Question

a solution was prepared by mixing 10 mole of alcohol and 10 mole of water. what is the composition of solution expressed in mole fraction

Answer 1

Task:

A solution was prepared by mixing 10 mole of alcohol and 10 mole of water. What is the composition of solution expressed in mole fraction?

Solution:

$C_{2}H_{5}OH + H_{2}O = C_{2}H_{5}OH + H_{2}O$ (Ethanol doesn't react with water)

The mole fraction $x_{i}$ is defined as the amount of a constituent $n_{i}$ divided by the total amount of all constituents in a mixture $n_{tot}$:

$$x_{i} = \frac{n_{i}}{n_{tot}}; \ x_{eth} = \frac{n_{eth}}{n_{tot}} = \frac{10}{20} = 0.5; \ x_{water} = \frac{n_{water}}{n_{tot}} = \frac{10}{20} = 0.5$$

The sum of all the mole fractions is equal to 1:

$$\sum_{i=1}^{N} n_{i} = n_{tot}; \ \sum_{i=1}^{N} x_{i} = 1$$

Answer:

$$x_{eth} = 0.5;$$ $$x_{water} = 0.5;$$ $$\sum_{i=1}^{N} x_{i} = 1$$