A 42-year-old woman with type 2 diabetes mellitus presents with nausea, vomiting, and rapid shallow breathing. She has a 2-week history of poor glycemic control and missed insulin doses. Arterial blood gas analysis shows: pH 7.18, PaCO₂ 24 mmHg, HCO₃⁻ 9 mEq/L, anion gap 18 mEq/L. What is the primary acid-base disturbance, and what is the expected PaCO₂ for appropriate respiratory compensation?