Calculate Molarity of Urea Solution from Density

To calculate the molarity of the urea solution, we follow these step-by-step calculations:

1. Calculate the number of moles of solute (urea):
   The formula for moles ($n$) is:
   $n = \frac{\text{Mass of urea}}{\text{Molar mass of urea}}$
   Given:

   • Mass of urea = $120\text{ g}$
   • Molar mass of urea = $60\text{ g/mol}$

   $n = \frac{120\text{ g}}{60\text{ g/mol}} = 2\text{ moles}$

2. Calculate the total mass of the solution:
   $\text{Mass of solution} = \text{Mass of urea} + \text{Mass of water}$
   $\text{Mass of solution} = 120\text{ g} + 1000\text{ g} = 1120\text{ g}$

3. Calculate the volume of the solution:
   Using the relation between mass, volume, and density ($d$):
   $\text{Volume of solution } (V) = \frac{\text{Mass of solution}}{\text{Density of solution}}$
   Given:

   • Density ($d$) = $1.15\text{ g/mL}$

   $V = \frac{1120\text{ g}}{1.15\text{ g/mL}} = \frac{1120}{1.15}\text{ mL}$

   Converting the volume from $\text{mL}$ to liters ($\text{L}$):
   $V_{\text{L}} = \frac{1120}{1.15 \times 1000}\text{ L} = \frac{1120}{1150}\text{ L} = \frac{112}{115}\text{ L}$

4. Calculate the molarity ($M$) of the solution:
   Molarity is defined as the number of moles of solute per liter of solution:
   $\text{Molarity } (M) = \frac{n}{V_{\text{L}}}$

   $M = \frac{2}{\frac{112}{115}} = \frac{2 \times 115}{112} = \frac{230}{112} \approx 2.0535\text{ M}$

Rounding off to two decimal places gives $2.05\text{ M}$.

Thus, the correct option is C.