Calculate mole fraction of alcohol in 2 molal aqueous ethanol.

Answer

To calculate the mole fraction of alcohol (ethanol) in a 2 molal aqueous ethanol solution, we can follow these steps:

### Step 1: Understand the Definition of Molality
Molality (m) is defined as the number of moles of solute (in this case, ethanol) per kilogram of solvent (water). A 2 molal solution means there are 2 moles of ethanol dissolved in 1 kg (1000 g) of water.

### Step 2: Calculate the Moles of Water
To find the number of moles of water, we use the formula:
\[ \text{Number of moles} = \frac{\text{mass (g)}}{\text{molar mass (g/mol)}} \]
The molar mass of water (H₂O) is approximately 18 g/mol. Therefore, the number of moles of water in 1000 g is:
\[ \text{Moles of water} = \frac{1000 \, \text{g}}{18 \, \text{g/mol}} \approx 55.56 \, \text{moles} \]

### Step 3: Calculate Total Moles in the Solution
Now, we can find the total number of moles in the solution by adding the moles of ethanol and the moles of water:
\[ \text{Total moles} = \text{Moles of ethanol} + \text{Moles of water} = 2 + 55.56 = 57.56 \, \text{moles} \]

### Step 4: Calculate the Mole Fraction of Ethanol
The mole fraction (X) of a component in a solution is calculated using the formula:
\[ X_{\text{component}} = \frac{\text{moles of component}}{\text{total moles in solution}} \]
For ethanol, the mole fraction is:
\[ X_{\text{ethanol}} = \frac{2 \, \text{moles}}{57.56 \, \text{moles}} \approx 0.0348 \]

### Step 5: Final Result
Thus, the mole fraction of ethanol in the 2 molal aqueous ethanol solution is approximately 0.0348.

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