Calculate the molarity of a solution of ethanol in water in which the mole fraction of ethanol is $0.040$.

[Assume the density of water to be one] 

The mole fraction of ethanol is equal to the ratio of the number of moles of ethanol to the total number of moles present in the solution.

For dilute solutions, 1 L of water (or 1 L of solution) contains $\frac{1000}{18}=55.55$ moles of water. 

Let n be the number of moles of ethanol. The mole fraction of ethanol is 0.040.

Hence, $0.040=\frac{n}{n+55.55}$

$n=0.040n+2.222$

$n=\frac{2.222}{1-0.040}=2.31$ moles.

The molarity of the solution is the ratio of the number of moles of solute present in 1 L of solution.

As 1 L of solution contains 2.31 moles of ethanol, the molarity of a solution is 2.31 M.