Question

How are 0.50m $N{{a}_{2}}C{{O}_{3}}$ and 0.50M $N{{a}_{2}}C{{O}_{3}}$ different?

Answer 1

Hint: Think about what the units ‘m’ and ‘M’ represent. The question is asking how both are different. Revise the concept of concentration of solution of solids in liquids to get the answer.

Complete step by step solution:
- Let’s have a look at the question. It is asking us how 0.5m and 0.5M Sodium carbonate solutions are different from each other. So, let us first see what ‘m’ and ‘M’ represent.
-‘m’ is the molality of a s solution and ‘M’ is the molarity of a solution.
- Molality (m) is defined as the number of moles of solute dissolved in one kilogram of solvent. Molality is the best way to express the concentration of a solution. Molality is a temperature independent quantity. Molality has the units ‘m’ or ‘mol/kg’ or ‘molal’.
\[\text{Molality=}\dfrac{\text{number}\,\text{of}\,\text{moles}\,\text{of}\,\text{solute}}{\text{1}\,\text{kg}\,\text{of}\,\text{solvent}}=\dfrac{n}{W}\] where n is the number of moles and W is the mass of solvent in kg.
- Molarity (M) is defined as the number of moles of solute dissolved in one litre of the solution. It is a good way of representing the concentration of solution and is more commonly used. But molarity is a volume dependent quantity and volume changes with change in temperature. So, molarity is a temperature dependent quantity. Molarity has the units ‘M’ or ‘mol/L’ or ‘molar’.
\[\text{Molarity=}\dfrac{\text{number}\,\text{of}\,\text{moles}\,\text{of}\,\text{solute}}{\text{1}\,L\,\text{of}\,\text{solution}}=\dfrac{n}{V}\] where n is the number of moles and V is the volume of solution in litres.
- Molarity and molality are completely different concentrations. One describes the concentration in the number of moles with respect to volume of solution and other with respect to weight of the solvent.
-Hence, it is proved that, 0.50m $N{{a}_{2}}C{{O}_{3}}$ and 0.50M $N{{a}_{2}}C{{O}_{3}}$ are different.

Note: Remember molarity is number of moles of solute in one litre of solution and molality is the number of moles of solute in one kilogram of solvent.