When a gas is adsorbed on a solid surface, its movement is restricted leading to a decrease in the entropy of the gas i.e. ΔS is negative. Now, we know that, for a process to be spontaneous, ΔG should be negative.
We know, ΔG=ΔH−TΔS
Since ΔS is negative, ΔH has to be negative so as to make ΔG negative. Hence adsorption is always an exothermic process.