Question

The density of 3 molal solution of NaOH is 1.110 g/mL. The molarity of the solution is:
A) 2.69 M
B) 2.97 M
C) 4.57 M
D) 6.70 M

Answer 1

Molarity is defined as the number moles of a solute present in one liter of a solution and it is denoted with a symbol ‘M’.
Molality is defined as the number of moles of solute present in 1 kg of a solvent and it is denoted with a symbol ‘m’.
The relationship between molality and molarity is as follows.

$M=\dfrac{1000md}{1000+m{{M}_{o}}}$

Here ${{M}_{o}}$= Molar mass
d = density
m = molality of the solution
M = molarity of the solution

Complete answer:
In the question it is given that the density of NaOH solution d = 1.110 g/mL
The molality of the NaOH solution = 3 molal
We know the molecular weight of NaOH, ${{M}_{o}}$ = 40 g
Substitute all the values in the following formula

$M=\dfrac{1000md}{1000+m{{M}_{o}}}$

$M=\dfrac{1000\times 3\times 1.110}{1000+3\times 40}$

$M=\dfrac{3330}{1120}=2.973$
Therefore the molarity of the solution is 2.973 mol/L.

So, the correct option is B.

Note: In case of an infinite dilute aqueous solution, molality (m) of the solution is equal to molarity (M) of the solution. Their volume will be equal to its mass.
Therefore, 1 kg of solution will weigh 1 L.
The number of moles of solute present in per liter of the solvent is equal to the number of moles of solute present in per kg of solvent.