The density of a solution prepared by dissolving 120 g of urea (mol. Mass=60 u) in 1000 g of water is 1.15 g/mL. The molarity if this solution is

Options

A. 0.50 M
B. 1.78 M
C. 1.02 M
D. 2.05 M

Answer

To find the molarity of the solution prepared by dissolving 120 g of urea in 1000 g of water, we can follow these steps:

### Step 1: Calculate the number of moles of urea
The number of moles of a substance can be calculated using the formula:

\[ \text{Number of moles} = \frac{\text{Mass of solute (g)}}{\text{Molar mass of solute (g/mol)}} \]

For urea:
- Mass of urea = 120 g
- Molar mass of urea = 60 g/mol

\[ \text{Number of moles of urea} = \frac{120 \, \text{g}}{60 \, \text{g/mol}} = 2 \, \text{moles} \]

### Step 2: Calculate the total mass of the solution
The total mass of the solution is the sum of the mass of the solute (urea) and the mass of the solvent (water).

\[ \text{Total mass of solution} = \text{Mass of urea} + \text{Mass of water} \]

\[ \text{Total mass of solution} = 120 \, \text{g} + 1000 \, \text{g} = 1120 \, \text{g} \]

### Step 3: Calculate the volume of the solution
We can calculate the volume of the solution using the density formula:

\[ \text{Density} = \frac{\text{Mass}}{\text{Volume}} \]

Rearranging gives us:

\[ \text{Volume} = \frac{\text{Mass}}{\text{Density}} \]

Given that the density of the solution is 1.15 g/mL:

\[ \text{Volume} = \frac{1120 \, \text{g}}{1.15 \, \text{g/mL}} \approx 973.91 \, \text{mL} \]

### Step 4: Convert volume from mL to L
To find molarity, we need the volume in liters:

\[ \text{Volume in L} = \frac{973.91 \, \text{mL}}{1000} \approx 0.97391 \, \text{L} \]

### Step 5: Calculate the molarity of the solution
Molarity (M) is defined as the number of moles of solute per liter of solution:

\[ \text{Molarity} = \frac{\text{Number of moles of solute}}{\text{Volume of solution in L}} \]

\[ \text{Molarity} = \frac{2 \, \text{moles}}{0.97391 \, \text{L}} \approx 2.0535 \, \text{M} \]

### Final Answer
The molarity of the solution is approximately **2.05 M**.

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