Question

An Aqueous solution of Alcohol contains 18 g of water and 414 g of ethyl alcohol .The mole fraction of water is

• A. 0.7
• B. 0.1
• C. 0.9
• D. 0.4

Answer 1

The Correct Option is B

Correct Answer: 0.1 

Explanation:
To find the mole fraction of water, we use the formula:
Mole fraction of water (χ_water) = moles of water / (moles of water + moles of alcohol)

Given:
• Mass of water = 18 g
• Molar mass of water (H₂O) = 18 g/mol → Moles of water = 18 / 18 = 1 mol

• Mass of ethyl alcohol (C₂H₅OH) = 414 g
• Molar mass of ethyl alcohol = 46 g/mol → Moles of alcohol = 414 / 46 ≈ 9 mol

Now, mole fraction of water:
\( \chi_{water} = \frac{1}{1 + 9} = \frac{1}{10} = 0.1 \)

Therefore, the mole fraction of water is 0.1.

Answer 2

To calculate the mole fraction of water in the given solution, we need to find the moles of water and moles of ethyl alcohol, and then divide the moles of water by the total moles in the solution.
First, we calculate the moles of water:
\(\text{Moles of water} = \frac{\text{Mass of water}}{\text{Molar mass of water}}\)

\(\text{Moles of water} = \frac{18 \, \text{g}}{18.015 \, \text{g/mol}} \, (\text{molar mass of water})\)

\(Moles of water = 0.9999 mol (approximately 1 mol)\)

Next, we calculate the moles of ethyl alcohol:
\(\text{Moles of ethyl alcohol} = \frac{\text{Mass of ethyl alcohol}}{\text{Molar mass of ethyl alcohol}}\)

\(\text{Moles of ethyl alcohol} = \frac{414 \, \text{g}}{46.07 \, \text{g/mol}} \, (\text{molar mass of ethyl alcohol})\)
Moles of ethyl alcohol = 8.986 mol (approximately 9 mol)

Now, we can calculate the mole fraction of water:
\(\text{Mole fraction of water} = \frac{\text{Moles of water}}{\text{Moles of water} + \text{Moles of ethyl alcohol}}\)

\(\text{Mole fraction of water} = \frac{1 \, \text{mol}}{1 \, \text{mol} + 9 \, \text{mol}}\)

\(\text{Mole fraction of water} = \frac{1}{10}\)
Mole fraction of water = 0.1
Therefore, the mole fraction of water in the given solution is (B) 0.1.