Question

A solution is prepared from 4.5715 g of magnesium chloride and 43.236 g of water. The vapor pressure of water above this solution is found to be 0.3622 atm at 348.0 K. The vapor pressure of pure water at this temperature is 0.3804 atm. Find the value of the van't Hoff factor i for magnesium chloride in this solution.

Answer 1

we know that

moles = mass / molar mass

so

moles of water = 43.236 / 18 = 2.402

moles of MgCl2 = 4.5715 / 95.211 = 0.048

now

total moles = 2.402 + 0.048 = 2.45

now

mole fraction of MgCL2 = moles of MgCl2 / total moles

mole fraction of MgCl2 = 0.048 / 2.45

mole fraction of MgCl2 = 0.0196

now

lowering in vapor pressure = 0.3804 - 0.3622 = 0.0182

now

lowering in vapor pressure = i x mol fraction of MgCl2 x vapor pressure of pure water

so

0.0182 = i x 0.0196 x 0.3804

i = 2.44

so

the value of vanthoff factor for MgCl2 in this solution is 2.44