Animated Solution for Chemistry - Surface Chemistry: A mixture of gases ${\text{O}}_2$, ${\text{H}}_2$ and $\text{CO}$ are taken in a closed vessel containing charcoal. The graph that represents the correct behaviour of pressure with time is

Gases in a Box

Imagine you are looking inside a sealed, rigid container. At the bottom of this container lies a bed of charcoal.

Above the charcoal, a mixture of gases—specifically ${\text{O}}_2$, ${\text{H}}_2$, and $\text{CO}$—is moving chaotically. These gas molecules are constantly colliding with each other and with the walls of the container.

These collisions are what generate the initial pressure, which we can call $P_0$. At this very first moment, the pressure is at its maximum because all the gas molecules are free to move.

Charcoal at Work

Now, charcoal is not just a passive rock; it is an incredibly porous material and a phenomenal adsorbent.

Because of the unbalanced residual forces on its surface, the charcoal begins to attract the gas molecules. When a gas molecule strikes the surface, it gets trapped there by weak van der Waals forces.

This surface-trapping phenomenon is known as adsorption. As time ticks forward, more and more molecules are pulled out of the chaotic gas phase and get stuck to the solid surface.

Fast Start, Slow Finish

Let's connect this physical reality to the math. According to the Ideal Gas Law, $PV=nRT$. Since the volume $V$ and temperature $T$ of our closed vessel are constant, the pressure $P$ is directly proportional to the number of free gas molecules $n$.

As adsorption proceeds, the number of free molecules $n$ decreases, which means the pressure $P$ must also decrease. But how fast does it decrease?

In the beginning, the entire surface of the charcoal is completely bare. Every molecule that hits the surface finds an empty spot to stick to. Therefore, the initial rate of adsorption is very high, leading to a steep, rapid drop in pressure.

However, as more molecules get adsorbed, the available surface area shrinks. The rate of adsorption begins to slow down, and the pressure drop becomes less steep, creating an exponential decay curve.

Dynamic Equilibrium

Adsorption is not a one-way street. While molecules are sticking to the surface, some of the already adsorbed molecules gain enough thermal energy to break free and re-enter the gas phase—a process called desorption.

Eventually, a critical point is reached where the rate at which molecules adsorb perfectly matches the rate at which they desorb.

This state is called dynamic equilibrium. At this point, the net number of free gas molecules stops changing. Consequently, the pressure stops dropping and settles at a constant equilibrium value, $P_{eq}$.

Looking at our options, the only graph that perfectly captures this story—a steep initial drop that gradually levels off to a constant, non-zero value—is Graph (c).