What is the mole fraction of glucose in 5% w/W glucose solution ?

Options

A. 0.005
B. 0.050
C. 0.500
D. 5.00

Explanation

To find the mole fraction of glucose in a 5% w/w glucose solution, we can follow these steps:

### Step 1: Understand the solution concentration
A 5% w/w glucose solution means there are 5 grams of glucose in 100 grams of the solution.

### Step 2: Calculate the mass of the solvent (water)
Since the total mass of the solution is 100 grams and there are 5 grams of glucose, the mass of the solvent (water) can be calculated as:
\[ \text{Mass of water} = \text{Total mass of solution} - \text{Mass of glucose} = 100 \, \text{g} - 5 \, \text{g} = 95 \, \text{g} \]

### Step 3: Calculate the number of moles of glucose
To find the number of moles of glucose, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
The molar mass of glucose (C₆H₁₂O₆) is approximately 180 g/mol. Thus, the number of moles of glucose is:
\[ \text{Moles of glucose} = \frac{5 \, \text{g}}{180 \, \text{g/mol}} \approx 0.0278 \, \text{moles} \]

### Step 4: Calculate the number of moles of water
Next, we calculate the number of moles of water. The molar mass of water (H₂O) is approximately 18 g/mol. Therefore, the number of moles of water is:
\[ \text{Moles of water} = \frac{95 \, \text{g}}{18 \, \text{g/mol}} \approx 5.28 \, \text{moles} \]

### 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:
\[ \text{Total moles} = \text{Moles of glucose} + \text{Moles of water} = 0.0278 + 5.28 \approx 5.3078 \, \text{moles} \]

### Step 6: Calculate the mole fraction of glucose
The mole fraction of glucose (X_glucose) is calculated using the formula:
\[ X_{\text{glucose}} = \frac{\text{Moles of glucose}}{\text{Total moles}} \]
Substituting the values we found:
\[ X_{\text{glucose}} = \frac{0.0278}{5.3078} \approx 0.00523 \]

### Final Answer
The mole fraction of glucose in a 5% w/w glucose solution is approximately **0.00523**.

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