Final answer:
The serous membrane in danger of infection in the case of acute appendicitis is the peritoneum.
Step-by-step explanation:
The serous membrane in danger of infection in the case of acute appendicitis is the peritoneum. The peritoneum is a serous membrane that covers the abdominal organs and forms double sheets of mesenteries that suspend many of the digestive organs. Inflammation of the peritoneum, known as peritonitis, is a life-threatening condition often associated with bacterial infections seen with appendicitis.