To calculate the molarity of a solution of ethanol in water with a mole fraction of 0.040, it is established that the mole fraction of water is 0.96, indicating the solution is 96% water and 4% ethanol. Molarity is defined as moles of solute divided by liters of solution. Assuming a basis of 100 moles, with 4 moles of ethanol and 96 moles of water, and an assumed volume of 150 liters, the molarity is calculated to be 0.0266. It is clarified that the mole fraction does not equate to weight/weight percentage, as the solution actually contains 9.6% w/w ethanol. The discussion emphasizes the importance of accurately representing the relationship between mole fraction and concentration.