Step 1: Recall principle of adsorption.
Extent of adsorption depends on the nature of the gas. More easily liquefiable gases are adsorbed more strongly.
Step 2: Compare given gases.
- H$_2$: Least adsorbed, as it is highly non-polar and light.
- CH$_4$: More adsorbed than H$_2$, but weak van der Waals forces.
- CO$_2$: More adsorbed due to higher polarity.
- NH$_3$: Maximum adsorption, as it is highly polar and strongly interacting.
Step 3: Conclusion.
Thus, NH$_3$ is adsorbed in the largest amount by charcoal.