A solution contains 90 g of `H_(2)O`, 6.4 g of methanol and 18.4 g of glycerol. What is the mole fraction of glycerol ? `("Glycerol "=CH_(2)OH-CHOH-CH_(2)OH)`

Explanation

To find the mole fraction of glycerol in the solution, we will follow these steps:

### Step 1: Write down the given data
- Mass of H₂O = 90 g
- Mass of Methanol (CH₃OH) = 6.4 g
- Mass of Glycerol (C₃H₈O₃) = 18.4 g

### Step 2: Calculate the number of moles of each component
1. **For H₂O:**
- Molecular weight of H₂O = 18 g/mol
- Number of moles of H₂O = Mass / Molecular weight = 90 g / 18 g/mol = 5 moles

2. **For Methanol (CH₃OH):**
- Molecular weight of Methanol = 32 g/mol
- Number of moles of Methanol = Mass / Molecular weight = 6.4 g / 32 g/mol = 0.2 moles

3. **For Glycerol (C₃H₈O₃):**
- Molecular weight of Glycerol = 92 g/mol
- Number of moles of Glycerol = Mass / Molecular weight = 18.4 g / 92 g/mol = 0.2 moles

### Step 3: Calculate the total number of moles
Total number of moles = Moles of H₂O + Moles of Methanol + Moles of Glycerol
= 5 + 0.2 + 0.2 = 5.4 moles

### Step 4: Calculate the mole fraction of Glycerol
Mole fraction of Glycerol = Moles of Glycerol / Total moles
= 0.2 moles / 5.4 moles ≈ 0.037

### Final Answer:
The mole fraction of glycerol is approximately **0.037**.

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