Question

Calculate the molarity of pure water if its density at room temperature is 1.0 kg/cm.

Answer 1

Molarity

• Molarity is defined as the number of moles of solute per volume of solution in liters.
• Molarity = $\frac{\mathrm{Number}\mathrm{of}\mathrm{moles}\mathrm{of}\mathrm{solute}}{\mathrm{Volume}\mathrm{of}\mathrm{solution}\left(\mathrm{L}\right)}$

Calculation of molarity from density

Step 1: Determination of the mass of 1 l of water
Density = $\frac{\mathrm{Mass}}{\mathrm{Volume}}$
$\mathrm{Mass}\mathrm{of}1\mathrm{L}\mathrm{of}\mathrm{water}=\mathrm{density}\mathrm{of}\mathrm{water}\times \mathrm{volume}$
Mass of 1 L of water = 1000 g

Step 2: Determination of the number of moles in the water
Number of moles of water = $\frac{\mathrm{Mass}\mathrm{of}\mathrm{water}}{\mathrm{Molar}\mathrm{mass}\mathrm{of}\mathrm{water}}$
The molar mass of water = 18 g/mol
Number of moles of water = $\frac{1000\mathrm{g}}{18{\displaystyle \raisebox{1ex}{$\mathrm{g}$}\!\left/ \!\raisebox{-1ex}{$\mathrm{mol}$}\right.}}$
The number of moles of water = 55.56 mol

Step 3: Determination of Molarity
Molarity = $\frac{55.56\mathrm{mol}}{1\mathrm{L}}$
Molarity = 55.56 mol/L

Therefore, the molarity is 55.56 mol/L