Question

A solution made by dissolving $40{\text{ g}}$ ${\text{NaOH}}$ in $1000{\text{ g}}$ of ${{\text{H}}_{\text{2}}}{\text{O}}$ is:
A. $1{\text{ molar}}$
B. $1{\text{ normal}}$
C. $1{\text{ molal}}$
D. None of these

Answer 1

We are given that $40{\text{ g}}$ of ${\text{NaOH}}$ is dissolved in $1000{\text{ g}}$ of water. $1000{\text{ g}}$ of water means $1{\text{ kg}}$ of water. Thus, the solute is dissolved in one kilogram of solvent. From this we can determine the concentration of the solution.

Formulae Used:
${\text{Number of moles}}\left( {{\text{mol}}} \right) = \dfrac{{{\text{Mass}}\left( {\text{g}} \right)}}{{{\text{Molar mass}}\left( {{\text{g/mol}}} \right)}}$

Complete answer:
First we will calculate the number of moles of ${\text{NaOH}}$ in $40{\text{ g}}$ of ${\text{NaOH}}$ using the equation as follows:
${\text{Number of moles}}\left( {{\text{mol}}} \right) = \dfrac{{{\text{Mass}}\left( {\text{g}} \right)}}{{{\text{Molar mass}}\left( {{\text{g/mol}}} \right)}}$
Substitute $40{\text{ g}}$ for the mass of ${\text{NaOH}}$, $40{\text{ g/mol}}$ for the molar mass of ${\text{NaOH}}$ and solve for the number of moles of ${\text{NaOH}}$. Thus,
${\text{Number of moles of NaOH}} = \dfrac{{{\text{40 g}}}}{{40{\text{ g/mol}}}}$
${\text{Number of moles of NaOH}} = 1{\text{ mol}}$
Thus, the number of moles of ${\text{NaOH}}$ in $40{\text{ g}}$ of ${\text{NaOH}}$ are $1{\text{ mol}}$.
We are given that $1{\text{ mol}}$ of ${\text{NaOH}}$ are dissolved in $1000{\text{ g}} = 1{\text{ kg}}$ of ${{\text{H}}_{\text{2}}}{\text{O}}$. Thus, the concentration of the solution when the number of moles of solute are dissolved in a kilogram of solvent is known as molality. The units of molality are ${\text{mol/kg or m}}$. Thus,
$\dfrac{{1{\text{ mol NaOH}}}}{{1{\text{ kg }}{{\text{H}}_2}{\text{O}}}} = 1{\text{ molal}}$
Thus, a solution made by dissolving $40{\text{ g}}$ ${\text{NaOH}}$ in $1000{\text{ g}}$ of ${{\text{H}}_{\text{2}}}{\text{O}}$ is $1{\text{ molal}}$.

**Thus, the correct option is (C) $1{\text{ molal}}$.

Additional Information:**
$1{\text{ molar}}$ solution is formed when moles of solute are dissolved in one litre of solvent. The unit of concentration is known as molarity. It is expressed in ${\text{mol/L}}$.
$1{\text{ normal}}$ solution is formed when the number of gram equivalent weights of solute are dissolved in one litre of solvent. The unit of concentration is known as normality. It is expressed in ${\text{g/L}}$.

Note:
Molar, normal and molal are all the units used to express the concentration of solution. Molality of a solution is affected by various factors such as temperature and pressure. This is because the volume of solution changes when the temperature and pressure is changed.