Question

The density of \[2.05\text{ }M\] solution of the acetic acid in water is \[1.02\text{ }\dfrac{g}{mL}\] The molality of the solution is:
A) \[1.14\text{ }mol\text{ }k{{g}^{-1}}\]
B) \[3.28\text{ }mol\text{ }k{{g}^{-1}}\]
C) \[2.28\text{ }mol\text{ }k{{g}^{-1}}\]
D) \[0.44\text{ }mol\text{ }k{{g}^{-1}}\]

Answer 1

Hint: We know that the concentration refers to the amount of solute which dissolves in the unit amount of solution/solvent. Here concentration of solution can be represented in various forms such as amount of solute dissolve in given mass/volume of solvent as well as amount of solute present in given amount volume/mass of a solution.

Complete step-by-step answer:
Concentration of solution is also defined as quantity of solute which is present in a particular quantity of a solution/solvent. Thus there are various different methods to define concentration of a solution like Molarity, Molality. Also the most common unit among concentration terms is molarity. It's much important as well as useful for calculating stoichiometry of reaction in solution. It’s defined as number of mole of a solute which is present in $1litre$ of solution as it's given as:
So, suppose volume of solution is around \[1000\text{ }ml\]
Here we have, \[1.02\text{ }gm\] of acetic acid in \[1\text{ }ml\] of soln.
\[1020\text{ }gm\] in \[1000\text{ }ml\] of solution.
Number of moles \[=\text{ }2.05M\text{ }\times \text{ }1\text{ }lit\text{ }=\text{ }2.05\text{ }mol\]
Mass of solute \[=\text{ }n\text{ }\times \text{ }Mwt\text{ }=\text{ }2.05\text{ }\times \text{ }60\text{ }=\text{ }123\text{ }gm\]
Mass of solvent \[=\text{ }1020\text{ }\text{ }123\text{ }=\text{ }897\text{ }gm\] and molality is given by, \[Molality\text{ }=\text{ }\dfrac{123}{60}\times \dfrac{1000}{897}\text{ }=\text{ }2.28\text{ }mol\cdot k{{g}^{-1}}\]
Therefore, molality of the solution is \[2.28\text{ }mol\cdot k{{g}^{-1}}\]

Note: Note that the concentration of solution is one of a type of macroscopic property. It also can be expressed in various forms like both quantity wise as well as quality wise. Thus quality can be quality can express as dilute solution or concentration of solution as well as the quantity wise it could be expressed as saturated or as unsaturated.