Vapour is injected at a uniform rate in a closed vessel which was initially evacuated. The pressure in the vessel (a) increases continuously (b) decreases continuously (c) first increases and then decreases (d) first increases and then becomes constant

When considering a scenario where vapour is injected into a closed vessel that was initially evacuated, we are dealing with a system where the volume is fixed and no substances can enter or leave the system other than the vapour being introduced. The fundamental concept to grasp here is that as vapour is injected, the amount of substance inside the vessel increases.

In a real-world application, this process could be akin to filling a tire with air or inflating a balloon, where you can intuitively understand that the more air you put in, the tighter or more inflated it gets. Similarly, when vapor enters the evacuated vessel, the space inside starts to get filled with vapor particles.

While this is conceptually simple, understanding what happens on the molecular level provides more insights. The vapor particles are constantly moving and colliding with the walls of the vessel. As more particles are injected, the frequency of collisions increases, which in turn increases the force exerted on the vessel's walls. This force, spread out over the area of the walls, is what we perceive as pressure.

The Ideal Gas Law, represented by the equation \( PV = nRT \), is a fundamental relationship in chemistry and physics that describes the behavior of ideal gases. It connects the pressure (P), volume (V), number of moles (n), the ideal gas constant (R), and temperature (T). When applying it to the scenario of vapour being injected into a closed vessel, several conditions are held constant.

Since the vessel's volume does not change and the process occurs at a uniform temperature, the variables V and T in the equation can be considered constants. The injection of vapour increases the number of moles (n), which directly influences the pressure (P) inside the vessel, as shown in the equation.

Understanding Moles and Pressure

A mole, often used in chemistry, is a unit that measures the amount of substance. In the context of the Ideal Gas Law, as the number of moles increases due to the continuous injection of vapor, the pressure must also rise to maintain the balance in the equation, assuming the volume and temperature do not change.

The pressure dynamics inside a closed system can be intriguing. When vapour is injected into a closed vessel, it leads to a pressure change in that confined space. Initially, with the introduction of vapor, pressure begins to rise. This is because the closed system does not allow the expanding vapor to escape, thereby increasing the frequency and force of particle collisions against the vessel's walls.

However, there comes a point where the system reaches its capacity, often referred to as saturation. At this stage, despite continuous injection, no more vapor can be accommodated within the fixed volume, and the pressure stabilizes.

Equilibrium and Maximum Capacity

The concept of equilibrium is paramount in understanding why the pressure eventually becomes constant. Once the maximum capacity is reached, any newly injected vapor molecules are escaping or condensing at the same rate as they are being introduced, due to the lack of space for expansion. The vessel's pressure thus becomes constant, which is the equilibrium point where the rate of injection equals the rate of condensation or escape of vapor.