**Core Concept**
Non-traumatic hemoperitoneum refers to the accumulation of blood in the peritoneal cavity due to internal bleeding. This condition can be caused by various factors, including vascular rupture, abdominal organ rupture, or bleeding disorders.

**Why the Correct Answer is Right**
The most common cause of non-traumatic hemoperitoneum is the rupture of an abdominal organ, particularly the spleen. This occurs when there is a sudden increase in pressure within the spleen, often due to a vascular malformation or a bleeding disorder. The splenic capsule can rupture, leading to massive bleeding into the peritoneal cavity. The spleen's rich vascular supply and its fragile capsule make it prone to rupture, especially in patients with underlying conditions such as portal hypertension or hematological disorders.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option is incorrect because it is too vague and does not specify a particular cause of non-traumatic hemoperitoneum. While vascular rupture is a possible cause, it is not the most common one.
* **Option B:** This option is incorrect because it refers to a condition that is less common than splenic rupture. Hepatic rupture can occur due to trauma or liver disease, but it is not the leading cause of non-traumatic hemoperitoneum.
* **Option C:** This option is incorrect because it is a bleeding disorder that can contribute to non-traumatic hemoperitoneum, but it is not the most common cause. Patients with bleeding disorders may be at increased risk of splenic rupture, but the disorder itself is not the primary cause of the condition.

**Clinical Pearl / High-Yield Fact**
In patients with non-traumatic hemoperitoneum, it is essential to quickly identify the underlying cause and initiate appropriate treatment. The spleen is the most common source of bleeding, and prompt splenectomy or embolization may be necessary to control the bleeding.

**Correct Answer:** D.