Question

What is the mole fraction of ethanol in solution containing \(46\) g of ethanol and \(180\) g of water?
(Molar mass of ethanol \(=46\) g mol\({}^{-1}\), Molar mass of water \(=18\) g mol\({}^{-1}\))

• A. \(0.25\)
• B. \(0.09\)
• C. \(0.15\)
• D. \(0.05\)

Hint:

Convert both masses to moles and divide the moles of ethanol by the total moles.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
Mole fraction of ethanol \(x=\dfrac{n_{ethanol}}{n_{ethanol}+n_{water}}\).

Step 2: Moles
\(n_{ethanol}=\dfrac{46}{46}=1\) mol
\(n_{water}=\dfrac{180}{18}=10\) mol

Step 3: Calculation
\(x=\dfrac{1}{1+10}=\dfrac{1}{11}\approx0.09\)

Step 4: Compare the options
The value matches option (B).

Final Answer:
The mole fraction of ethanol is about 0.09. \[ \boxed{\text{(B) }\text{0.09}} \]