Q146CP - Chemistry: Molecular Nature Of Matter And Change

Question

Derive a general equation that expresses the relationship between the molarity and the molality of a solution. Why are the numerical values of these two terms approximately equal for very dilute aqueous solutions?

Step-by-Step Solution

Answer

Numerical values of molarity and molality are approximately equal for very dilute solutions because for all aqueous solution total mass of solvent is approximately equal to the total volume of solution.

Relationship between molarity and molality:

Molarity is defined as the number of moles of solute dissolved in one liter of solution.

Molality is defined as the number of moles of solutes in per kilogram of solvent. 

 

This clearly indicates that molarity is a function of the volume of the solution. A change in the temperature of the system can affect the molarity of the solution.

The relationship between the molarity and molality of the solution:

For a very dilute solution, the mass of solute is very negligible when compared with the mass of the solution. Hence, you can neglect that term. Therefore, you have, the equation for molality as,

$\text{Molality}=\frac{\text{moles of solute}}{(\text{density of solution}\times \text{volume of solution})}$  

The equation for molarity as,

$\text{Molarity}=\frac{\text{moles of solute}}{\text{volume of solution}}$  

 

Putting the above equation into the equation of molarity, you get

$\text{Molality}=\frac{\text{molarity}}{\text{density of solution}}$ 

 

Hence, the relation between molarity and molality is,

$\text{molarity}=\text{molality}\times \text{density of solution}$ 

Numerical values of these two terms approximately equal:

Molarity and molality for very dilute aqueous solution is approximately the same because for all aqueous solution total mass of solvent is approximately equal to the total volume of solution and the density of solutions is relatively close to  $1\raisebox{1ex}{$\text{g}$}\!\left/ \!\raisebox{-1ex}{$\text{mL}$}\right.$.