Question

Diethyl ether has a vapor pressure of 400.0 torr at 18°C. When a sample of benzoic acid (a non-volatile compound) is dissolved in ether, the vapor pressure of the solution is 342 torr. What is the mole fraction of benzoic acid in the solution?

Answer 1

Answer:

Mole fraction of benzoic acid = 0.855

Explanation:

Vapour pressure of diethyl ether = 400.0 torr

Vapour pressure of the solution = 342 torr

When a non-volatile sotule is added to a volatile solvent, then vapour pressure of solvent decreases and vapour pressure of the solution is directly proportional to mole fraction of the solute.

$P_{total}=x \times P^0_{solvent}$

P_total = Vapour pressure of the solution = 342 torr

$P^0_{solvent}= 400\ torr$

x = Mole fraction of the solute

$P_{total}=x \times P^0_{solvent}$

$342 = x \times 400$

$x = \frac{342}{400} = 0.855$

Mole fraction of benzoic acid = 0.855

Answer 2

The mole fraction of benzoic acid in the solution is 0.855.

What is benzoic acid?

Benzoic acid is a white solid which is a carboxylic acid based on benzene.

The vapor pressure of the solution is directly proportional to the mole fraction of the solute

$P_t = x \times P^\circ _s$

t = total pressure

s = solvent

Given, the vapor pressure of diethyl ether 400.0 torr

The vapor pressure of the solution is 342 torr

Putting the values

$342 = x \times 400\\\\x = \dfrac{342}{400} = 0.855$

Thus, the mole fraction of benzoic acid is 0.855

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