Here's how to calculate the mole fraction of ethanol in the solution:

1. Understand Mole Fraction

Mole fraction (χ) is the ratio of the number of moles of a specific component in a mixture to the total number of moles of all components in the mixture.

2. Calculate the Total Moles

* Total moles = moles of ethanol + moles of water

* Total moles = 3.00 moles + 5.00 moles = 8.00 moles

3. Calculate the Mole Fraction of Ethanol

* Mole fraction of ethanol (χ_ethanol) = (moles of ethanol) / (total moles)

* χ_ethanol = 3.00 moles / 8.00 moles = 0.375

Therefore, the mole fraction of ethanol in the solution is 0.375.