What is the mole fraction of glucose in 25% w/W glucose solution ?

Options

A. 0.32
B. 0.032
C. 0.132
D. 0.013

Explanation

To find the mole fraction of glucose in a 25% w/w glucose solution, we can follow these steps:

### Step 1: Understand the Composition of the Solution
A 25% w/w glucose solution means that there are 25 grams of glucose in 100 grams of the solution. This implies that the remaining mass (100 g - 25 g) is water.

### 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. Thus, the moles of glucose can be calculated as:
\[ \text{Moles of glucose} = \frac{25 \, \text{g}}{180 \, \text{g/mol}} \approx 0.1389 \, \text{moles} \]

### Step 3: Calculate the Moles of Water
Next, we calculate the mass of water in the solution:
\[ \text{Mass of water} = 100 \, \text{g} - 25 \, \text{g} = 75 \, \text{g} \]
Now, we calculate the number of moles of water. The molar mass of water (H₂O) is approximately 18 g/mol. Thus, the moles of water can be calculated as:
\[ \text{Moles of water} = \frac{75 \, \text{g}}{18 \, \text{g/mol}} \approx 4.1667 \, \text{moles} \]

### Step 4: Calculate the Total Moles of the Solution
Now, we find the total number of moles in the solution by adding the moles of glucose and the moles of water:
\[ \text{Total moles} = \text{Moles of glucose} + \text{Moles of water} = 0.1389 + 4.1667 \approx 4.3056 \, \text{moles} \]

### Step 5: Calculate the Mole Fraction of Glucose
The mole fraction of glucose (X_glucose) is calculated using the formula:
\[ X_{\text{glucose}} = \frac{\text{Moles of glucose}}{\text{Total moles of solution}} \]
Substituting the values we calculated:
\[ X_{\text{glucose}} = \frac{0.1389}{4.3056} \approx 0.0322 \]

### Final Answer
The mole fraction of glucose in a 25% w/w glucose solution is approximately **0.0322**.

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