Mass percentage (w/w) of ethylene glycol `(HOCH_(2)-CH_(2)OH)` in a aqueous solution is 20, then mole fraction of solute is

Options

A. `0.5`
B. `0.067`
C. `0.1`
D. `0.4`

Explanation

To find the mole fraction of ethylene glycol in a 20% (w/w) aqueous solution, we can follow these steps:

### Step 1: Understand the Mass Percentage
The mass percentage of ethylene glycol is given as 20%. This means that in 100 g of the solution, there are 20 g of ethylene glycol and 80 g of water (the solvent).

### Step 2: Calculate the Moles of Ethylene Glycol
To calculate the moles of ethylene glycol, we need its molecular weight. The molecular formula for ethylene glycol is \(HOCH_2-CH_2OH\).

- **Molecular Weight Calculation:**
- Carbon (C): 2 atoms × 12 g/mol = 24 g/mol
- Hydrogen (H): 6 atoms × 1 g/mol = 6 g/mol
- Oxygen (O): 2 atoms × 16 g/mol = 32 g/mol
- Total = 24 + 6 + 32 = 62 g/mol

Now, using the mass of ethylene glycol (20 g):
\[ \text{Moles of ethylene glycol} = \frac{\text{mass}}{\text{molecular weight}} = \frac{20 \text{ g}}{62 \text{ g/mol}} \approx 0.3226 \text{ moles} \]

### Step 3: Calculate the Moles of Water
Next, we calculate the moles of water using its molecular weight (H₂O = 18 g/mol).

- Given mass of water = 80 g
\[ \text{Moles of water} = \frac{80 \text{ g}}{18 \text{ g/mol}} \approx 4.4444 \text{ moles} \]

### Step 4: Calculate the Total Moles
Now, we can find the total moles in the solution:
\[ \text{Total moles} = \text{Moles of ethylene glycol} + \text{Moles of water} = 0.3226 + 4.4444 \approx 4.767 \text{ moles} \]

### Step 5: Calculate the Mole Fraction of Ethylene Glycol
The mole fraction of ethylene glycol (X) is given by the formula:
\[ X_{\text{ethylene glycol}} = \frac{\text{Moles of ethylene glycol}}{\text{Total moles}} = \frac{0.3226}{4.767} \approx 0.0676 \]

### Final Answer
The mole fraction of ethylene glycol in the solution is approximately **0.0676**.

---