Question

The molarity of urea (molar mass 60g/mol) solution by dissolving 15g of urea in $500c{{m}^{3}}$ of water is?
[A] $2\text{ mol d}{{\text{m}}^{-3}}$
[B] $0.5\text{ mol d}{{\text{m}}^{-3}}$
[C] $0.125\text{ mol d}{{\text{m}}^{-3}}$
[D] $0.0005\text{ mol d}{{\text{m}}^{-3}}$

Answer 1

Hint: Molarity is a measure of concentration of solution. It is calculated by dividing the number of moles of solute by the volume of the solvent in litres. We can use the mass and molar mass of urea to find out its number of moles and then divide it by the volume to get the molarity.

Complete step by step answer:
We use the term molarity for the measurement of concentration of a solution. We know that the concentration is the amount of solvent dissolved in the solution.
Molarity is the measure of concentration of a given solution and it is given as the number of moles of solute dissolved per litre of solvent.
In the given question, 15g of urea is dissolved in 500$c{{m}^{3}}$ of water. To find out the molarity, firstly we have to find the number of moles of urea.
We can find the number of moles dividing the mass of the solute (in grams) dissolved in the solvent by the molar mass ( in g/mol) of the solute.
Therefore, the number of moles of urea will be the mass of urea dissolved in water divided by the molar mass of urea which is given to us.
Number of moles of urea = $\dfrac{Mass}{Molar\text{ mass}}=\dfrac{15g}{60g/mol}0.25mol$.
Now, the next part is the volume of the solvent and it is given as 500 $c{{m}^{3}}$ but we have to convert it to litre.
We know that 1 cubic-cm is equal to 0.001 L or 1L is equal to 1000 cubic-cm.
Therefore, 500 cubic-cm will be equal to 0.5L.

Now that we know the number of moles of solute and the volume of the solution we can find the molarity of the solution easily by putting these values in the molarity equation.
Molarity = $\dfrac{number\text{ of moles of solute}}{\text{ litre of solvent}}=\dfrac{0.25}{0.5}mol/d{{m}^{3}}=0.5mol/d{{m}^{3}}$
As we can see from the above calculation, the molarity of the solution is $0.5mol/d{{m}^{3}}$.
So, the correct answer is “Option B”.

Note: We should not be confused between normality, molarity and molality. All of these areas measure the concentration of solution but they are not the same. Normality is the number of equivalents per litre of solvent and molality is the number of moles of solute per kilogram of the solvent and as we have discussed above, molarity is the number of moles of solute per litre of the solvent.