What is the mole fraction of glucose in 40% w/W glucose solution ?

Options

A. 0.061
B. 0.612
C. 0.016
D. 0.15

Explanation

To find the mole fraction of glucose in a 40% w/w glucose solution, follow these steps:

### Step 1: Understand the Composition of the Solution
A 40% w/w glucose solution means that there are 40 grams of glucose in 100 grams of the solution. This implies that the remaining mass (100 g - 40 g) is the solvent, which is water.

### Step 2: Calculate the Number of Moles of Glucose
To calculate the number of moles of glucose, use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
The molar mass of glucose (C₆H₁₂O₆) is 180 g/mol.

\[ \text{Number of moles of glucose} = \frac{40 \text{ g}}{180 \text{ g/mol}} = 0.222 \text{ moles (approximately 0.22 moles)} \]

### Step 3: Calculate the Mass of the Solvent (Water)
The mass of the solvent (water) is:
\[ \text{Mass of water} = 100 \text{ g (total solution)} - 40 \text{ g (glucose)} = 60 \text{ g} \]

### Step 4: Calculate the Number of Moles of Water
Using the molar mass of water (H₂O), which is 18 g/mol:
\[ \text{Number of moles of water} = \frac{60 \text{ g}}{18 \text{ g/mol}} = 3.33 \text{ moles} \]

### Step 5: Calculate the Total Number of Moles in the Solution
Now, add the number of moles of glucose and the number of moles of water:
\[ \text{Total moles} = \text{moles of glucose} + \text{moles of water} = 0.22 + 3.33 = 3.55 \text{ moles} \]

### Step 6: Calculate the Mole Fraction of Glucose
The mole fraction of glucose (X_glucose) is given by the formula:
\[ X_{\text{glucose}} = \frac{\text{moles of glucose}}{\text{total moles of solution}} = \frac{0.22}{3.55} \]
Calculating this gives:
\[ X_{\text{glucose}} \approx 0.0617 \text{ (approximately 0.061)} \]

### Final Answer
The mole fraction of glucose in a 40% w/w glucose solution is approximately **0.061**.

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