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The correct answer is gout, which is a form of arthritis that occurs due to the accumulation of uric acid crystals in the joints, particularly in the big toe. This condition is often hereditary, meaning it can run in families. Gout is characterized by sudden and severe episodes of pain, swelling, and redness in the affected joint, usually occurring at night. It is classified as a type of metabolic arthritis because it is related to the body's metabolism of purines, substances found in various foods and beverages, which are broken down into uric acid.
The other conditions listed do not fit the description of hereditary metabolic acute arthritis. Hematoma refers to a localized collection of blood outside blood vessels, typically due to trauma, and does not involve metabolic processes. Hernia is the protrusion of an organ or tissue through an abnormal opening, which is unrelated to arthritis or metabolic disorders. Glaucoma refers to a group of eye conditions that damage the optic nerve, often linked to high eye pressure, and again does not relate to arthritis or metabolic conditions.