The molality of the solution containing 55g of glucose dissolved in 2kg of water is ?

Options

A. 0.15m
B. 0.25m
C. 0.35m
D. 0.45m

Explanation

To find the molality of the solution containing 55g of glucose dissolved in 2kg of water, we can follow these steps:

### Step 1: Calculate the moles of glucose
To find the number of moles of glucose, 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 = 55 g
- Molar mass of glucose (C₆H₁₂O₆) = 180 g/mol

Now, substituting the values:

\[ \text{Moles of glucose} = \frac{55 \text{ g}}{180 \text{ g/mol}} \approx 0.3056 \text{ moles} \]

### 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:

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

Given:
- Moles of glucose ≈ 0.3056 moles
- Mass of water (solvent) = 2 kg

Now, substituting the values:

\[ \text{Molality} = \frac{0.3056 \text{ moles}}{2 \text{ kg}} \approx 0.1528 \text{ mol/kg} \]

### Step 3: Round the answer
Rounding 0.1528 to two decimal places gives us approximately 0.15 mol/kg.

### Final Answer
The molality of the solution is approximately **0.15 mol/kg**.

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