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 = $${\displaystyle \frac{\text{number of moles of the solute}}{\text{volume of the solution in liter}}}$$

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
$$\begin{array}{rl}& =d\times V\\ & =1{\displaystyle \frac{Kg}{L}}\times 1L\\ & =1Kg\\ & =1000g\end{array}$$
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 = $${\displaystyle \frac{mass}{molarmass}}\to (1)$$

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
$$\begin{array}{rl}& ={\displaystyle \frac{mass}{molarmass}}\\ & ={\displaystyle \frac{1000}{18}}\\ & =55.56moles\end{array}$$

Therefore the molarity of water
 $$\begin{array}{rl}& ={\displaystyle \frac{\text{number of moles of the solute}}{\text{volume of the solution in liter}}}\\ & ={\displaystyle \frac{55.56moles}{1L}}\\ & =55.56M\end{array}$$
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 = $${\displaystyle \frac{\text{number of moles of the solute}}{1Kgofthesolvent}}$$
Molality can be calculated as the ratio of the number of moles of solute to one Kg of the solvent.