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?

Answer 1

For very diluted aqueous solutions, molarity and molality are roughly equivalent.

What is Molarity ?

Molarity (M) is the amount of a substance in a certain volume of solution. Molarity is defined as the moles of a solute per liters of a solution. Molarity is also known as the molar concentration of a solution.

The relation between molarity (M) and molality (m)  is given by

$\(m = \frac{1000M}{1000p - MM_1}\)$

where (ρ = density of solution (mg/mL) , M1 = molecular weight of solute. Molarity and molality are terms used to express the concentration of a solution. The quantity of the solute in the solution determines its concentration. Molarity and Molality are used to quantitatively express the strength of the solution (concentrated or dilute).  Molarity is concentration expressed in terms of moles per unit volume. Molality is concentration expressed in terms of moles per unit mass.

In extremely diluted solutions, there is an excessive amount of solvent compared to solute. Therefore, the amount of solution and the amount of solvent are about equal.

Therefore Molarity and molality for very dilute aqueous solution is approximately equal.

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