Question

Calculate the Molarity of pure water using the density to be $1000\text{ kg }{{\text{m}}^{-3}}$

Answer 1

Hint: The molarity of the solution is the ratio of the number of moles to the volume of the solution. The number of moles can be calculated by dividing the given mass to the molar mass of the compound.


Complete step by step answer:
Molarity: The molarity of the solution is defined as the number of moles of the solute which is present in 1 L volume of the solution. We can represent it by the symbol, M.
Its formula is:
\[Molarity=\frac{\text{Moles of the solute}}{\text{Volume of the solution}}\]
Moles of the component is defined as the ratio of a given mass to the molar mass.
Its formula is:
\[Moles=\frac{given\text{ }mass}{\text{molar mass }}\]
Given the density of pure water is $1000\text{ kg }{{\text{m}}^{-3}}$
We know 1 kg of water contains 1000 g of water.
$1\text{ kg = 1000 g}$
And we know that a 1-meter cube is equal to 1000 liter.
$1\text{ }{{\text{m}}^{3}}=\text{ 1000L}$
So we can express the density of water in $g\text{ }{{\text{L}}^{-1}}$.
So, the$1000\text{ kg }{{\text{m}}^{-3}}$is equal to:
$\frac{1000}{1000}\text{ x 1000= 1000 g}{{\text{L}}^{-1}}$
So, the density is $1000g{{L}^{-1}}$
From this, the mass of the water is 1000 g in the volume of 1 Liter of solution.
The molecular mass of water = $18\text{ g mo}{{\text{l}}^{-1}}$
The moles of the water can be calculated as:
\[Moles=\frac{given\text{ }mass}{\text{molar mass }}=\frac{1000}{18}=55.55\]
Now, we know that the volume of the solution is 1 L, the molarity of the solution is calculated by:
\[Molarity=\frac{\text{Moles of the solute}}{\text{Volume of the solution}}=\frac{55.55}{1}=55.55\text{ M}\]

So the Molarity of pure water is 55.55 M.


Note: The volume of the solution must be taken in liters only. If the concentration or density of the solute is given in kg or any other unit, it has to be converted into grams because these are the standard units taken for the calculation of Molarity.