A solution of glucose in water is labelled as `10` percent `w//w`, what would be the molality and mole fraction of each component in the solution? If the density of the solution is `1.2 g mL^(-1)`, then what shall be the molarity of the 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) Calculation of molality
Mass of glucose = 10g
Moles of glucose `=10/180 = 0.0556`
(Molar mass of glucose = 180)
Mass of water = 90g
`therefore` Molality =(Moles of glucose =180)
Mass of water = 90 g
`therefore` Molality `=("moles of glucose")/("Mass of water") xx 1000`
`=(0.056)/90 xx 1000= 0.618`m
(ii) Calculation of molarity
Moles of glucose = 0.0556
Volume of solution `=("Mass")/("Density")`
`=100/1.20 = 83.3` mL
Molarity `=("Moles of glucose")/("Vol. of solution") xx 1000`
`=(0.0556)/83.3 xx 1000 = 0.667` M .
(iii) Calculation of mole fraction of components
Moles of glucose = 0.0556
Moles of water `=90/18 = 5.0`
Total mass = 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`