Question

The molality of the solution containing 20% w/w solution of NaOH is:
A. 4.5 m
B. 6.25 m
C. 0.3 m
D. 1 m

Answer 1

Hint: We know that molality is a method of expression of concentration of a solution. Molality is defined as the ratio of moles of solute to the volume of solvent in kg. Here, we have to use the formula of molality, that is, Molality = $\dfrac{{{\rm{Moles}}\,{\rm{of}}\,{\rm{solute}}}}{{{\rm{Volume}}\,{\rm{of}}\,{\rm{solvent}}\,{\rm{in}}\,{\rm{kg}}}}$.

Complete step by step answer:
Given that the solution consists of 20% w/w solution of NaOH. That means, the mass of the NaOH is 20 g and mass of solution is 100 g.
To calculate molality we need moles of solute and mass of solvent. So, first we calculate the number of moles of solute. The formula is,
Moles of solute = $\dfrac{{{\rm{Mass}}}}{{{\rm{Molar}}\,{\rm{mass}}}}$
The mass is given as 20 g and
Molar mass of NaOH = $23 + 16 + 1 = 40\,{\rm{g}}\,{\rm{mo}}{{\rm{l}}^{ - 1}}$
So, moles of NaOH=$\dfrac{{20\,{\rm{g}}}}{{40\,{\rm{g}}\,{\rm{mo}}{{\rm{l}}^{ - 1}}}} = \dfrac{1}{2}\,{\rm{mol}}$
Now, we have to calculate the mass of solvent. Given that mass of solution is 100 g and mass of solute is 20 g.
So, mass of solvent = 100-20 = 80 g
Now, we have to put the values of moles of solute and volume of solvent in the formula of molality.
Molality=$\dfrac{{{\rm{Moles}}\,{\rm{of}}\,{\rm{NaOH}}}}{{{\rm{Volume}}\,{\rm{in}}\,{\rm{kg}}}}$
$ \Rightarrow $Molality=$ = \dfrac{{\dfrac{1}{2}}}{{\dfrac{{80}}{{1000}}}} = 6.25\,{\rm{m}}$
Therefore, the molality of the solution is 6.25 m

So, the correct answer is Option B.

Note: Always remember that molarity is also used to express concentration of a solution. Molality is defined as the number of moles of solute present in 1 litre of solution. The difference between molality and molarity is that the latter is calculated with respect to the volume of the solution and former is calculated with respect to mass of solvent.