Question

A sugar syrup of weight 214.2 g contains 34.2 g of sugar ($C_{12}{H}_{22}{O}_{11}$). Calculate the mole fraction of the sugar in the syrup.
(If the answer is X then write 100011X )

Answer 1

Hint: The mole fraction of the component can be calculated by dividing the number of moles of the component by the number of moles of the solution and the number of moles of solutions can be calculated by adding the number of moles of solute and solvent.

Complete Solution :
The formula which we are going to use here is,
$\text{Mole fraction of sugar=}{\displaystyle \frac{\text{Moles of the sugar}}{\text{Moles of the solution}}}$
We can find the moles of the compound by dividing the given mass of the compound to the molecular mass of the compound.
Here we have the weight of sugar syrup = 214.2 g
And the weight of sugar in the syrup = 34.2 g
So, weight of water in the syrup will be = 214.2 – 34.2 = 180.0 g

- Now, let’s calculate the moles of each sugar and water in the solution,
Molecular weight of sugar, $C_{12}{H}_{22}{O}_{11}$ = 12(12) + 22(1) + 11(16) = 342
Moles of sugar = ${\displaystyle \frac{34.2}{342}}$ = 0.1 mole
Molecular weight of water, $$H_{2}O$$ = 2(1) + 1(16) = 18
Moles of water = ${\displaystyle \frac{180}{18}}$ = 10 mole

- Now we know the formula for mole fraction is,
$\text{Mole fraction of sugar=}{\displaystyle \frac{\text{Moles of the sugar}}{\text{Moles of the solution}}}$
Insert all the values in this formula,
$\text{Mole fraction of sugar=}{\displaystyle \frac{0.1}{0.1+10}}=0.0099$

We have the answer 0.0099, which is equal to X.
Now, we will convert this to 100011 X , the final answer will be 0.9.
Therefore, we can conclude the correct answer to this question is 0.9.

Note: We should know that Inverted sugar syrup (also called invert syrup, or invert sugar) is an edible mixture of two simple sugars—glucose and fructose—that is made by heating sucrose (table sugar) with water.