Question

The density of 3M solution of NaCl is 1.25g/mL. Calculate molality of the solution.

Answer 1

Hint: In the given question, we have been provided with the molarity and density of the solution. Therefore, we need to use these two terms and establish such a relation so as to calculate the molality of the solution.


Complete step by step solution:
Concentration is basically a measure to find the amount of solute present in solvent which together forms a solution. Molality is a term to express the concentration of a solution.
Molality of any solution is defined as, “the number of moles of solute present per kg of solvent”. Therefore, its unit is mol/kg.
It is denoted by ‘m’.

The formula of molality is –
\[\text{Molality=}\frac{\text{moles of solute (mol)}}{\text{weight of solvent (kg)}}\text{x}1000\].
Molality can be related to molarity using the density of the solution as –
\[m=\frac{M\text{ x }1000}{1000\rho -M\text{ x }w}\]
Where,
M = Molarity = moles solute/Litre solution
M = molality = moles solute/kg solvent
\[\rho \]= density = g solution/ mL solution
w = molecular weight (molar mass) of solute in g/mole = 58.44 g/mol
Therefore, putting all the values, we get –
\[m=\frac{\text{3 x }1000}{(1000\text{ x }1.25)-3\text{ x 58}\text{.44}}\]
m = 2.79 mol/kg.
Therefore, the answer is – The molality of the given solution is 2.79 mol/kg.

Additional information: We can convert Molality to Molarity by the following formula: \[M=\frac{1000\text{x }m\text{ x}\rho }{1000+\text{m x w}}\].


Note: Students often confuse between molarity and molality. Molarity is the method to define concentration of a solution in units of mol/L. Molarity of any solution is defined as, “number of moles of solute per litre of solution”.
It is represented by the symbol ‘M’.
The formula of molarity is –
\[\text{Molarity=}\frac{\text{moles of solute (mol)}}{\text{volume of solution (L)}}\text{x}1000\].