Calculate the molality of sugar `(C_(12)H_(22)O_(11))` in an aqueous solution that is `5.30%` sugar by mass.
Strategy: To calculate molality, we must find the number of moles of sugar and mass of water (solvent). From the given mass percent, we can find the mass of sugar in `100 g` of solution. The difference will give us the mass of solute.

Explanation

From the given mass percent, we can say that there is `5.30 g` of sugar in every `100 g` of solution. Since the solution consista of only sugar and water, `100 g` of solution must contain `100 g-5.30 g=94.70 g` of water.
A table of atomic masses shows that the molecular mass of sugar is `342.0 u`. Therefore in the `1000 g` sample of solution there is,
`5.30 g sugarxx(1 mol sugar)/(342.0 g sugar mol^(-1))=0.0155` mol sugar
Using Equation `(2.39)`, we can find molarity
`m=(0.0155 mol sugar)/(94.7 g H_(2)O)xx(1000 g)/(kg)`
`=0.164 mol//kg`
Thus the solution is said to be `0.164 m` in sugar.