Explain the process of gas exchange in the human respiratory system

Explain the process of gas exchange in the human respiratory system, focusing on the mechanisms involved in both the lungs and the tissues. Start by describing how oxygen is transported from the environment into the lungs through inhalation and diffusion across the respiratory membrane into the bloodstream. Next, detail the transport of oxygen via hemoglobin molecules and its release to tissues with lower partial pressure. Then, elaborate on the exchange of carbon dioxide in tissues, its transport as bicarbonate ions in the blood, and its release into the alveoli for exhalation. Additionally, discuss the role of respiratory pigments like hemoglobin and factors affecting oxygen-hemoglobin dissociation.