What is the mole fraction of glucose in 10% w/W glucose solution ?

Options

A. 0.01
B. 0.02
C. 0.03
D. 0.04

Explanation

To find the mole fraction of glucose in a 10% w/w glucose solution, we can follow these steps:

### Step 1: Understand the Composition of the Solution
A 10% w/w glucose solution means that there are 10 grams of glucose in 100 grams of the solution.

### Step 2: Calculate the Mass of Water
Since the total mass of the solution is 100 grams and the mass of glucose is 10 grams, we can find the mass of water:
\[ \text{Mass of water} = \text{Total mass of solution} - \text{Mass of glucose} = 100 \, \text{g} - 10 \, \text{g} = 90 \, \text{g} \]

### Step 3: Calculate the Number of Moles of Glucose
To find the number of moles of glucose, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
The molar mass of glucose (C₆H₁₂O₆) is approximately 180 g/mol.
\[ \text{Number of moles of glucose} = \frac{10 \, \text{g}}{180 \, \text{g/mol}} = \frac{1}{18} \, \text{mol} \approx 0.0556 \, \text{mol} \]

### Step 4: Calculate the Number of Moles of Water
The molar mass of water (H₂O) is approximately 18 g/mol.
\[ \text{Number of moles of water} = \frac{90 \, \text{g}}{18 \, \text{g/mol}} = 5 \, \text{mol} \]

### Step 5: Calculate the Total Number of Moles
Now, we can find the total number of moles in the solution:
\[ \text{Total number of moles} = \text{Number of moles of glucose} + \text{Number of moles of water} = \frac{1}{18} + 5 \]

### Step 6: Calculate the Mole Fraction of Glucose
The mole fraction of glucose (X_glucose) is given by:
\[ X_{\text{glucose}} = \frac{\text{Number of moles of glucose}}{\text{Total number of moles}} = \frac{\frac{1}{18}}{\frac{1}{18} + 5} \]
Calculating this gives:
\[ X_{\text{glucose}} = \frac{0.0556}{0.0556 + 5} \approx \frac{0.0556}{5.0556} \approx 0.01098 \]

### Final Answer
Thus, the mole fraction of glucose in a 10% w/w glucose solution is approximately 0.011.

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