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

Explanation

To find the molality of the solution containing 50g of glucose dissolved in 2kg of water, we can 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:
\[ m = \frac{\text{moles of solute}}{\text{mass of solvent in kg}} \]

### Step 2: Calculate the moles of glucose
To find the 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 (solute) = 50g
- Molar mass of glucose (C₆H₁₂O₆) = 180 g/mol

Now, we can calculate the moles of glucose:
\[ \text{moles of glucose} = \frac{50 \, \text{g}}{180 \, \text{g/mol}} \]
Calculating this gives:
\[ \text{moles of glucose} = 0.2778 \, \text{moles} \approx 0.28 \, \text{moles} \]

### Step 3: Identify the mass of the solvent
The mass of the solvent (water) is given as:
- Mass of water = 2 kg

### Step 4: Calculate the molality
Now, we can substitute the values into the molality formula:
\[ m = \frac{\text{moles of glucose}}{\text{mass of solvent in kg}} \]
Substituting the values:
\[ m = \frac{0.28 \, \text{moles}}{2 \, \text{kg}} \]
Calculating this gives:
\[ m = 0.14 \, \text{mol/kg} \]

### Final Answer
The molality of the solution is approximately **0.14 mol/kg**.

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