Question

How to calculate the molarity of pure water if its density is given as 1000kg/m³.

Answer 1

Definition of molarity:

Molarity of solution is a weight by volume relationship to represent its strength and is defined as 'the number of moles of solute dissolved in one litre of solution.

Mathematically it is represented as,

$\frac{\mathrm{Moles}\mathrm{of}\mathrm{solute}}{\mathrm{Volume}\mathrm{of}\mathrm{solution}\left(\mathrm{l}\right)}$

Step 1: Calculation of molar mass of water

$\mathrm{Density}=\frac{\mathrm{Mass}}{\mathrm{Volume}}$
1 liter of water = 1 kg.
( Since Density is$1000\mathrm{kg}{\mathrm{m}}^{-3}$)

Thus, 1000 ml of water = 1 kg.
(Since, $1\mathrm{liter}=1000\mathrm{ml}$)

Now, the Mass of Water$=1\mathrm{kg}.$
$=1000g.$
One mole of water is made up of 2 moles of hydrogen atoms and 1 mole of oxygen atoms.

Mass of 1 mole of Hydrogen atoms= $1\mathrm{g}{\mathrm{mol}}^{-1}$

Mass of 1 mole of Oxygen atoms = $16\mathrm{g}{\mathrm{mol}}^{-1}$

Mass of two moles of hydrogen atoms

$$\begin{gathered} =2\mathrm{x}1\mathrm{g}{\mathrm{mol}}^{-1} \\ =2\mathrm{g}{\mathrm{mol}}^{-1} \end{gathered}$$

Step 2 : Calculation of molar mass of oxygen

Mass of one mole of oxygen atoms

$$\begin{gathered} 1\mathrm{x}16\mathrm{g}{\mathrm{mol}}^{-1} \\ =16\mathrm{g}{\mathrm{mol}}^{-1} \end{gathered}$$

On adding all the above-obtained values we get,

Step 3: Calculation of total mass

Total Mass of one mole of water

$$\begin{gathered} 2\mathrm{g}{\mathrm{mol}}^{\mathit{-}\mathit{1}}+16\mathrm{g}{\mathrm{mol}}^{-1} \\ =18\mathrm{g}{\mathrm{mol}}^{-1} \end{gathered}$$

The molar mass of water = $18\mathit{}\mathrm{g}{\mathrm{mol}}^{\mathit{-}\mathit{1}}$

Therefore,

Step 4: Calculation of Molarity

Molarity

$$\begin{gathered} =\frac{1000}{18} \\ =55.56\mathrm{mol}{\mathrm{L}}^{-1} \end{gathered}$$

The molarity of pure water, if its density, is given as $1000\mathrm{kg}{\mathrm{m}}^{-3}\mathrm{is}55.56\mathrm{mol}{\mathrm{L}}^{-1}$.