An aqueous solution of urea containing 18 g urea in 1500 `cm^(3)` of solution has a density of 1.5 `g//cm^(3)` . If the molecular weight of urea is 60. Then the molality of solution is:

Options

A. 0.134 m
B. 0.192 m
C. 0.064 m
D. 0.205 m

Answer

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

### Step 1: Calculate the mass of the solution
Given:
- Density of the solution = 1.5 g/cm³
- Volume of the solution = 1500 cm³

Using the formula for mass:
\[ \text{Mass of solution} = \text{Density} \times \text{Volume} \]
\[ \text{Mass of solution} = 1.5 \, \text{g/cm}^3 \times 1500 \, \text{cm}^3 = 2250 \, \text{g} \]

### Step 2: Calculate the mass of the solvent (water)
We know the mass of the solute (urea):
- Mass of urea = 18 g

Now, we can find the mass of the solvent (water):
\[ \text{Mass of solvent} = \text{Mass of solution} - \text{Mass of solute} \]
\[ \text{Mass of solvent} = 2250 \, \text{g} - 18 \, \text{g} = 2232 \, \text{g} \]

### Step 3: Convert the mass of the solvent to kilograms
To convert grams to kilograms:
\[ \text{Mass of solvent in kg} = \frac{2232 \, \text{g}}{1000} = 2.232 \, \text{kg} \]

### Step 4: Calculate the number of moles of urea
Using the molecular weight of urea:
- Molecular weight of urea = 60 g/mol

Number of moles of urea can be calculated as:
\[ \text{Moles of urea} = \frac{\text{Mass of urea}}{\text{Molecular weight of urea}} \]
\[ \text{Moles of urea} = \frac{18 \, \text{g}}{60 \, \text{g/mol}} = 0.3 \, \text{mol} \]

### Step 5: Calculate the molality of the solution
Molality (m) is defined as:
\[ \text{Molality} = \frac{\text{Moles of solute}}{\text{Mass of solvent in kg}} \]
Substituting the values we have:
\[ \text{Molality} = \frac{0.3 \, \text{mol}}{2.232 \, \text{kg}} \approx 0.134 \, \text{mol/kg} \]

### Final Answer
The molality of the solution is approximately 0.134 mol/kg.

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