Final answer:
The nurse's priority for a client with a closed traumatic brain injury on mechanical ventilation is to maintain a PaCO2 of approximately 35 mm Hg due to its impact on intracranial pressure.
Step-by-step explanation:
The nurse's priority when caring for a client with a closed traumatic brain injury receiving mechanical ventilation is to maintain a PaCO2 of approximately 35 mm Hg. This is crucial because the level of carbon dioxide in the blood can affect intracranial pressure, which is a significant concern after a brain injury. Excessive carbon dioxide can lead to increased intracranial pressure, potentially worsening the brain injury or causing additional damage. Therefore, monitoring and managing PaCO2 takes precedence over pain management, temperature checks, and repositioning in this particular scenario.