
Concept explainers
Interpretation:
The relation between molality and molarity is to be derived, and the fact that, for dilute aqueous solutions, molality is equal to molarity is to be proved.
Concept introduction:
Molality is defined as the ratio of the number of moles of the solute to the mass of the solvent (in kilograms). It is expressed as follows:
Here,
Molarity is defined as the ratio of the number of moles of the solute to the volume of the solution (in liters). It is expressed as follows:
Here,
Density is defined as the ratio of mass to volume. It is expressed as follows:
Here,

Answer to Problem 118AP
Solution:
(a)
The relation between molality and molarity has been derived.
(b)
For dilute solutions, molality and molarity are equal.
Explanation of Solution
a)Drive the equation relating the molality and molarity of a solution
The mass of the solvent (in kilograms) is calculated as follows:
Or
Consider
Density is calculated as follows:
Rearrange the above equation for the calculation of mass as follows:
Calculate the mass of the solution from the molarity and its molar mass, as follows:
Number of moles is calculatedas follows:
By substituting equation (3) in equation (2), we will get:
Rearrange the above equation for the calculation of mass as follows:
Substituting these expressions into equation (1),
Or
Molality is defined as the number of moles of the solute divided by the mass of the solvent (in kilograms).
It is expressed as follows:
Rearrange the above equation for the calculation of mass as follows:
Consider
Substituting the above equation back into equation (4) gives the following equation:
Taking the inverse of both sides of the equation gives the following equation:
or
Hence, the above equation is the relation between the molality of a solution to its molarity.
b) For any aqueous solution, molality is equal to molarity.
The density of water is approximately
In dilute solutions,
Consider a
The derived equation reduces to the equation given below:
When the density becomes equal to
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