Final answer:
The brain, specifically the medulla oblongata and pons, governs Qi and respiration by controlling the rate and depth of breathing. These respiratory centers monitor and adjust the breathing rate based on the body's needs.
Step-by-step explanation:
The organ that governs Qi and respiration is the brain. Specifically, the medulla oblongata and the pons in the brainstem are responsible for controlling the rate and depth of breathing. They act as respiratory centers and regulate the muscles involved in breathing, such as the diaphragm and intercostal muscles. These respiratory centers continuously monitor and adjust the breathing rate based on the body's needs, including factors like blood acidity and carbon dioxide levels.