If the rate of evaporation is y, and the rate of condensation is x, then, a vapour is saturated when

Analysis

The question asks for the condition under which a vapour is considered "saturated." In thermodynamics, saturation refers to a state of dynamic equilibrium between a liquid and its vapour phase.

Concept Explanation

• Evaporation: This is the process where molecules escape from the surface of a liquid into the space above it. The rate of evaporation ($y$) depends primarily on temperature.
• Condensation: This is the process where vapour molecules collide with the liquid surface and return to the liquid state. The rate of condensation ($x$) depends on the concentration (or pressure) of the vapour.
• Dynamic Equilibrium: A vapour is said to be saturated when the number of molecules leaving the liquid surface (evaporation) is exactly equal to the number of molecules returning to the liquid surface (condensation) per unit time. At this point, the vapour pressure is at its maximum for that specific temperature.

Step-by-Step Solution

1. Identify the variables: • $y$ = Rate of evaporation • $x$ = Rate of condensation
2. Define the state of saturation: Saturation occurs when the system reaches equilibrium.
3. Apply the principle: For equilibrium to exist, the rate at which molecules enter the vapour phase must equal the rate at which they leave it.
4. Mathematical expression: If $y$ is the rate of leaving (evaporation) and $x$ is the rate of returning (condensation), then for saturation: $$x = y$$

Conclusion

When the rate of condensation equals the rate of evaporation, the amount of vapour in the space remains constant. This is the definition of a saturated vapour.

The correct option is C.

Exam Tip

Think of a "saturated" state like a crowded room with one door: if the number of people entering the room ($y$) is exactly the same as the number of people leaving the room ($x$), the total number of people inside stays constant. That is dynamic equilibrium!