Question

What is the concentration of sugar $\left( {{C_{12}}{H_{22}}{O_{11}}} \right)$ in ${\text{mol }}{{\text{L}}^{ - 1}}$. If it's ${\text{20 g}}$ are dissolved in enough water to make a final volume up to ${\text{2 L}}$.

Answer 1

Hint:Concentration of any solution defines the quantity of the solute that is present in a particular quantity of the solvent or the solution. Molarity is the most common unit of concentration, which is equivalent to the number of moles of solute present in ${\text{V}}$ volume of solution in litres.

Complete step by step answer:
 Sugar has formula $\left( {{C_{12}}{H_{22}}{O_{11}}} \right)$. So, its molar mass is given by:
= $12{\text{ }} \times {\text{ Mass of C - atom + 22 }} \times {\text{ Mass of H - atom + 11}} \times {\text{ Mass of O - atom}}$
= $11 \times 12 + 22 \times 1 + 11 \times 16$
= ${\text{342 g mo}}{{\text{l}}^{ - 1}}$
So, Molar mass of sugar is ${\text{342 g mo}}{{\text{l}}^{ - 1}}{\text{ }}..........{\text{(1)}}$
Given mass of the sugar is ${\text{20 g }}...........{\text{(2)}}$
Number of moles of sugar = $\dfrac{{{\text{Given mass of sugar}}}}{{{\text{Volume of solution in L}}}}$
From equation ${\text{(1) and (2)}}$,
Or, number of moles of sugar = $\dfrac{{20}}{{342}}{\text{ }}..........{\text{(3)}}$
Here, sugar is the solute, and water is the solution, and it is given that these two solutes and solvent make up a solution of volume ${\text{2 L}}$.
So, volume of the solution in litre is ${\text{2 L }}..........{\text{(4)}}$
We have to calculate the concentration of this solution, which will be equal to the molarity of the solution. Molarity of a solution is given by:
Molarity = $\dfrac{{{\text{Number of moles of solute}}}}{{{\text{Volume of solution in Litre}}}}$
From equation ${\text{(3) and (4)}}$,
$ \Rightarrow $ Molarity of sugar solution ${\text{ = }}\dfrac{{20}}{{342}} \times \dfrac{1}{2}$
$ \Rightarrow $ Molarity of sugar solution = $0 \cdot 029{\text{ mol }}{{\text{L}}^{ - 1}}$

Hence, $0 \cdot 029{\text{ mol }}{{\text{L}}^{ - 1}}$ is the concentration of sugar.


Note:Another unit of concentration is Molality. Because of the similar names, molality, and molarity are mixed together, but they are very different in a way. Molality is the number of moles of solute per kilogram of solvent, whereas, molarity is the number of moles of solute per litre of solution.