Final answer:
Vecuronium is the drug administered to synchronize a patient's breathing with the ventilator when they attempt to breathe at a different rate, as it acts as a neuromuscular blocker to temporarily paralyze voluntary muscles.
Step-by-step explanation:
When a patient is on a ventilator and wakes up, attempting to breathe at a rate different from the ventilator's settings, it can lead to patient ventilator asynchrony. To ensure synchronization and to prevent the patient from 'fighting' the ventilator, a healthcare provider may administer a neuromuscular blocking agent. The correct drug from the options provided is d) Vecuronium.
Vecuronium is a medication that works as a muscle relaxant by blocking the signals between the nerves and the muscles. This can temporarily paralyze the patient's voluntary muscles, making them unable to move or breathe on their own, which allows the ventilator to fully control the breathing without competition from the patient's breathing efforts. It is important to note that such medication should be administered only under strict clinical supervision and with appropriate sedation and analgesia to ensure patient comfort and safety.