3.42 g of a substance of molecular weight 342 is present in 250g of water. Molality of this solution is

Options

A. 0.4 m
B. 0.04 m
C. 0.8 m
D. 4 m

Explanation

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

### Step 1: Understand the formula for molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent. The formula is:
\[ \text{Molality (m)} = \frac{\text{Number of moles of solute}}{\text{Weight of solvent in kg}} \]

### Step 2: Convert the weight of the solvent from grams to kilograms
The weight of the solvent (water) is given as 250 g. To convert this to kilograms:
\[ \text{Weight of solvent in kg} = \frac{250 \, \text{g}}{1000} = 0.250 \, \text{kg} \]

### Step 3: Calculate the number of moles of solute
The number of moles of solute can be calculated using the formula:
\[ \text{Number of moles} = \frac{\text{Weight of solute}}{\text{Molecular weight of solute}} \]
Given:
- Weight of solute = 3.42 g
- Molecular weight of solute = 342 g/mol

Now substituting the values:
\[ \text{Number of moles} = \frac{3.42 \, \text{g}}{342 \, \text{g/mol}} \]

Calculating this gives:
\[ \text{Number of moles} = 0.01 \, \text{mol} \]

### Step 4: Substitute the values into the molality formula
Now we can substitute the number of moles of solute and the weight of the solvent in kg into the molality formula:
\[ \text{Molality (m)} = \frac{0.01 \, \text{mol}}{0.250 \, \text{kg}} \]

Calculating this gives:
\[ \text{Molality (m)} = 0.04 \, \text{mol/kg} \]

### Step 5: Conclusion
The molality of the solution is:
\[ \text{Molality} = 0.04 \, \text{mol/kg} \]