Spontaneous adsorption of a gas on a solid surface is exothermic process because:

Spontaneous adsorption of a gas on a solid surface is exothermic process because entropy decreases. With adsorption, the unpredictability of gas molecules likewise declines. Hence, $\mathrm{\Delta S}$ is also negative.

Therefore, $\mathrm{T\Delta S}\text{ is -ve. }$

$\mathrm{\Delta H}=\mathrm{\Delta G}+\mathrm{T\Delta S}$

Therefore, $\mathrm{\Delta H}=-\mathrm{ve}$