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. This implies that the remaining 90 grams of the solution is water.

### Step 2: 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 molecular formula of glucose (C₆H₁₂O₆) has a molar mass of 180 g/mol. Therefore, the number of moles of glucose is:
\[ \text{Moles of glucose} = \frac{10 \text{ g}}{180 \text{ g/mol}} = 0.0556 \text{ moles} \]

### Step 3: Calculate the number of moles of water
Next, we calculate the number of moles of water. The mass of water in the solution is 90 grams. The molar mass of water (H₂O) is 18 g/mol. Thus, the number of moles of water is:
\[ \text{Moles of water} = \frac{90 \text{ g}}{18 \text{ g/mol}} = 5 \text{ moles} \]

### Step 4: Calculate the mole fraction of glucose
The mole fraction (X) of a component in a solution is given by the formula:
\[ X_{\text{solute}} = \frac{\text{moles of solute}}{\text{moles of solute} + \text{moles of solvent}} \]
In this case, glucose is the solute and water is the solvent. Thus, we can substitute the values we calculated:
\[ X_{\text{glucose}} = \frac{0.0556}{0.0556 + 5} = \frac{0.0556}{5.0556} \approx 0.01098 \]

### Step 5: Final result
The mole fraction of glucose in the 10% W/W glucose solution is approximately 0.011.