What is the mole fraction of glucose in 35% w/W glucose solution ?

Options

A. 0.05
B. 0.50
C. 0.15
D. 0.25

Explanation

To find the mole fraction of glucose in a 35% w/w glucose solution, we can follow these steps:

### Step 1: Understand the Given Information
A 35% w/w glucose solution means that there are 35 grams of glucose in 100 grams of the solution.

### 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 molar mass of glucose (C₆H₁₂O₆) is approximately 180 g/mol. Therefore:
\[ \text{Number of moles of glucose} = \frac{35 \text{ g}}{180 \text{ g/mol}} \approx 0.194 \text{ moles} \]

### Step 3: Calculate the Mass of Solvent (Water)
Since the total mass of the solution is 100 grams and we have 35 grams of glucose, the mass of the solvent (water) is:
\[ \text{Mass of water} = 100 \text{ g} - 35 \text{ g} = 65 \text{ g} \]

### Step 4: Calculate the Number of Moles of Water
Using the molar mass of water (H₂O), which is approximately 18 g/mol, we can calculate the number of moles of water:
\[ \text{Number of moles of water} = \frac{65 \text{ g}}{18 \text{ g/mol}} \approx 3.61 \text{ moles} \]

### Step 5: Calculate the Total Number of Moles in the Solution
Now, we can find the total number of moles in the solution by adding the moles of glucose and the moles of water:
\[ \text{Total moles} = \text{moles of glucose} + \text{moles of water} = 0.194 + 3.61 \approx 3.804 \text{ moles} \]

### Step 6: Calculate the Mole Fraction of Glucose
The mole fraction of glucose (X_glucose) is calculated using the formula:
\[ X_{\text{glucose}} = \frac{\text{moles of glucose}}{\text{total moles of solution}} = \frac{0.194}{3.804} \approx 0.051 \]

### Final Answer
The mole fraction of glucose in the 35% w/w glucose solution is approximately **0.051**.

---