Solutions — Practice

Question 1

Calculate the mole fraction of ethanol in a solution containing 46 g of ethanol and 54 g of water.

Accepted Answer

Convert both masses to moles, then divide by the total. Answer: x(ethanol) = 0.25.

Question 2

The vapour pressure of pure water at 298 K is 23.8 mm Hg. Find the vapour pressure of a solution in which the mole fraction of a non-volatile solute is 0.02.

Accepted Answer

Apply p = p(pure) times the mole fraction of the solvent. Answer: 23.3 mm Hg.

Question 3

Find the boiling point elevation when 18 g of glucose is dissolved in 500 g of water. Kb = 0.52 K kg/mol.

Accepted Answer

Compute the molality first, then apply the elevation relation. Answer: 0.104 K.

Question 4

A 15% by mass aqueous solution of a solute of molar mass 60 has density 1.10 g/mL. Find its molality and molarity.

Accepted Answer

Take 100 g of solution and use the density only for the volume. Answer: Molality 2.94 mol/kg; molarity 2.75 M.

Question 5

The Henry's law constant for nitrogen in water at 298 K is 8.68 x 10^4 bar. Find the mole fraction of nitrogen dissolved under a partial pressure of 0.79 bar.

Accepted Answer

Rearrange p = K_H x for the mole fraction. Answer: 9.1 x 10^-6.

Question 6

A solution of 2.5 g of a non-volatile solute in 100 g of benzene lowers the freezing point by 1.28 K. Kf for benzene is 5.12 K kg/mol. Find the molar mass of the solute.

Accepted Answer

Rearrange the depression relation for the molar mass, keeping the solvent mass in kilograms. Answer: 100 g/mol.

Question 7

A mixture of acetone and carbon disulphide shows a vapour pressure higher than Raoult's law predicts. State the type of deviation and the sign of the enthalpy of mixing.

Accepted Answer

Relate the vapour pressure to the relative strength of the unlike interaction. Answer: Positive deviation; enthalpy of mixing is positive, so mixing is endothermic.

Question 8

0.6 g of acetic acid dissolved in 100 g of benzene lowers the freezing point by 0.256 K. Kf for benzene is 5.12 K kg/mol. Find the van't Hoff factor and state what it indicates.

Accepted Answer

Compare the observed depression with the value calculated for undissociated acetic acid. Answer: i = 0.5, indicating that acetic acid dimerises in benzene.

Question 9

Find the osmotic pressure at 300 K of a 0.01 M solution of K3PO4, assuming complete dissociation.

Accepted Answer

Count the ions produced per formula unit to fix i, then apply the van't Hoff equation. Answer: i = 4; osmotic pressure about 0.985 atm.

Question 10

Two volatile liquids A and B have pure vapour pressures of 300 and 500 mm Hg. For an equimolar mixture, find the total vapour pressure and the mole fraction of A in the vapour.

Accepted Answer

Apply Raoult's law for the total, then Dalton's law for the vapour composition. Answer: 400 mm Hg; y(A) = 0.375.

Practice — Solutions

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