Final answer:
The nurse should prioritize the nursing diagnosis of 'Risk for Infection Related to Possible Rupture of Appendix' for a patient with appendicitis to prevent peritonitis.
Step-by-step explanation:
The nursing diagnosis that should be prioritized for a 16-year-old patient diagnosed with appendicitis is Risk for Infection Related to Possible Rupture of Appendix. Appendicitis is a condition where the appendix becomes infected and inflamed and can lead to severe complications if the appendix ruptures, spreading infection throughout the abdominal cavity and potentially leading to peritonitis, which is a life-threatening condition. Early recognition and prompt surgical intervention to remove the infected appendix are critical in preventing the spread of infection.