What is the mole fraction of glucose in 15% w/W glucose solution ?

Options

A. 0.017
B. 0.17
C. 0.37
D. 0.027

Explanation

To find the mole fraction of glucose in a 15% w/w glucose solution, we can follow these steps:

### Step 1: Understand the given information
A 15% w/w glucose solution means that there are 15 grams of glucose in 100 grams of the solution.

### Step 2: Calculate the number of moles of glucose
To find the number of moles of glucose, we use the formula:

\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]

The molar mass of glucose (C6H12O6) is approximately 180 g/mol. Therefore, the number of moles of glucose is calculated as follows:

\[ \text{Number of moles of glucose} = \frac{15 \, \text{g}}{180 \, \text{g/mol}} = 0.0833 \, \text{moles} \]

### Step 3: Calculate the mass of the solvent (water)
Since the total mass of the solution is 100 grams and we have 15 grams of glucose, the mass of the solvent (water) is:

\[ \text{Mass of water} = 100 \, \text{g} - 15 \, \text{g} = 85 \, \text{g} \]

### Step 4: Calculate the number of 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:

\[ \text{Number of moles of water} = \frac{85 \, \text{g}}{18 \, \text{g/mol}} \approx 4.72 \, \text{moles} \]

### Step 5: Calculate the total number of moles in the solution
Now, we can find the total number of moles in the solution by adding the moles of glucose and the moles of water:

\[ \text{Total moles} = \text{moles of glucose} + \text{moles of water} = 0.0833 + 4.72 \approx 4.8033 \, \text{moles} \]

### Step 6: Calculate the mole fraction of glucose
The mole fraction of glucose is given by the formula:

\[ \text{Mole fraction of glucose} = \frac{\text{moles of glucose}}{\text{total moles}} \]

Substituting the values we calculated:

\[ \text{Mole fraction of glucose} = \frac{0.0833}{4.8033} \approx 0.0173 \]

### Final Answer
The mole fraction of glucose in a 15% w/w glucose solution is approximately **0.0173**.

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