Question

When 46 g of ethyl alcohol is dissolved in 162 g of water, the mole fraction of ethyl alcohol and water respectively is

• A. 0.9, 0.1
• B. 0.78, 0.22
• C. 0.1, 0.9
• D. 0.22, 0.78

Hint:

In mole fraction calculations, always ensure you first convert the mass to moles using the molar mass, then use the mole fraction formula to find the respective fractions.

Answer 1

The Correct Option is C

Step 1: Formula for mole fraction.
The mole fraction of a component \( i \) in a solution is given by the formula: \[ X_i = \frac{n_i}{n_{\text{total}}} \] where \( n_i \) is the number of moles of component \( i \), and \( n_{\text{total}} \) is the total number of moles in the solution.
Step 2: Calculating moles of ethyl alcohol and water.
Moles of ethyl alcohol (C$_2$H$_5$OH) = \(\frac{46}{46} = 1\) mole. Moles of water (H$_2$O) = \(\frac{162}{18} = 9\) moles.
Step 3: Calculating mole fractions.
Total moles in the solution = \( 1 + 9 = 10 \) moles. Mole fraction of ethyl alcohol = \(\frac{1}{10} = 0.1\). Mole fraction of water = \(\frac{9}{10} = 0.9\).
Step 4: Conclusion.
The correct answer is (C) 0.1, 0.9, as these are the mole fractions of ethyl alcohol and water, respectively.