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 the solution is `1.2 g ml^(-1)`, then what shall be the molarity of the solution ?

Explanation

10 g glucose is present in 100 g solution, i.e. there is 90 g of water = 0.090 kg of water
`= (10)/(180) mol = 0.0555` mol
Number of moles of 90g of `H_(2)O = (90)/(18) = 5 mol`
Molality of glucose `= (0.0555 mol)/(0.090 kg) = 0.617 m`
Mole fraction of glucose, `chi_("glucose") = (0.0555)/(5 + 0.0555) = 0.01`
`chi_((H_(2)O)) = 1 - 0.01 = 0.99`
`because` Density of solution `= 1.2 g mL^(-1)`
`therefore` Volume of 100 g solution `= (100)/(1.2) mL`
`= 83.33 mL = 0.08333L`
Thus , molarity `= (0.0555 mol)/(0.08333 L) = 0.67 M`