78}{78}}$

$\to\sf{ n_a=1\:mole }$

Similarly,

b) Moles of toluene = 0.5 moles.

c) Mole fraction of benzene

$\to\sf{ X_a=\dfrac{n_a}{n_a+ n_c}}$

$\to\sf{ X_a=\dfrac{1}{1.5}}$

$\to\sf{ X_a=0.67}$

d) Partial vapour pressure of benzene

$\to\sf{P_a= X_a.P_a^{\circ}}$

$\to\sf{P_a=0.67 x 75}$

$\to\boxed{\sf{P_a=50.25\: torr} }$

The partial vapour pressure of benzene at 20°C is 50 torr.