What is the mole fraction of glucose in 20% w/W glucose solution ?

Options

A. 0.24
B. 0.024
C. 0.42
D. 0.042

Explanation

To find the mole fraction of glucose in a 20% w/w glucose solution, we can follow these steps:

### Step 1: Understand the composition of the solution
A 20% w/w glucose solution means that there are 20 grams of glucose in 100 grams of the solution.

### Step 2: Calculate the mass of water in the solution
Since the total mass of the solution is 100 grams and it contains 20 grams of glucose, the mass of water in the solution is:
\[ \text{Mass of water} = 100 \, \text{grams (solution)} - 20 \, \text{grams (glucose)} = 80 \, \text{grams (water)} \]

### Step 3: Calculate the number of moles of glucose
The molecular mass of glucose (C₆H₁₂O₆) is approximately 180 g/mol. The number of moles of glucose can be calculated using the formula:
\[ \text{Number of moles of glucose} = \frac{\text{mass of glucose}}{\text{molar mass of glucose}} \]
\[ \text{Number of moles of glucose} = \frac{20 \, \text{grams}}{180 \, \text{g/mol}} \approx 0.111 \, \text{moles} \]

### Step 4: Calculate the number of moles of water
The molecular mass of water (H₂O) is approximately 18 g/mol. The number of moles of water can be calculated as follows:
\[ \text{Number of moles of water} = \frac{\text{mass of water}}{\text{molar mass of water}} \]
\[ \text{Number of moles of water} = \frac{80 \, \text{grams}}{18 \, \text{g/mol}} \approx 4.444 \, \text{moles} \]

### Step 5: Calculate the total number of moles in the solution
The total number of moles in the solution is the sum of the moles of glucose and the moles of water:
\[ \text{Total moles} = \text{moles of glucose} + \text{moles of water} \]
\[ \text{Total moles} = 0.111 + 4.444 \approx 4.555 \, \text{moles} \]

### Step 6: Calculate the mole fraction of glucose
The mole fraction of glucose (X_glucose) is calculated using the formula:
\[ X_{\text{glucose}} = \frac{\text{moles of glucose}}{\text{total moles}} \]
\[ X_{\text{glucose}} = \frac{0.111}{4.555} \approx 0.0244 \]

### Final Answer
The mole fraction of glucose in a 20% w/w glucose solution is approximately **0.0244**.

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