What is the mole fraction of glucose in 45% w/W glucose solution ?

Options

A. 0.058
B. 0.075
C. 0.057
D. 0.750

Explanation

To find the mole fraction of glucose in a 45% w/w glucose solution, follow these steps:

### Step 1: Understand the Composition of the Solution
In a 45% w/w glucose solution, there are 45 grams of glucose in 100 grams of the solution.

### Step 2: Calculate the Mass of the Solvent
To find the mass of the solvent (water), subtract the mass of glucose from the total mass of the solution:
- Mass of solvent (water) = Total mass of solution - Mass of glucose
- Mass of solvent = 100 g - 45 g = 55 g

### Step 3: Calculate the Number of Moles of Glucose
Using the molar mass of glucose (C6H12O6), which is 180 g/mol:
- Number of moles of glucose = Mass of glucose / Molar mass of glucose
- Number of moles of glucose = 45 g / 180 g/mol = 0.25 moles

### Step 4: Calculate the Number of Moles of Water
Using the molar mass of water (H2O), which is 18 g/mol:
- Number of moles of water = Mass of water / Molar mass of water
- Number of moles of water = 55 g / 18 g/mol ≈ 3.05 moles

### Step 5: Calculate the Total Number of Moles in the Solution
Total moles in the solution = Moles of glucose + Moles of water
- Total moles = 0.25 moles + 3.05 moles = 3.30 moles

### Step 6: Calculate the Mole Fraction of Glucose
Mole fraction of glucose (X_glucose) is calculated using the formula:
- Mole fraction of glucose = Moles of glucose / Total moles of solution
- Mole fraction of glucose = 0.25 moles / 3.30 moles ≈ 0.07576

### Final Answer
The mole fraction of glucose in the 45% w/w glucose solution is approximately **0.07576**.

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