Hint: It’s important to understand that Raoult’s law is connected to vapor pressure. Additionally, knowing that volatility refers to a substance’s tendency to evaporate readily at standard temperatures is essential. With this knowledge, answering this question becomes straightforward.
Complete step by step answer:
Raoult’s Law – The vapor pressure of a solution containing a non-volatile solute is equal to the vapor pressure of the pure solvent at the same temperature, multiplied by the mole fraction of the solvent in the solution.
In mathematical terms, Raoult’s law is expressed as:
[latex]P_{\text{solution}} = P^{0}_{\text{solvent}} X_{\text{solvent}}[/latex]
In this equation, [latex]P^{0}_{\text{solvent}}[/latex] is the vapour pressure of the pure solvent at a particular temperature,
[latex]P^{0}_{\text{solution}}[/latex] is the total pressure of the solution, [latex]X_{\text{solvent}}[/latex] is the mole fraction of the solvent.
Proof of Raoult’s Law for a Non-Volatile Solute in a Volatile Solvent:
In a solution containing a volatile solute (A) and a solvent (B), the total pressure is the sum of the partial pressures of both components, expressed as:
[latex]P_{\text{solution}} = P^{0}_{A} X_{A} + P^{0}_{B} X_{B}[/latex]
As we know [latex]X_{A} + X_{B} = 1[/latex], Or we can write this as [latex]X_{A} = 1 – X_{B}[/latex]
Now place this value in above equation,
[latex]P_{\text{solution}} = P^{0}_{A} (1 – X_{B}) + P^{0}_{B} X_{B}[/latex],
Now rearrange this equation,
[latex]P_{\text{solution}} = P^{0}_{A} + (P^{0}_{B} – P^{0}_{A}) X_{B}[/latex]
We know that, for non-volatile solute [latex]P^{0}_{A} = 0[/latex]
Thus, [latex]P_{\text{solution}} = P^{0}_{B} X_{B}[/latex]
Limitations of Raoult’s Law:
The intermolecular forces between the solvent and solute must be similar to those present between the individual molecules. Additionally, the gaseous phase is assumed to behave ideally, allowing for the application of the ideal gas law.
Thus, we have articulated and demonstrated Raoult’s law for a non-volatile solute in a volatile solvent, along with the law’s limitations.
Note: We can compare Raoult’s law and Henry’s law to highlight their differences. Henry’s law is a limiting law that is applicable only to “sufficiently dilute” solutions, whereas Raoult’s law is typically valid when the liquid phase is nearly pure or for mixtures of comparable substances.