An aqueous solution containing 6 g of urea in 500 mL of solution has a density equal to 1.05. If the molar mass of urea is 60, then the molality of solution is :

Options

A. 0.2
B. 0.19
C. 0.1
D. 1.2

Explanation

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

### Step 1: Calculate the moles of solute (urea)
The formula for calculating moles is:
\[ \text{Moles of solute} = \frac{\text{mass of solute (g)}}{\text{molar mass of solute (g/mol)}} \]
Given:
- Mass of urea = 6 g
- Molar mass of urea = 60 g/mol

Substituting the values:
\[ \text{Moles of urea} = \frac{6 \, \text{g}}{60 \, \text{g/mol}} = 0.1 \, \text{moles} \]

### Step 2: Calculate the mass of the solution
To find the mass of the solution, we use the formula:
\[ \text{Mass of solution} = \text{Volume of solution} \times \text{Density of solution} \]
Given:
- Volume of solution = 500 mL
- Density of solution = 1.05 g/mL

Substituting the values:
\[ \text{Mass of solution} = 500 \, \text{mL} \times 1.05 \, \text{g/mL} = 525 \, \text{g} \]

### Step 3: Calculate the mass of the solvent
The mass of the solvent can be calculated by subtracting the mass of the solute from the mass of the solution:
\[ \text{Mass of solvent} = \text{Mass of solution} - \text{Mass of solute} \]
Substituting the values:
\[ \text{Mass of solvent} = 525 \, \text{g} - 6 \, \text{g} = 519 \, \text{g} \]

### Step 4: Convert the mass of the solvent to kilograms
Since molality is defined as moles of solute per kilogram of solvent, we need to convert grams to kilograms:
\[ \text{Mass of solvent in kg} = \frac{519 \, \text{g}}{1000} = 0.519 \, \text{kg} \]

### Step 5: Calculate the molality of the solution
The formula for molality (m) is:
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}} \]
Substituting the values:
\[ m = \frac{0.1 \, \text{moles}}{0.519 \, \text{kg}} \approx 0.1926 \, \text{mol/kg} \]

### Final Answer
The molality of the solution is approximately **0.1926 mol/kg**.

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