A mixture of gases $$O_2$$, $$H_2$$ and CO are taken in a closed vessel containing charcoal. The graph that represents the correct behaviour of pressure with time is:

Charcoal acts as an excellent adsorbent for gases. When a mixture of gases is enclosed in a vessel with charcoal, the gas molecules accumulate on the solid surface of the charcoal through adsorption.

• As time progresses, the number of free gas molecules in the gaseous phase steadily decreases because they are being trapped on the charcoal's surface.
• According to the ideal gas law ($$P \propto n$$ at constant volume and temperature), a decrease in the number of moles ($$n$$) of free gas directly causes the total pressure ($$P$$) inside the vessel to drop.
• Eventually, the rate of adsorption equals the rate of desorption, and the system reaches an adsorption equilibrium. At this point, the pressure stabilizes and becomes constant.

Detailed Evaluation of Each Option:

• Option A: Linear Decrease to Zero

  This graph shows pressure dropping linearly at a constant rate until it hits zero. This is incorrect because adsorption is a surface phenomenon that slows down as active sites become occupied, and pressure never reaches zero since equilibrium is established.




• Option B (Green Checkmark): Exponential Decay to a Constant Value

  This graph shows pressure starting high, decreasing rapidly at first (when many charcoal sites are vacant), then curving gradually to level off horizontally. This perfectly depicts the system reaching a state of dynamic equilibrium where pressure remains constant over time.




• Option C & D: Increasing or Constant Pressure

  These graphs represent pressure either rising or remaining perfectly unchanged from the start, completely ignoring the gas removal caused by the charcoal's adsorption capacity.

Conclusion:

The pressure decreases non-linearly with time and eventually levels out horizontally due to the establishment of adsorption equilibrium.

Answer: Option B