Question

What is the concentration of sugar $\left( {{\text{C}}_{12}}{{\text{H}}_{22}}{{\text{O}}_{11}} \right)$ in mol/L, if 20g of it is dissolved in enough water to make a final volume up to 2 L?

Answer 1

The molarity of a solution is the number of moles of solute dissolved in one litre of solution. It is denoted by (M). Molarity is also known as the molar concentration of a solution.
Formula used:
$\text{M=}\dfrac{\text{W}}{\text{MW}}\text{ }\\!\\!\times\\!\\!\text{ }\dfrac{\text{1000}}{\text{Vml}}$

Complete step by step answer:
When we will solve this question we will get our answer i.e. 0.029 M.
Step by step solution: According to the question we have to calculate molarity of sugar for that we have to calculate molar weight of sugar$\left( {{\text{C}}_{12}}{{\text{H}}_{22}}{{\text{O}}_{11}} \right)$.
For calculating molar weight,atomic weight of the Carbon = 12 g.
atomic weight of the Hydrogen = 1 g.
atomic weight of the Oxygen = 16 g.
Given, chemical formula of sugar is$\left( {{\text{C}}_{12}}{{\text{H}}_{22}}{{\text{O}}_{11}} \right)$
Molar weight or molar mass = 12 atom of carbon x 12 atomic weight + 22 atom of hydrogen x 1 atomic weight + 11 atom of oxygen x 16 atomic weight.
Molar weight =$12\times 12+22\times 1+16\times 11$
Molar weight = $144+22+176$
Molar weight = 342 g/mole
Now convert volume litre into millilitre i.e.
$\text{2L}=\text{2000ml}$
Weight of sugar is given i.e. = $20gm$
Now substitute these values in this formula
$\text{M=}\dfrac{\text{W}}{\text{MW}}\text{ }\\!\\!\times\\!\\!\text{ }\dfrac{\text{1000}}{\text{Vml}}$
$\text{M=}\dfrac{\text{20}}{\text{342}}\text{ }\\!\\!\times\\!\\!\text{ }\dfrac{\text{1000}}{\text{2000}}$
$\text{M}=\dfrac{\text{20}}{\text{342}}\text{ }\\!\\!\times\\!\\!\text{ }\dfrac{\text{1}}{\text{2}}$
$\text{M}=\dfrac{10}{342}$
$\text{M}=0.029\text{ M}$
$\text{M}=0.029\text{ mole/L}$
So this much sugar is required for making a solution.

Note:
According to the question, molar masses of different atoms helps us to calculate molar mass or molar weight of a substance. Dilution is the process of reducing the concentration of a solute in a solution, usually by adding more solvent. This relationship is represented by the equation ${{\text{c}}_{\text{1}}}{{\text{V}}_{\text{1}}}\text{ }\\!\\!~\\!\\!\text{ = }{{\text{c}}_{\text{2}}}{{\text{V}}_{\text{2}}}\text{ }\\!\\!~\\!\\!\text{ }$, where ${{\text{c}}_{1}}$ and ${{\text{c}}_{\text{2}}}\text{ }\\!\\!~\\!\\!\text{ }$ are the initial and final concentrations, and${{\text{V}}_{\text{1}}}$ ,${{\text{V}}_{\text{2}}}$ are the initial and final volumes of the solution. This is another way to calculate molarity.