What is the mole fraction of glucose in 9% w/W glucose solution ?

Options

A. 0.090
B. 0.009
C. 0.900
D. 9.00

Explanation

To find the mole fraction of glucose in a 9% w/w glucose solution, we can follow these steps:

### Step 1: Understand the Composition of the Solution
A 9% w/w glucose solution means that there are 9 grams of glucose in 100 grams of the solution.

### Step 2: Calculate the 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, the number of moles of glucose is:
\[ \text{Moles of glucose} = \frac{9 \text{ g}}{180 \text{ g/mol}} = 0.05 \text{ moles} \]

### Step 3: Calculate the Mass of the Solvent (Water)
Since the total mass of the solution is 100 g and we have 9 g of glucose, the mass of the solvent (water) is:
\[ \text{Mass of water} = 100 \text{ g} - 9 \text{ g} = 91 \text{ g} \]

### Step 4: Calculate the 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:
\[ \text{Moles of water} = \frac{91 \text{ g}}{18 \text{ g/mol}} \approx 5.0556 \text{ moles} \]

### Step 5: Calculate the Total Moles in the Solution
Now we can find the total number of moles in the solution:
\[ \text{Total moles} = \text{Moles of glucose} + \text{Moles of water} = 0.05 + 5.0556 \approx 5.1056 \text{ moles} \]

### Step 6: Calculate the Mole Fraction of Glucose
The mole fraction of glucose (X_glucose) is calculated using the formula:
\[ X_{\text{glucose}} = \frac{\text{Moles of glucose}}{\text{Total moles}} = \frac{0.05}{5.1056} \approx 0.0098 \]

### Conclusion
Thus, the mole fraction of glucose in the 9% w/w glucose solution is approximately **0.0098**.

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