Question

20g of NaOH (molar mass = 40g/mol) is dissolved in $500c{{m}^{3}}$ of water. Molality of the resulting solution is:
[A] 0.1m
[B] 0.5m
[C] 1.5m
[D] 1.0m

Answer 1

Hint: To solve this question, start by finding the number of moles of solute by dividing its mass used by its molecular weight. Then calculate the mass of solute by using its density and volume and do not forget to convert it into kilograms. Use this to find the molality as molality is the number of moles of solute per kilogram of solvent.

Complete step by step answer:
We know that we can measure concentration of a solution in different concentration terms like molarity, normality and molality.
Molality is the number of moles of solute per kilogram of the solvent.
So first of all we have to calculate the number of moles of solute i.e. NaOH here. We can calculate the number of moles by dividing the mass used by its molecular weight.
Molecular weight of NaOH = 40g/mol and the mass of sodium hydroxide used here is 20g.
Therefore, we can write that, number of moles of NaOH = $\dfrac{20g}{40g/mol}=0.5mol$
Now we have to calculate the mass of the solvent in kilograms. Here the solvent is water. We can use the relation that mass is equal to density times volume.
As we know, the density of water is 1g/cc and the volume of water used here is 500cc.
Therefore, mass of water (in grams) = $1g/cc\times 500cc=500g$
Now, to convert it to kilogram, we have to divide it by thousand as 1kg is equal to 1000g.
Therefore, mass of water (in kilograms) = $\dfrac{500}{1000}=0.5kg$
Now, we know the number of moles of solute and mass of solvent in kilogram therefore, we can

calculate the molality of the solution-
     \[molality=\dfrac{no.of\text{ moles of solute}}{mass\text{ of }solute\text{(kg)}}=\dfrac{0.5mol}{0.5kg}=1mol/kg=1molal\]
We can see from the above calculation that the molality of the solution is 1molal or 1m.
So, the correct answer is “Option C”.

Note: We should not be confused between normality, molarity and molality of a solution even though we use them for the same purpose i.e. concentration of solution. Molarity is the number of moles of solute per litre of solvent. Normality of a solution is the gram equivalent of solute per litre of the solvent and we’ve already discussed molality above, which is the number of moles of solute per kilogram of solvent.