Question

Calculate molarity of pure water. (d = 1g/ml)

Answer 1

Hint: Molarity of a solution can be defined as the number of moles of solute present in per liter of the solution. It can be represented with a symbol ‘M’.
To know the molarity of the water there is a formula to calculate.
Molarity = \[\dfrac{\text{number of moles of the solute}}{\text{volume of the solution in liter}}\]

Complete step by step answer:
In the question they gave the density of the water as 1 g/ml.
We can also write the density of water as 1Kg/L as 1000 gm = 1 Kg and 1000 ml = 1 L.
Thus the mass of the one liter of water is = \[d\times V\]
Where d = Density of the water
And V = volume

Substitute the values of density and volume in the above formula to get mass of the water.
Mass of the water
\[\begin{align}
 & =d\times V \\
 & =1\dfrac{Kg}{L}\times 1L \\
 & =1Kg \\
 & =1000g \\
\end{align}\]
From the mass of water we can calculate the number of moles in 1Kg of water.
Thus number of moles in 1 Kg of water = \[\dfrac{mass}{molar\text{ }mass}\to (1)\]

We know that the mass of water = 1000 gm and molar mass (molecular weight) of the water is 18.
Substitute these known values in equation 1 to get the number of moles present in 1 Kg of water.
Number of moles in 1 Kg of water
\[\begin{align}
 & =\dfrac{mass}{molar\text{ }mass} \\
 & =\dfrac{1000}{18} \\
 & =55.56moles \\
\end{align}\]

Therefore the molarity of water
 \[\begin{align}
 & =\dfrac{\text{number of moles of the solute}}{\text{volume of the solution in liter}} \\
 & =\dfrac{55.56moles}{1L} \\
 & =55.56M \\
\end{align}\]
Molarity of the pure water having a density of 1 gm/ml is 55.56 M.

Note: In case of pure water molarity is equal to molality of the water.
Molality = m = \[\dfrac{\text{number of moles of the solute}}{1Kg\text{ }of\text{ }the\text{ }solvent}\]
Molality can be calculated as the ratio of the number of moles of solute to one Kg of the solvent.