Two beakers are placed in a closed container. Beaker A initially contains 0.15 mole of naphthalene (C10H8) in 100 g of benzene (C6H6), and beaker B initially contains 31 g of an unknown compound dissolved in 100 g of benzene. At equilibrium, beaker A is found to have lost 7.0 g of benzene. Assuming ideal behavior, calculate the molar mass of the unknown compound. State any assumptions made.

Molar mass of the unknown compound is 192.2 g/mol

Explanation:

Assumption:

At equilibrium, molality of beaker A = molality of beaker B

Molality of beaker A = moles of naphthalene/kg of benzene

Mass of benzene = 100 - 7 = 93 g = 93/1000 = 0.093 kg

Molality of beaker A = 0.15/0.093 = 1.613 m

Molality of beaker B = moles of unknown compound (y) / kg of benzene

Mass of benzene = 100 g = 100/1000 = 0.1 kg

Molality of beaker B = (y/0.1) m

y/0.1 = 1.613

y = 0.1*1.613 = 0.1613 mol of unknown compound

Molar mass of unknown compound = mass/number of moles = 31 g / 0.1613 mol = 192.2 g/mol