Question

The vapor pressure of water is 3.1672 kPa at 25^oC. If the vapor pressure over a non-electrolyte solution of the nonvolatile solute urea is 3.1232 kPa when the mass fraction of urea is 0.0450, what is the experimental value of the molar mass of urea?

Answer 1

molar mass of urea = 60.06 g/mol

let mass of urea = 1 g

since mass fraction is 0.0450,

mass of non electrolyte = 0.0450 g

According to Raoult’s law:

P = Po*X(solvent)

3.1232 = 3.1672*X(solvent)

X(solvent) = 0.9861

This is mole fraction of urea

mass of urea = 1 g

we have below equation to be used:

number of mol of urea,

n = mass of urea/molar mass of urea

=(1.0 g)/(60.06 g/mol)

= 1.665*10^-2 mol

X(urea) = n(urea)/( n(urea) + n(solute))

0.9861 = 1.665*10^-2 / ( 1.665*10^-2+n(solute))

1.642*10^-2+0.9861*n(solute) = 1.665*10^-2

0.9861*n(solute) = 2.313*10^-4

n(solute) = 2.346*10^-4 mol

mass of solute = 0.0450 g

we have below equation to be used:

number of mol = mass / molar mass

2.346*10^-4 mol = (0.045 g)/molar mass

molar mass = 192 g/mol

Answer: 192 g/mol