What is the mole fraction of glucose in 30% w/W glucose solution ?

Options

A. 0.04
B. 0.40
C. 0.14
D. 0.014

Answer

To find the mole fraction of glucose in a 30% w/w glucose solution, we can follow these steps:

### Step 1: Understand the composition of the solution
A 30% w/w glucose solution means that there are 30 grams of glucose in 100 grams of the solution. This implies that the remaining mass (100 g - 30 g) is the solvent, which is water.

### Step 2: Calculate the mass of the solvent
The mass of the solvent (water) in the solution is:
\[ \text{Mass of water} = 100 \, \text{g} - 30 \, \text{g} = 70 \, \text{g} \]

### Step 3: Calculate the number of moles of glucose
To find the number of moles of glucose, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass}}{\text{molar mass}} \]
The molar mass of glucose (C₆H₁₂O₆) is approximately 180 g/mol.

Thus, the number of moles of glucose is:
\[ \text{Moles of glucose} = \frac{30 \, \text{g}}{180 \, \text{g/mol}} = 0.1667 \, \text{moles} \]

### Step 4: Calculate the number of moles of water
Next, we calculate the number of moles of water. The molar mass of water (H₂O) is approximately 18 g/mol.

Thus, the number of moles of water is:
\[ \text{Moles of water} = \frac{70 \, \text{g}}{18 \, \text{g/mol}} \approx 3.8889 \, \text{moles} \]

### Step 5: Calculate the total number of moles in the solution
The total number of moles in the solution is the sum of the moles of glucose and the moles of water:
\[ \text{Total moles} = \text{Moles of glucose} + \text{Moles of water} \]
\[ \text{Total moles} = 0.1667 + 3.8889 \approx 4.0556 \, \text{moles} \]

### Step 6: Calculate the mole fraction of glucose
The mole fraction of glucose (X_glucose) is calculated using the formula:
\[ X_{\text{glucose}} = \frac{\text{Moles of glucose}}{\text{Total moles}} \]
\[ X_{\text{glucose}} = \frac{0.1667}{4.0556} \approx 0.0411 \]

### Final Answer
The mole fraction of glucose in a 30% w/w glucose solution is approximately **0.0411**.

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