‘x’ grams of water is mixed in 69 g of ethanol Mole fraction of ethanol in the resultant solution is 0.6. What is the value of ‘x’ in grams?

18

The correct answer is option 4. 18.

To determine the value of \(x\) (the mass of water), we need to use the concept of mole fraction. The mole fraction of ethanol in the resultant solution is given as 0.6.

\(\text{Mole fraction of ethanol} = \frac{\text{Moles of ethanol}}{\text{Moles of ethanol} + \text{Moles of water}}\)

Given: Mole fraction of ethanol = 0.6

Therefore,

\(0.6 = \frac{\text{Moles of ethanol}}{\text{Moles of ethanol} + \text{Moles of water}}\)

Molar mass of ethanol (\(\text{C}_2\text{H}_5\text{OH}\)) = 46 g/mol

Mass of ethanol = 69 g

Moles of ethanol:

\(\text{Moles of ethanol} = \frac{\text{Mass}}{\text{Molar mass}} = \frac{69}{46} \approx 1.5 \text{ moles}\)

Let \(x\) be the mass of water.

Molar mass of water (\(\text{H}_2\text{O}\)) = 18 g/mol

Moles of water:

\(\text{Moles of water} = \frac{x}{18}\)

Using the mole fraction formula:

\(0.6 = \frac{1.5}{1.5 + \frac{x}{18}}\)

Rearranging to solve for \(x\):

\(0.6 \left(1.5 + \frac{x}{18}\right) = 1.5\)

\(0.9 + \frac{0.6x}{18} = 1.5\)

\(\frac{0.6x}{18} = 1.5 - 0.9\)

\(\frac{0.6x}{18} = 0.6\)

\(0.6x = 0.6 \times 18\)

\(x = 18\)

Conclusion: The mass of water \(x\) needed to produce a solution with a mole fraction of ethanol of 0.6 is 18 grams.