Question

Molarity of $1\mathrm{m}$ aqueous $\mathrm{NaOH}$ solution [Density of the solution Is $1.02\mathrm{g}{\mathrm{ml}}^{-1}$]

• A. $0.98\mathrm{M}$
• B. $1.2\mathrm{M}$
• C. $1.02\mathrm{M}$
• D. $1\mathrm{M}$

Answer 1

The correct option is A

$0.98\mathrm{M}$

The explanation for correct answers:

Option A $0.98\mathrm{M}$

Step 1 Weight of the solution.

The density of the solution is $1.02{\mathrm{gml}}^{-1}$ .

$1\mathrm{m}$ is defined as when one mole of solute is present in $1\mathrm{kg}$ of the solvent.

Therefore, the molality is $1\mathrm{m}$ that means, 1 mole of $\mathrm{NaOH}$ in $1\mathrm{kg}$ of the $\mathrm{NaOH}$ solution.
The molar mass of the $\mathrm{NaOH}$ is $40\mathrm{g}$.
$\mathrm{Weight}\mathrm{of}\mathrm{the}\mathrm{solute}\mathrm{NaOH}\left(w\right)=\mathrm{Number}\mathrm{of}\mathrm{moles}\left(n\right)\times \mathrm{Molar}\mathrm{mass}\left(m\right)$
Substituting the values, we get

$$\begin{gathered} \mathrm{w}=1\times 40 \\ \mathrm{w}=40\mathrm{g} \end{gathered}$$

Weight of $\mathrm{NaOH}$ is $40\mathrm{g}$.

The weight of the solvent is $1\mathrm{kg}$ that is $1000g$
The total weight of the solution is;
$W_{solution}=W_{Solvent}+W_{solute}$
Where,

$W_{Solution}$ is the weight of the solution.
$W_{Solvent}$ is the weight of the solvent.
$W_{Solute}$ is the weight of the solute.

Substituting the values,

$$\begin{gathered} W_{Solution}=1000+40 \\ {W}_{Solution}=1040g \end{gathered}$$

Step 2 Volume of the solution

The density is given by,
$\mathrm{D}=\frac{\mathrm{M}}{\mathrm{V}}$
Where,

$\mathrm{D}$ is the density of the solution
$\mathrm{M}$ is the weight of the solution
$\mathrm{V}$ is the volume of the solution
Now substituting the values,
$$\begin{gathered} \mathrm{V}=\frac{\mathrm{M}}{\mathrm{D}} \\ \mathrm{V}=\frac{1040}{1.02} \\ \mathrm{V}=1019.608\mathrm{ml} \end{gathered}$$

Step 3 Molarity of the solution:

The molarity is given by,

$\mathrm{M}=\frac{{\mathrm{n}}_{\mathrm{solute}}}{\mathrm{V}(\mathrm{in}\mathrm{litre})}$
Where,

$\mathrm{M}$ is the molarity
${\mathrm{n}}_{\mathrm{solute}}$ is the number of moles of the solute
$\mathrm{V}$ is the volume of the solution
Now, substituting the values we get,
$$\begin{gathered} \mathrm{M}=\frac{1\times 1000}{1019.60} \\ \mathrm{M}=0.98\mathrm{M} \end{gathered}$$
The molarity of the solution is $0.98\mathrm{M}$

Hence, Option A $0.98\mathrm{M}$ is correct.