Question

In a mixture of volatile substances, the vapor pressure of the solution depends on the vapor pressure of both substances (solute and solvent). Each component can evaporate, but its vapor pressure is lowered by the presence of the other substance following Rault's law. The vapor pressure of the solvent is calculated using P_solvent = X_solvent*P^o_solvent and the vapor pressure of the solute is calculated using P_solute = X_solute*P^o_solute. The total vapor pressure can be calculated by Dalton's law of partial pressures, P_total = P_solvent + P_solute.

At 25^oC, the vapor pressure of pure benzene (C₆H₆, 78.11 g/mol) is 96 torr. At the same temperature, the vapor pressure of pure toluene (C₇H₈, 92.14 g/mol) is 14 torr. Consider a solution containing 1.85 mol of benzene and 7.98 mol of toluene. Calculate the vapor pressure above the solution.  

Enter your answer in units of torr to three significant figures.

Answer 1

Answer :-

Given :-

No. of moles of benzene = n_benzene = 1.85 mol

No. of moles of toluene = n_toluene = 7.98 mol

Vapour pressure of pure benzene = = 96 torr

Vapour pressure of pure toluene =   = 14 torr

To find :-

Mole fraction of benzene = X_benzene = ?
Mole fraction of toluene  = X_toluene = ?

Vapour pressure of solution = P_solution = ?

Solution :-

I] Mole fraction of benzene :-

X_benzene = n_benzene / (n_benzene + n_toluene)

  X_benzene = (1.85) / (1.85 + 7.98)

  X_benzene = (1.85) / (9.83)

  X_benzene = 0.1882

  X_benzene = 0.19

II] Mole fraction of toluene :-

X_toluene = n_toluene / (n_toluene + n_benzene)

X_toluene = (7.98) / (7.98 + 1.85)

X_toluene = (7.98) / (9.83)

X_toluene = 0.8118

X_toluene = 0.81

III] Vapour pressure of solution :-

Raoult's Law states that the partial pressure of each component of an ideal mixture of liquids is equal to the vapour pressure of the pure component multiplied by its mole fraction in the mixture.

The idea here is that the vapour pressures of benzene and toluene will contribute to the total vapour pressure of the solution proportionally to their respective mole fraction.

Mathematically, you can express this by the following equation

P_solution = X_benzene . + X_toluene .

P_solution = (0.19)(96) + (0.81)(14)

P_solution = 18.24 + 11.34

P_solution = 29.58

P_solution = 29.6 torr

Therefore, the vapour pressure of the given solution of benzene and toluene is 29.6 torr.

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