Question

An aqueous sugar syrup of mass 224.2 g contains 34.2 g of sugar ( ${{C}_{12}}{{H}_{22}}{{O}_{11}}$ ). Calculate
(i) The molality of the solution
(ii) The mole fraction of sugar solution.

Answer 1

Hint: There is formula to calculate the molality of the solution and it is as follows
$Molality =$ $\dfrac{W}{M.W}\times \dfrac{1000}{V(in\text{ }kg)}$
Here W = weight of the solute
M.W = Molecular weight of the solute
V = Volume of the solvent in kg.
The formula to calculate the mole fraction of a chemical = $\dfrac{\text{number of moles of the chemical}}{\text{total number of moles of the chemical}}$

Complete step by step solution:
- In the question it is given that an aqueous solution of sugar syrup (mass = 224.2 g) contains 34.2 g of sugar.
- We have to calculate the molality of the solution and mole fraction of the sugar solution.
(i) Molality of the solution.
- The mass of the water in the solution = Mass of the sugar syrup – mass of the sugar
The mass of the water in the solution = 224.2-34.2 = 190 g.
- The mass of the water in solution in Kg = 0.19 Kg.
- Substitute all the known values in the below equation to get the molality of the solution.
$Molality =$ $\dfrac{W}{M.W}\times \dfrac{1000}{V(in\text{ }kg)}$
Here W = weight of the sugar = 34.2
M.W = Molecular weight of the solute = 342
V = Volume of the solvent in kg. = 0.19 Kg
Molality of the solution
\[\begin{align}
&\implies \dfrac{34.2}{342}\times \dfrac{1000}{0.19} \\
&\implies 0.5263m \\
\end{align}\]
- Therefore the molality of the solution is 0.5263m.
(ii) Mole fraction the sugar solution.
Mole fraction of the sugar solution = $\dfrac{\text{number of moles of the sugar}}{\text{total number of moles of the sugar solution}}$
Number of moles of the sugar = $\dfrac{34.2}{342}=0.1mole$
Total number of moles water = $\dfrac{190}{18}=10.55$
Total number of sugar solution = 10.55+ 0.1 = 10.65
- Substitute all the known values in the above equation to get mole fraction of the sugar solution.
Mole fraction of the sugar solution
\[\begin{align}
&\implies \dfrac{\text{number of moles of the sugar}}{\text{total number of moles of the sugar solution}} \\
&\implies \dfrac{0.1}{10.65} \\
&\implies 0.00938 \\
\end{align}\]
- The mole fraction of the sugar solution is 0.00938.

Note: Mole fraction of sugar solution is nothing but the number of moles of the sugar is present in the total number of moles of the sugar solution. Mole fraction of sugar solution is different from the mole fraction of the total solution.