TECHNOLOGY FOCUS - INORGANIC CHEMISTRY - Preferred Process: The basic nitrogenous compound is grafted onto the porous solid oxide by chemical reaction. The sorption and desorption steps are conducted at different pressures, where the total pressure of the desorption step is lower than the total pressure of the sorption step, and the partial pressure of hydrogen sulfide in the desorption step is less than the partial pressure of hydrogen sulfide in the sorption step. The sorption and desorption steps are conducted at different temperatures. In the process, at least a portion of the sorbed hydrogen sulfide is desorbed by a non-sorbing inert purge gas and/or by a displacement purge gas. The pressure in the sorption step is such as to cause carbon dioxide to be sorbed from the gas stream in addition to the hydrogen sulfide. In the process, desorption is carried out in at least two steps under conditions of different pressure in each step with the pressure of the first desorption step being higher than the pressure of the second desorption step so that most of the carbon dioxide sorbed in the sorption step is desorbed in the first desorption step and most of the hydrogen sulfide sorbed in the sorption step is desorbed in the second desorption step. The process is operated cyclically between the sorption and desorption conditions with a total cycle time of less than one minute. In the process-1, a greater mole% of hydrogen sulfide is sorbed by the basic compound than carbon dioxide sorbed by the sorbent. The sorption and desorption steps are conducted at different pressures, where (aa) the total pressure of the desorption step is lower than the total pressure of the sorption step, (bb) the partial pressure of hydrogen sulfide in the desorption step is less than the partial pressure of hydrogen sulfide in the sorption step, or (cc) both (aa) and (bb). In the process-1, at least a portion of the sorbed hydrogen sulfide is desorbed by a non-sorbing inert purge gas and/or by a displacement purge gas. The process-2 further comprises sending at least a portion of the hydrogen sulfide-rich stream to a Claus plant, and recovering sulfur from the hydrogen sulfide-rich stream. In the process-3 at least a portion of the hydrogen sulfide-rich product stream is passed to a Claus plant for the recovery of sulfur. Preferred Components: The basic nitrogenous compound is supported on a porous solid. The porous solid comprises: a porous solid oxide; a mesoporous or macroporous solid oxide; a mesoporous silica; or a mesoporous solid oxide comprising mobile crystalline material (MCM)-41, MCM-48, SBA-1, SBA-2, SBA-3, SBA-15, KIT-1, KIT-5 and/or KIT-6. The CO2 and hydrogen sulfide partial pressures during the asorption step are less than 1 bar. The feed gas mixture contains less than 5 mole% water. The natural gas feed stream contains 10-10000 parts per million by volume (vppm) hydrogen sulfide, where the natural gas product stream contains less than 4 vppm hydrogen sulfide. The natural gas feed stream contains at least 5 mole% carbon dioxide, where the natural gas product stream contains at most 5 mole% less carbon dioxide than the natural gas feed stream. The carbon dioxide rich product stream has a lower mole% of hydrogen sulfide than the feed gas stream. The feed gas stream comprises at least a combined total of 50 mole% hydrogen sulfide and carbon dioxide, where the feed gas stream is a pre-separated contaminant stream resulting from the separation of hydrogen sulfide and carbon dioxide from a natural gas stream from a producing formation and the carbon dioxide-rich stream is re-injected into the producing formation.    TECHNOLOGY FOCUS - ORGANIC CHEMISTRY - Preferred Components: The basic nitrogenous compound comprises a tertiary amine, or an amidine, guanidine, or biguanidine. The tertiary amine comprises triethylamine, triethanolamine or methyldiethanolamine.