A solution of glucose in water is labelled as 10% w/w, what would be the molality and mole fraction of each component in the solution? If the density of solution is 1.2 g mL-1, then what shall be the molarity of the solution?
10% w/w glucose solution corresponds to 10 g glucose present in 100 g of solution which contains 90 g of water.
(i) Molality is the number of moles of glucose present in 1 kg of water. Number of moles of glucose is the ratio of mass (10g) of glucose to its molar mass (180 g/mol).
Molality = 10/180 × 0.090 = 0.618 m
Note: 90 g corresponds to 0.090 lg.
(ii) Molarity is the ratio of number of moles of glucose to volume of solution (in L).
Since, density of solution is 1.20 g/mL, the volume of solution is 100/1.20 mL or 100/1.20 × 1000 L.
Molarity = 10/(180 × 100/1.20 × 1000) = 0.667 M
(iii) Number of moles of glucose = 10/180 = 0.0556
Number of moles of water = 90/18 = 5.0
Mole fraction of glucose = 0.0556/0.0556 + 5.0 = 0.011
Mole fraction of water = 1 − 0.011 = 0.989