A solution of glucose in water is labelled as 10% (W/W).

Calculate:

a. Molality

b. Molarity of the solution.

[Given: Density of solution is 1.20 g mL^{-1} and molar mass of glucose is 180 g mol^{-1} ]

#### Solution

Given: Glucose solution is 10% W/W, Density of solution = 1.20 g mL^{-1}

To find: a. Molality b. Molarity

`1. "Molality" = "Number of moles of solute"/"Mass of solvent in kg"`

`2. "Molarity" = "Number of moles of solute"/"Volumeof solution in L"`

Calculation: 10 % W/W of glucose solution means 100 g of solution contains 10 g of glucose.

Mass of glucose = 10 g

Mass of solution = 100 g

Mass of H2O = 100 – 10 = 90 g = 0.090 kg

Molar mass of glucose = 180 g mol^{-1}

`"Number of moles of glucose" = " Massof glucose"/"Molar massof glucose"`

`=(10 g)/(180 g mol^-1)=0.0556 mol`

From formula (1),

`"Molality of glucose solution "="Number of molesof glucose"/"Massof H2Oin kg"`

= 0.0556 mol/0.090 kg

= 0.618 m

`b. "Density of solution" =" Massof solution"/"Volumeof solution"`

Volume of solution = 100g/1.20g mL^{-1} = 83.33 mL = 0.08333 L

`"Molarity of glucose solution "= "Number of molesof glucose"/"Volume of solution in L"`

= 0.0556 mol/0.08333 L

= 0.67 M