A solution of glucose in water is labelled as 10% (w/W). The density of the solution is `1.20 g mL^(-1)` Calculate
(i) molality
(ii) molarity and
(iii) mole fraction of each component in solution.

Explanation

10% (w/W) solution of glucose means that 10 g of glucose is present in 100 g of solution or in 90 g of water.
(i) Molality `= ("Moles of solute")/("Mass of solvent in g")xx1000`
Moles of glucose `= 10/180 = 0.0556`
Mass of solvent (water) = 90 g
`:. " Molality " = (0.0556)/90 xx 1000 = 0.618 m`
Molarity `= ("Moles of solute")/("Volume of solution")xx1000`
Moles of glucose = 0.0556
Volume of solution `= ("Mass")/("Density")= 100/1.20 = 83.3 mL`
`:. " Molarity " = (0.0556)/(83.3) xx 1000 = 0.667 M`
(iii) Moles of glucose = 0.0556
Moles of water `= 90/18 = 5.0`
Total moles = 5.0+ 0.0556 = 5.0556
Mole fraction of glucose `= (0.0556)/(5.0556)= 0.011`
Mole fraction of water `(5.0)/(5.0556)= 0.989`