Final answer:
The most appropriate device to administer oxygen to the unconscious, breathing patient in this scenario would be the Non-rebreathing mask, as it delivers a high concentration of oxygen and prevents the patient from rebreathing exhaled air.
Step-by-step explanation:
In this scenario, the patient is unconscious but breathing, and has a red skin color. This suggests that the patient may be experiencing hypoxia, which is a condition where there is a low level of oxygen in the blood. To provide oxygen to the patient, a device that can deliver a high concentration of oxygen is needed. The most appropriate device in this situation would be the Non-rebreathing mask. This mask has a reservoir bag that can deliver oxygen at a higher concentration compared to other devices, and it also prevents the patient from rebreathing exhaled air.