Step 1: Understanding the Concept:
Each bacterium listed is well known for causing one specific disease, so the question can be answered by matching organism to disease rather than by any calculation.
Step 2: Key Concept or Approach:
Recall the classic organism to disease pairing for syphilis and rule out the other three organisms by their own well known diseases.
Step 3: Detailed Explanation:
Vibrio cholerae is tied to cholera, a water-borne diarrheal illness.
Bacillus pertussis, properly Bordetella pertussis, is tied to whooping cough, a respiratory infection.
Clostridium tetani produces the toxin responsible for tetanus, a nervous system disease.
Treponema pallidum is the spirochete bacterium that causes syphilis, a sexually transmitted disease that moves through primary, secondary and tertiary stages if left untreated.
Step 4: Final Answer:
The causative organism for syphilis is Treponema pallidum.