To determine the correct statement for the spontaneous adsorption of a gas, we need to consider the thermodynamics involved.$\\$The spontaneity of a process is determined by the Gibbs free energy change $(\Delta G). \\$For a process to be spontaneous, $\Delta G$ must be negative. The relation is given by:$\\ \Delta G = \Delta H - T\Delta S \\$Where:$\\$• $\Delta G$ is the change in Gibbs free energy.$\\$• $\Delta H$ is the change in enthalpy.$\\$• $T$ is the temperature in Kelvin.$\\$• $\Delta S$ is the change in entropy.$\\$For adsorption of a gas onto a surface:$\\$• The process is exothermic, so $\Delta H$ is typically negative.$\\$• The entropy change $(\Delta S)$ is negative because the gas molecules lose freedom when adsorbed onto a surface.$\\$Thus, for spontaneous adsorption:$\\$• $\Delta H$ should be negative (exothermic).$\\$• $\Delta S$ is negative.$\\$Substituting these into the Gibbs free energy equation:$\\ \Delta G = \Delta H - T\Delta S \\$Since both $\Delta H$ is negative and $\Delta S$ is negative, $\Delta G$ will be negative, ensuring spontaneity.$\\$Therefore, the correct option is:$\\$Option 2: $\Delta S$ is negative and $\Delta H$ should be highly negative.