Question

What is the molarity of a solution that contains $40gms$ of $NaOH$ in $0.5L$ of solution?
A) $0mol/L$
B) $40mol/L$
C) $2mol/L$
D) $0.5mol/L$

Answer 1

We must have to remember that the number of moles is the given mass of compound divided by its molar mass. Molarity and Molality are two different concepts.

Complete step by step answer:
We need to remember that the molarity can be defined as the number of moles divided by the volume of a solution in Litres.
Unit of Molarity is $mol/L$.
$No.of moles = \dfrac{{{\text{Given mass}}}}{{{\text{Molar mass}}}}$
For calculating the number of moles of $NaOH$
Given mass= $40gm$
For Molar mass, Atomic mass of $Na = 23$; mass of $O = 16$; mass of $H = 1$
Therefore molar mass of $NaOH$
$23 + 16 + 1 = 40$
So no. of moles$= \dfrac{{40}}{{40}}$
$No.of moles = 1$
$Molarity = \dfrac{{{\text{No}}{\text{. of moles}}}}{{{\text{Volume of solution(L)}}}}$
Now we can substitute the given values we get,
$= \frac{1}{{0.5}}$
On simplification we get,
$\Rightarrow Molarity = 2mol/L$
Option A) this is an incorrect option as the solution is shown above, molarity of a solution that contains 40 gms of $NaOH$ in 0.5 L of solution is not 0 $mol/L$.
Option B) This is an incorrect option as $40$ is the molar mass of $NaOH$which cannot be the molarity in this case.
Option C) this is a correct option as calculated above the molarity comes out to be $2mol/L$.
Option D) this is an incorrect option as $1$ is the no. of moles in this case which cannot be the molarity according to the formula.

Note: We must have to remember that in this case molar mass and given mass turns out to be the same due to which no. of moles comes out to be $1$ . As we know that if the volume of a solution is given in $mL$ then we need to divide the volume by $1000$.