Given that 10g of a dibasic acid (molar mass = 100) are present in 600 mL of the solution. The density of the solution is `1.02 g mL^(-1)`. Molality of solution is

Options

A. 0.17
B. 0.34
C. 0.99
D. 0.01

Answer

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

### Step 1: Calculate the number of moles of the dibasic acid.
The formula for calculating the number of moles is:

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

Given:
- Mass of dibasic acid = 10 g
- Molar mass of dibasic acid = 100 g/mol

\[ \text{Number of moles} = \frac{10 \text{ g}}{100 \text{ g/mol}} = 0.1 \text{ moles} \]

### Step 2: Calculate the mass of the solution.
To find the mass of the solution, we can use the formula:

\[ \text{Mass of solution} = \text{Volume} \times \text{Density} \]

Given:
- Volume of solution = 600 mL = 0.6 L (since 1 L = 1000 mL)
- Density of solution = 1.02 g/mL

Convert volume to grams:

\[ \text{Mass of solution} = 600 \text{ mL} \times 1.02 \text{ g/mL} = 612 \text{ g} \]

### Step 3: Calculate the mass of the solvent.
To find the mass of the solvent, we need to subtract the mass of the solute from the mass of the solution.

\[ \text{Mass of solvent} = \text{Mass of solution} - \text{Mass of solute} \]

Given:
- Mass of solute (dibasic acid) = 10 g

\[ \text{Mass of solvent} = 612 \text{ g} - 10 \text{ g} = 602 \text{ g} \]

### 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.

\[ \text{Mass of solvent in kg} = \frac{602 \text{ g}}{1000} = 0.602 \text{ kg} \]

### Step 5: Calculate the molality of the solution.
The formula for molality (m) is:

\[ \text{Molality (m)} = \frac{\text{Number of moles of solute}}{\text{Mass of solvent (kg)}} \]

Substituting the values we have:

\[ \text{Molality (m)} = \frac{0.1 \text{ moles}}{0.602 \text{ kg}} \approx 0.166 \text{ mol/kg} \]

### Conclusion
Thus, the molality of the solution is approximately **0.166 mol/kg**.

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