Final answer:
For a barbiturate overdose, activated charcoal is the appropriate substance to administer from an emergency drug cart, as it can prevent further absorption of the drug in the gastrointestinal tract.
Step-by-step explanation:
When a patient is admitted to the emergency department with an overdose of a barbiturate, the appropriate emergency medication to administer would be activated charcoal. This substance is used because it can bind to the drug in the stomach and intestines, reducing the amount that is absorbed into the blood. Naloxone (Narcan) would not be suitable as it is an opioid antagonist and does not reverse the effects of barbiturates. Flumazenil (Romazicon) is an antidote for benzodiazepine overdose, not barbiturate poisoning. Ipecac syrup was once used to induce vomiting in poisoning cases but is no longer recommended due to potential complications and lack of efficacy in many scenarios.