Question

575 g of glaubers salt are dissolved in water to obtain 1dm3 of a solution of density of 1077.2 kg/m3. Calculate the molarity , molality and mole fraction of na2so4 in the solution

Answer 1

Glauber's salt is common name of sodium sulphate decahydrate or, $Na_2SO_4.10H_2O$

molar mass of Glauber's salt = 322g/mol

given mass of Glauber's salt = 575 g

then, number of mole of Glauber's salt = 322/575 = 0.56 mol

now, volume of solution = 1dm³ = 1L = 10^-3 m³

molarity = number of mole of solute/volume of solution in L

= 0.56/1L = 0.56M

density of solution = 1077.2 kg/m³

so, mass of solution = volume of solution × density of solution

= 10^-3 m³ × 1077.2 kg/m³

= 1.0772 kg = 1077.2g

mass of solvent = mass of solution - mass of solute

= 1077.2 - 575 = 502.2g

now molality = number of mole of solute/mass of solvent in kg

= 0.56 × 1000/(502.2)

= 560/502.2

= 1.115m

number of mole of water = mass of water/molar mass of water

= 502.2/18 = 27.9 mol

mole fraction of na2SO4 = mole of na2SO4/(mole of na2SO4 + mole of water)

= 0.56/(27.9 + 0.56)

= 0.0196767393 ≈ 0.02