Question

An aqueous solution of $NaOH$ is 40% by weight of solution. Thus, its molarity is
A.$10.1molal$
B.$10.4molal$
C.$20.15molal$
D.$16.67molal$

Answer 1

Hint:In this question we will be learning about the number of moles in a solution and how to calculate the moles present in one given solution. Then, we will see how to calculate the molality of the solution using the given parameters.

Complete step by step answer:
Let us first consider the following,
Let the weight be $100g$
So, as per the given parameters in the question, 40% $NaOH$ $w/w$ is simply considered as $40g$.
Now, calculating the,
number of moles of $NaOH$ = $n$ = $\dfrac{{mass}}{{Molarmass}}$ = $\dfrac{{40}}{{40}}$ = 1
Now, let’s next calculate the,
Weight of the Solvent = 100 – 40 = $60g$
Then, Let’s calculate the Molality of the solution,
Molality = $\dfrac{{moles(solute)}}{{mass(solvent)}}$
Now, substituting the values we got in the above equation, we get,
Molality = $\dfrac{{1000}}{{60}}$ = $16.67molal$
And hence option D is the correct answer.

Additional information
What is molality?
Molality is otherwise called molal concentration. It is a proportion of solute concentration in a solution.
What is a mole?
The mole is the unit of estimation for measure of substance in the International System of Units (SI). A mole of a substance or a mole of particles is characterized as precisely $6.022140 \times {10^{23}}$ particles, which might be ions, atoms, particles, or electrons. So, for particles, $1mol$ = $6.02214076 \times {10^{23}}$ .

Note:
You need to remember the formulae of number of moles, molality, weight of solvent and also need to remember the conversions. One needs to identify which is solvent and which one is solute so that they can substitute correct values to find out molality.