Mass percentage (w/w) of ethylene glycol. `(HOCH_2 - CH_2OH)` in an aqueous solution is 20. Calculate mole fraction of solute.

Answer

To calculate the mole fraction of ethylene glycol in an aqueous solution where the mass percentage of ethylene glycol is 20%, we can follow these steps:

### Step 1: Understand the Mass Percentage
The mass percentage of ethylene glycol (C2H6O2) in the solution is given as 20%. This means that in 100 grams of the solution, there are 20 grams of ethylene glycol and 80 grams of water.

### Step 2: Calculate the Number of Moles of Ethylene Glycol
First, we need to calculate the molecular weight of ethylene glycol (C2H6O2):
- Carbon (C): 12 g/mol × 2 = 24 g/mol
- Hydrogen (H): 1 g/mol × 6 = 6 g/mol
- Oxygen (O): 16 g/mol × 2 = 32 g/mol

Adding these together:
\[ \text{Molecular weight of ethylene glycol} = 24 + 6 + 32 = 62 \text{ g/mol} \]

Now, we can calculate the number of moles of ethylene glycol:
\[ n_1 = \frac{\text{mass of ethylene glycol}}{\text{molecular weight}} = \frac{20 \text{ g}}{62 \text{ g/mol}} \approx 0.323 \text{ moles} \]

### Step 3: Calculate the Number of Moles of Water
Next, we calculate the number of moles of water (H2O):
- The mass of water in the solution is 80 grams.
- The molecular weight of water is:
- Hydrogen (H): 1 g/mol × 2 = 2 g/mol
- Oxygen (O): 16 g/mol × 1 = 16 g/mol
\[ \text{Molecular weight of water} = 2 + 16 = 18 \text{ g/mol} \]

Now, we can calculate the number of moles of water:
\[ n_2 = \frac{\text{mass of water}}{\text{molecular weight}} = \frac{80 \text{ g}}{18 \text{ g/mol}} \approx 4.444 \text{ moles} \]

### Step 4: Calculate the Mole Fraction of Ethylene Glycol
The mole fraction of a component is given by the formula:
\[ \text{Mole fraction of solute (ethylene glycol)} = \frac{n_1}{n_1 + n_2} \]

Substituting the values we calculated:
\[ \text{Mole fraction of ethylene glycol} = \frac{0.323}{0.323 + 4.444} \approx \frac{0.323}{4.767} \approx 0.0677 \]

### Final Answer:
The mole fraction of ethylene glycol in the solution is approximately **0.0677**.

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