What is the mole fraction of glucose in 18% w/W glucose solution ?

Options

A. 0.210
B. 0.021
C. 0.121
D. 0.005

Explanation

To find the mole fraction of glucose in an 18% w/w glucose solution, we can follow these steps:

### Step 1: Understand the Composition of the Solution
An 18% w/w glucose solution means that there are 18 grams of glucose in 100 grams of the solution.

### Step 2: Calculate the Mass of the Solvent
Since the solution is 100 grams and contains 18 grams of glucose, the mass of the solvent (water) can be calculated as:
\[ \text{Mass of water} = \text{Total mass of solution} - \text{Mass of glucose} = 100 \, \text{g} - 18 \, \text{g} = 82 \, \text{g} \]

### 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 180 g/mol. Therefore, the number of moles of glucose is:
\[ \text{Moles of glucose} = \frac{18 \, \text{g}}{180 \, \text{g/mol}} = 0.1 \, \text{moles} \]

### 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 18 g/mol. Thus, the number of moles of water is:
\[ \text{Moles of water} = \frac{82 \, \text{g}}{18 \, \text{g/mol}} = 4.56 \, \text{moles} \, (\text{approximately } 4.5 \, \text{moles}) \]

### 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:
\[ \text{Total moles} = \text{Moles of glucose} + \text{Moles of water} = 0.1 + 4.5 = 4.6 \, \text{moles} \]

### Step 6: Calculate the Mole Fraction of Glucose
The mole fraction of glucose (X_glucose) is given by the formula:
\[ X_{\text{glucose}} = \frac{\text{Moles of glucose}}{\text{Total moles}} \]
Substituting the values we calculated:
\[ X_{\text{glucose}} = \frac{0.1}{4.6} \approx 0.02174 \]

### Final Answer
The mole fraction of glucose in the 18% w/w glucose solution is approximately **0.02174**.

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