how adsorption process is spontaneous in nature? 

Adsorption is a spontaneous process

For reaction or process to be spontaneous, there must be decreases in free energy of the system i.e. ΔG of the system must have negative value.

Also we know, ΔG = ΔH – TΔS

And during this process of adsorption, randomness of the molecule decreases which means ΔS is negative. We can rewrite above equation as

Therefore for a reaction to be spontaneous ΔH has to be negative and

Adsorption process takes place by adsorbate getting adsorbed on adsorbent .Forces of attraction exist between adsorbate and adsorbent and due to these forces of attraction, heat energy is released. So adsorption is an exothermic process.

Hence  Δ H is negative and adsorption is a spontaneous process.