Question

What is the molarity of $40\% $ NaOH solution (by mass) if density of solution is $1.2g/ml$?
a) 10$M$
b) 12$M$
c) 5$M$
d) 6$M$

Answer 1

Hint: we can find out the volume of the solution by using given density and then putting the value of volume in molarity formula.Molarity is defined as the number of moles of solute to the volume of solution in litres. Molarity is temperature dependent as volume changes with temperature.whereas density is defined as mass by volume.

Complete step by step answer:
According to the definition of molarity
Molarity ($M$) = $\dfrac{n}{v}$
Where, $n$ is the number of moles of solute and $v$ is volume of the given solution in litres.
according to definition of density
$Density$ = $\dfrac{{mass}}{{volume}}$ $ \Rightarrow $ $1.2$ = $\dfrac{{100}}{v}$
$ \Rightarrow $ $v$ = $\dfrac{{100}}{{1.2}}$ = $83.3$
Hence the volume of the given solution is $83.3ml$.
Now, we can easily find out the molarity of $40\% $ NaOH solution by first calculating the number of moles of solute by using the formula $n$ = $\dfrac{w}{W}$ where, $w$ is given mass of solute and $W$ is molar mass of solute .
So the number of moles of solute $n$ = $\dfrac{{40}}{{40}}$ = $1$ mol
Now putting the value of $n$ and $v$ in molarity formula, we get
 $M$ = $\dfrac{{n \times 1000}}{v}$ ( here we are multiplying by $1000$ to convert volume in litres )
$ \Rightarrow $ $M$= $\dfrac{{1 \times 1000}}{{83.3}}$ = $\dfrac{{1000}}{{83.3}}$= $12.00$
The molarity of $40\% $ NaOH solution is $12M$.

So, the correct option is b.

Note: Do not get confused between molarity and molality. Both the concentration terms are quite similar but have a huge difference between them. Molality is defined as the number of moles of solute to mass of solvent in $kg$ and it is denoted by m. Molality is temperature independent as it does not depend on volume.