Question

Calculate the molarity of solution of ethanol in water in which he mole fraction of ethanol is 0.04(assume density of water to be. 1g/cc).

Answer 1

Mole fraction of ethanol is n₁/(n₁+n₂) = 0.04
where n₁ is the number of moles of ethanol and n₂ is the number of moles of water.

$$\begin{gathered} \frac{n_1}{n_1+n_2}=0.04 \\ {n}_1=0.04n_1+0.04n_2 \\ 0.96n_1=0.04n_2 \\ 96n_1=4n_2 \\ 24n_1=n_2 \end{gathered}$$
Density of water = 1 g cm^-3

Mass of water = density$\times$volume
Consider the volume of water is 1 L
Mass of water = 1 g cm^-3$\times$1000 cm³= 1000 g (As 1 L = 1000 cm³)
Number of moles of water, n₂ = 1000/18 = 55.55 (Molar mass of water = 18 g mol^-1)
​As 24 n₁ = n₂
n₁ = n₂/24
n₁ = 55.55/24
n₁ = 2.31
Number of moles of ethanol = 2.31
Molarity = $\frac{numberofmolesofethanol}{Volumeofsolution(inL)}$ (volume of water is equivalent to the volume of solution)