Final answer:
The primary diagnosis is likely congestive heart failure, followed by secondary diagnoses like respiratory failure that occurred after admission, with intubation and ventilator management coded separately.
Step-by-step explanation:
The correct coding and sequencing of the diagnoses for a patient admitted to the hospital with shortness of breath and congestive heart failure, who subsequently develops respiratory failure and undergoes intubation with ventilator management, can be complex. It typically follows specific guidelines such as the International Classification of Diseases (ICD) codes. The principal diagnosis would be the condition that after study is established as chiefly responsible for the patient's admission to the hospital. As the patient initially came in with symptoms of congestive heart failure, this might be considered the principal diagnosis. The secondary diagnosis would be respiratory failure, as it developed after hospital admission. Procedures such as intubation and ventilator management are usually coded separately. In practice, coding professionals would refer to the most recent ICD coding manual and guidelines, and collaborate with healthcare providers to ensure accurate and compliant coding.