Question

For dilute aqueous solutions, molality and molarity concentration values are similar. Why?

Short answer

For dilute solutions, the volume of the solution (in liters) is almost equal to the mass of the solvent (in kilograms), due to the density of water. Thus, since molarity is moles of solute per liter of solution and molality is moles of solute per kilogram of solvent, their values become very close in dilute solutions.

Step-by-step solution

Defining Molarity and Molality

Molarity (\(M\)) is a measure of concentration of a solution, defined as the number of moles of solute per liter of solution. Molality (\(m\)) is another measure of concentration, defined as the number of moles of solute per kilogram of solvent.

Understanding the Nature of Dilute Solutions

In a dilute solution, the amount of solute is much less than that of the solvent. Therefore, the volume of the solvent is very close to the volume of the solution. Moreover, for dilute aqueous solutions, the density of the solution is close to that of water, which is approximately 1 kg/L.

Comparing Molarity and Molality in Dilute Solutions

Now, if the solution is dilute, its volume in liters is approximately equal to the mass of water in kilograms, because of the density of water being about 1kg/L. Therefore, the amount of solute per liter of solution (molarity) and the amount of solute per kilogram of water (molality) will be nearly the same.