An aqueous solution of urea containing 18 g urea in 1500 `cm^3` of solution has a density of 1.052 g/`cm^3` . If the molecular weight of urea is 60, then the molality of solution is-

Options

A. 0.2
B. 0.192
C. 0.064
D. 1.2

Answer

To find the molality of the urea solution, we will follow these steps:

### Step 1: Calculate the weight of the solution
We know the density of the solution and its volume. The formula for density is:

\[ \text{Density} = \frac{\text{Weight of Solution}}{\text{Volume of Solution}} \]

Given:
- Density = 1.052 g/cm³
- Volume = 1500 cm³

Rearranging the formula to find the weight of the solution:

\[ \text{Weight of Solution} = \text{Density} \times \text{Volume} \]

Substituting the values:

\[ \text{Weight of Solution} = 1.052 \, \text{g/cm}^3 \times 1500 \, \text{cm}^3 = 1578 \, \text{g} \]

### Step 2: Calculate the weight of the solvent
The weight of the solvent can be calculated by subtracting the weight of the solute (urea) from the weight of the solution.

Given:
- Weight of solute (urea) = 18 g

So,

\[ \text{Weight of Solvent} = \text{Weight of Solution} - \text{Weight of Solute} = 1578 \, \text{g} - 18 \, \text{g} = 1560 \, \text{g} \]

### Step 3: Convert the weight of the solvent to kilograms
Since molality is defined as moles of solute per kilogram of solvent, we need to convert the weight of the solvent from grams to kilograms:

\[ \text{Weight of Solvent in kg} = \frac{1560 \, \text{g}}{1000} = 1.56 \, \text{kg} \]

### Step 4: Calculate the number of moles of urea
To find the number of moles of urea, we use the formula:

\[ \text{Number of moles} = \frac{\text{Weight of Solute}}{\text{Molecular Weight of Solute}} \]

Given:
- Weight of solute (urea) = 18 g
- Molecular weight of urea = 60 g/mol

Calculating the number of moles:

\[ \text{Number of moles of urea} = \frac{18 \, \text{g}}{60 \, \text{g/mol}} = 0.3 \, \text{mol} \]

### Step 5: Calculate the molality of the solution
Now we can calculate the molality (m) using the formula:

\[ \text{Molality (m)} = \frac{\text{Number of moles of solute}}{\text{Weight of solvent in kg}} = \frac{0.3 \, \text{mol}}{1.56 \, \text{kg}} \]

Calculating molality:

\[ \text{Molality (m)} = \frac{0.3}{1.56} \approx 0.192 \, \text{mol/kg} \]

### Final Answer
The molality of the urea solution is approximately **0.192 mol/kg**.

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