Question

When an ideal binary solution is in equilibrium with its vapour, the molar ratio of the two components in the solution and the vapour phase is:
A) same
B) Different
C) May or may not be the same depending upon the volatile nature of the two components
D) None of the above

Answer 1

Hint: The ideal binary solution is a mixture of two components. The vapour pressure on the solution can be expressed in terms of molar ratio. The relation between the vapour pressure and molar ratio is given by Raoult's law.

Complete step by step answer:
According to Raoult's law, the partial pressure of any volatile component of a solution at any temperature is equal to the vapour pressure of the pure component multiplied by the mole fraction of that component in the solution.
For a binary solution let’s made of the $\text{ }{{\text{n}}_{\text{A}}}\text{ }$moles of volatile liquid A and $\text{ }{{\text{n}}_{\text{B}}}\text{ }$moles of a volatile liquid B. If $\text{ }{{P}_{A}}\text{ }$and $\text{ }{{P}_{B}}\text{ }$are the partial pressure of the two liquid components, then, according to the Raoult’s law,
$\text{ }{{P}_{A}}\text{ = }{{x}_{A}}\text{ }p_{A}^{0}\text{ }$ and $\text{ }{{P}_{B}}\text{ = }{{x}_{B}}\text{ }p_{B}^{0}\text{ }$
Where, ${{x}_{A}}$ is the mole fraction of component A and ${{x}_{B}}$ is the mole fraction of B.
Raoult’s law is obeyed for the binary solution. The law is obeyed perfectly for the ideal solutions.
Let us consider a binary solution of two components A and B. The graph of the partial pressure of each component against the mole fraction in the solution is a straight line and the total vapour pressure of the solution for any given composition is equal to the sum of the partial vapour pressure of the two constituents.
The partial vapour pressure of component A is given as ${{x}_{A}}\text{ }p_{A}^{0}\text{ }$and that of component B is given by${{x}_{B}}\text{ }p_{B}^{0}\text{ }$. The total vapour pressure of the solution is given by, ${{x}_{A}}\text{ }p_{A}^{0}\text{ + }{{x}_{B}}\text{ }p_{B}^{0}\text{ }$.
Now, if the component of the binary solution is similar, this implies that the intermolecular or cohesive forces in these are completely uniform i.e. the magnitude of these forces between molecules A and B, B and B, and A and B are of the same magnitude.
But, if the binary solution is made out of the component A and B are different. The vapour pressure depends on the escaping tendency or volatile nature of the components. if a component A is volatile then it can easily overcome the intermolecular forces of attraction between the surrounding molecules. The vapour phase composition of the component will be equal to the product of partial pressure and mole fraction. Since, the component is volatile, easily escapes from the mixture, it has the most vapour pressure and hence, the mole fraction of the volatile component will not be equal to the mole fraction of component B.
Thus, the molar ration in the ideal binary solution may or may not be the same depending upon the volatile nature of the two components

Hence, (C) is the correct option.

Note: Note that, it is immaterial for a molecule as to what type of neighbours it has. It means the molecule A can be surrounded by the component B or A. The escaping tendency of the component from the ideal solution is the same as that from the pure liquid except the fact that the proportionality may reduce the mole fraction from the molecule.
Some of the examples of the ideal solutions are as follows:
Ethylene bromide and ethylene chloride, n-hexane and n-heptane etc.