What is the mole fraction of glucose in 50% w/W glucose solution ?

Explanation

To find the mole fraction of glucose in a 50% w/w glucose solution, follow these steps:

### Step 1: Understand the Composition of the Solution
A 50% w/w glucose solution means that there are 50 grams of glucose in 100 grams of the solution. This implies that there are 50 grams of water (the solvent) in the solution as well.

### Step 2: Calculate the Number of Moles of Glucose
To calculate 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.

\[ \text{Moles of glucose} = \frac{50 \text{ g}}{180 \text{ g/mol}} \approx 0.2778 \text{ moles} \]

### Step 3: 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.

\[ \text{Moles of water} = \frac{50 \text{ g}}{18 \text{ g/mol}} \approx 2.7778 \text{ moles} \]

### Step 4: 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 together.

\[ \text{Total moles} = \text{Moles of glucose} + \text{Moles of water} = 0.2778 + 2.7778 \approx 3.0556 \text{ moles} \]

### Step 5: Calculate the Mole Fraction of Glucose
The mole fraction of glucose is calculated using the formula:

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

\[ \text{Mole fraction of glucose} = \frac{0.2778}{3.0556} \approx 0.0909 \]

### Final Answer
The mole fraction of glucose in a 50% w/w glucose solution is approximately **0.0909**.

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