Question

A solution of glucose in water is labelled as 10{\text{% w}}/{\text{w}}. What would be the molarity of the solution?

Answer 1

We have been given the mass percentage of glucose in the question. The density of the water can be considered $1{\text{ g}}/{\text{mL}}$. Using the formula for number of moles, we can calculate the molarity.

Formula used: ${\text{Density}} = \dfrac{{{\text{mass}}}}{{{\text{volume}}}}$
${\text{no}}{\text{. of moles }} = \dfrac{{{\text{mass}}}}{{{\text{molar mass}}}}$
${\text{Molarity }} = \dfrac{{\text{n}}}{{{\text{V in mL}}}} \times 1000$
Here n is the number of moles and V is the volume of solution. The term 1000 is used to convert the volume into liters.

Complete step-by-step answer: Mass percentage of w by w means the amount of substance in grams that is present in hundred grams of the solution. So according to this 10 percent ${\text{w}}/{\text{w}}$ or weight by weight means 10 gram of glucose is present in 100 gram of solvent which is water hence,
Mass of glucose is 10 gram and the mass of solution is 100 gram.
Using the density of water as $1{\text{ g}}/{\text{mL}}$, the volume of solution will also be 100 mL as follow:
${\text{Volume of solution}} = 100{\text{ mL}} \times 1{\text{ g}}/{\text{mL}} = 100{\text{ mL}}$
The molecular formula of glucose is ${{\text{C}}_6}{{\text{H}}_{12}}{{\text{O}}_6}$.
Hence the molecular mass will be 180 amu
The number of moles can be calculated using the formula:
${\text{no}}{\text{. of moles }} = \dfrac{{{\text{10}}}}{{{\text{180}}}}$
Now we will substitute the known variables in the formula of molarity as follow:
${\text{Molarity }} = \dfrac{{10}}{{{\text{180}} \times 100}} \times 1000 = 0.55{\text{ M}}$

Note: Molarity is the number of moles of solute present per liter of solution. It is a concentration term that is used to define the concentration of any substance. It is temperature dependent because it includes volume and volume changes as temperature changes. Those terms which include only masses in their formula are temperature independent because mass does not change with the temperature for example, number of moles, mole fraction or molality. The other concentration terms are percentage by weight or percentage by volume, molality, and normality.