Question

$1$ molal solution is one that contains one mole of solute in:
A. ${\rm{1000}}\;{\rm{g}}$ of solvent
B. ${\rm{1}}{\rm{.0}}\;{\rm{L}}$ of solvent
C. ${\rm{1}}{\rm{.00}}\;{\rm{L}}$ of solution
D. \[{\rm{22}}{\rm{.4}}\;{\rm{L}}\] of solution

Answer 1

Hint: We know that, for any given solution, molarity is the total number of solute’s mole present in a liter of solution. So molarity depends on the volume of solution, whereas molality depends on the solvent mass.

Complete step by step answer:
We know that, the concentration of the solution can be measured in terms of molarity or molality. The number of moles of the component can be expressed in terms of molality and molarity. Let’s consider them in detail.
The number of moles present in the solution can be calculated by dividing mass of substance with their molar mass. The number of moles of the component which is present in a small amount in a liter solution is termed as the molarity of the solution. The S.I. unit of molarity is moles per liter. On the other hand, the number of moles of the component which is present in a small amount in ${\rm{1}}\;{\rm{kg}}$ or ${\rm{1000}}\;{\rm{g}}$of solvent is termed as the molality of the solution. The S.I. unit of molality is moles per kg.
So we can express molality mathematically as shown below.
$\begin{array}{c}
{\rm{Molality}}\left( m \right) = \dfrac{{{\rm{Moles}}\;{\rm{of}}\;{\rm{solute}}}}{{{\rm{Mass}}\;{\rm{of}}\;{\rm{solvent}}\;{\rm{in}}\;\left( {{\rm{1}}\;{\rm{Kg}}} \right)}}\\
 = \dfrac{{{\rm{Moles}}\;{\rm{of}}\;{\rm{solute}}}}{{{\rm{Mass}}\;{\rm{of}}\;{\rm{solvent}}\;{\rm{in}}\;\left( {{\rm{1000}}\;{\rm{g}}} \right)}}
\end{array}$
Hence, we can say that, $1$ molal solution is one that contains one mole of solute in ${\rm{1000}}\;{\rm{g}}$ of solvent.

Thus, the correct option is A.

Note:
Do not confuse Molality with molarity. In molarity we use the volume of the solution which is a variable quantity wrt temperature. However in molality the divisor is the mass of the solution which makes it a more reliable quantity.