Question

What is the molarity of pure water?
(A). 18
(B). 5.6
(C). 55.5
(D). 100

Answer 1

- Hint: We know that the density of water is 1 Kg/L. Using this value, we can easily calculate the molarity of pure water. The mass of the pure water can be taken as 1 Kg and the volume can be taken as 1 L.

Formula Used: Molarity = ${\displaystyle \frac{Numberofmolesofsolute}{Volumeofthesolutioninlitre}}$

Complete step-by-step solution -
Molarity of a solution can be defined as the number of moles of the solute present per litre of the solution. Now, let us know about solutions. A solution is a mixture of two substances in which one of them is dissolved into the other. The substance which is dissolved is called a solute and the substance in which the other substance is dissolved is called the solvent.
We all know that the density of pure water is ${\displaystyle \frac{1g}{1ml}}$. As we can see from the formula that molarity is calculated in terms of litre, not millilitre so we have to convert the density term into the terms of litre.
Now, 1000ml = 1 L and 1000g = 1 Kg
So, ${\displaystyle \frac{1g}{1ml}}={\displaystyle \frac{1\times 1000g}{1\times 1000ml}}={\displaystyle \frac{1Kg}{1L}}$
Therefore, density of water is ${\displaystyle \frac{1Kg}{1L}}$
Now, from the definition, density is the ratio of mass and volume. So accordingly, from the density value of water we can get that,
Mass of pure water = 1 Kg
Volume of pure water = 1 L
Now we have to find the number of moles of water present in 1 kg of water. The number of moles of a substance can be calculated as the ratio of the weight of the substance to the gram molecular mass of the substance. Gram molecular mass is the same as that of molecular mass and the only difference is that it has a unit – gram.
We can calculate the molecular weight of water by calculating the sum of all the individual atomic masses. In water $(H_{2}O)$ there are 2 atoms of hydrogen and 1 atom of oxygen.
Atomic mass of oxygen = 16
Atomic mass of 2 hydrogens = $1\times 2=2$
So, molecular mass of water = 16+2=18
Gram molecular mass = 18 gm
Weight of pure water = 1 Kg = 1000 gm
So, number of moles of pure water = ${\displaystyle \frac{Weightofpurewater}{Grammolecularmass}}$
= ${\displaystyle \frac{1000}{18}}=55.56moles.$
Now, as we know, Molarity = ${\displaystyle \frac{Numberofmolesofsolute}{Volumeofthesolutioninlitre}}$
$\therefore Molarity={\displaystyle \frac{55.56moles}{1L}}$
Thus, the molarity of pure water is 55.56 moles per litre. So, option C is the correct one.

Note: We have to change the unit of density of water from gm/ml to Kg/L to calculate the molarity of pure water. This is because the molarity is calculated per litre of the solution and we have to make sure that the units are the same.