Calculate the molality of aq. Glucose solution in which mole fraction of glucose is 0.05.

Answer

To calculate the molality of an aqueous glucose solution in which the mole fraction of glucose is 0.05, we can follow these steps:

### Step 1: Understand the definition of mole fraction
Mole fraction (X) is defined as the number of moles of solute (in this case, glucose) divided by the total number of moles of the solution (solute + solvent).

### Step 2: Identify the number of moles of solute and solvent
Given that the mole fraction of glucose (X_glucose) is 0.05, we can set up the following:
- Moles of glucose (solute) = 0.05
- Moles of solution = 1 (since mole fraction is calculated per mole of solution)

### Step 3: Calculate the number of moles of solvent
To find the number of moles of solvent (water), we can use the formula:
\[ \text{Moles of solvent} = \text{Moles of solution} - \text{Moles of solute} \]
\[ \text{Moles of solvent} = 1 - 0.05 = 0.95 \]

### Step 4: Calculate the mass of the solvent
To find the mass of the solvent (water), we use the number of moles of solvent and the molar mass of water (approximately 18 g/mol):
\[ \text{Mass of solvent (water)} = \text{Moles of solvent} \times \text{Molar mass of water} \]
\[ \text{Mass of solvent} = 0.95 \, \text{moles} \times 18 \, \text{g/mol} = 17.1 \, \text{g} \]

### Step 5: Convert mass of solvent to kg
Since molality is defined in terms of kg of solvent, we convert grams to kilograms:
\[ \text{Mass of solvent in kg} = \frac{17.1 \, \text{g}}{1000} = 0.0171 \, \text{kg} \]

### Step 6: Calculate the molality
Molality (m) is defined as the number of moles of solute per kilogram of solvent:
\[ m = \frac{\text{Number of moles of solute}}{\text{Mass of solvent in kg}} \]
\[ m = \frac{0.05 \, \text{moles}}{0.0171 \, \text{kg}} \approx 2.92 \, \text{mol/kg} \]

### Final Answer
The molality of the aqueous glucose solution is approximately **2.92 mol/kg**.

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