The molality of the solution containing 50g of glucose dissolved in 2kg of water is ?

Options

A. 0.135m
B. 0.315m
C. 0.145m
D. 0.258m

Explanation

To calculate the molality of a solution containing 50g of glucose dissolved in 2kg of water, we can follow these steps:

### Step 1: Calculate the number of moles of glucose.
To find the number of moles, we use the formula:
\[ \text{Moles of solute} = \frac{\text{mass of solute (g)}}{\text{molar mass of solute (g/mol)}} \]

Given:
- Mass of glucose (solute) = 50g
- Molar mass of glucose (C₆H₁₂O₆) = 180 g/mol

Now, substituting the values:
\[ \text{Moles of glucose} = \frac{50 \text{ g}}{180 \text{ g/mol}} \approx 0.2778 \text{ moles} \]

### Step 2: Calculate the molality of the solution.
Molality (m) is defined as the number of moles of solute per kilogram of solvent. The formula for molality is:
\[ \text{Molality (m)} = \frac{\text{moles of solute}}{\text{mass of solvent (kg)}} \]

Given:
- Mass of solvent (water) = 2 kg

Now, substituting the values:
\[ \text{Molality} = \frac{0.2778 \text{ moles}}{2 \text{ kg}} \approx 0.1389 \text{ m} \]

### Final Answer:
The molality of the solution is approximately **0.139 m**.

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