Question

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

Answer 1

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

& =d\times V \\\ & =1\dfrac{Kg}{L}\times 1L \\\ & =1Kg \\\ & =1000g \\\ \end{aligned}$$ From the mass of water we can calculate the number of moles in 1Kg of water. Thus number of moles in 1 Kg of water = $$\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{aligned} & =\dfrac{mass}{molar\text{ }mass} \\\ & =\dfrac{1000}{18} \\\ & =55.56moles \\\ \end{aligned}$$ Therefore the molarity of water $$\begin{aligned} & =\dfrac{\text{number of moles of the solute}}{\text{volume of the solution in liter}} \\\ & =\dfrac{55.56moles}{1L} \\\ & =55.56M \\\ \end{aligned}$$ Molarity of the pure water having a density of 1 gm/ml is 55.56 M. **Note:** In case of pure water molarity is equal to molality of the water. Molality = m = $$\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.