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Question: What is the concentration of sugar \(\left( {{C_{12}}{H_{22}}{O_{11}}} \right)\) in \({\text{mol }}{...

What is the concentration of sugar (C12H22O11)\left( {{C_{12}}{H_{22}}{O_{11}}} \right) in mol L−1{\text{mol }}{{\text{L}}^{ - 1}}. If it's 20 g{\text{20 g}} are dissolved in enough water to make a final volume up to 2 L{\text{2 L}}.

Explanation

Solution

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 V{\text{V}} volume of solution in litres.

Complete step by step answer:
Sugar has formula (C12H22O11)\left( {{C_{12}}{H_{22}}{O_{11}}} \right). So, its molar mass is given by:
= 12 × Mass of C - atom + 22 × Mass of H - atom + 11× Mass of O - atom12{\text{ }} \times {\text{ Mass of C - atom + 22 }} \times {\text{ Mass of H - atom + 11}} \times {\text{ Mass of O - atom}}
= 11×12+22×1+11×1611 \times 12 + 22 \times 1 + 11 \times 16
= 342 g mol−1{\text{342 g mo}}{{\text{l}}^{ - 1}}
So, Molar mass of sugar is 342 g mol−1 ..........(1){\text{342 g mo}}{{\text{l}}^{ - 1}}{\text{ }}..........{\text{(1)}}
Given mass of the sugar is 20 g ...........(2){\text{20 g }}...........{\text{(2)}}
Number of moles of sugar = Given mass of sugarVolume of solution in L\dfrac{{{\text{Given mass of sugar}}}}{{{\text{Volume of solution in L}}}}
From equation (1) and (2){\text{(1) and (2)}},
Or, number of moles of sugar = 20342 ..........(3)\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 2 L{\text{2 L}}.
So, volume of the solution in litre is 2 L ..........(4){\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 = Number of moles of soluteVolume of solution in Litre\dfrac{{{\text{Number of moles of solute}}}}{{{\text{Volume of solution in Litre}}}}
From equation (3) and (4){\text{(3) and (4)}},
⇒\Rightarrow Molarity of sugar solution  = 20342×12{\text{ = }}\dfrac{{20}}{{342}} \times \dfrac{1}{2}
⇒\Rightarrow Molarity of sugar solution = 0⋅029 mol L−10 \cdot 029{\text{ mol }}{{\text{L}}^{ - 1}}

Hence, 0⋅029 mol L−10 \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.