The most likely diagnosis is a complex mixed acid-base disorder consisting of respiratory alkalosis, increased anion gap metabolic acidosis, and metabolic alkalosis. Analysis of acid-base disorders requires the identification of the likely dominant acid-base disorder, followed by an assessment of the secondary, compensatory response. When measured values fall outside the range of the predicted secondary response, a mixed acid-base disorder is present; multiple acid-base disturbances may coexist in a single patient. This patient's dominant acid-base disorder is alkalosis, as indicated by the blood pH of 7.56. The low PCO₂ indicates a respiratory component to the alkalosis. The expected compensation for chronic respiratory alkalosis is a decrease in the serum bicarbonate of 4 to 5 mEq/L (4-5 mmol/L) for each 10 mm Hg (1.3 kPa) decrease in the PCO₂. The expected serum bicarbonate concentration in this patient is calculated to be 14 to 16 mEq/L (14-16 mmol/L), and the measured serum bicarbonate of 20 mEq/L (20 mmol/L) suggests coexistence of a metabolic alkalosis. This patient also has an elevated anion gap indicating the presence of an increased anion gap metabolic acidosis. The change of the anion gap from normal is 10 mEq/L (10 mmol/L). Calculating the ratio of the change in the anion gap (Δ anion gap) to the change in bicarbonate level (Δ bicarbonate), or the “Δ-Δ ratio,” can help confirm if there is a coexisting acid-base disturbance. A ratio of <1 may reflect the presence of concurrent normal anion gap metabolic acidosis, whereas a ratio of >2 may indicate the presence of metabolic alkalosis. This patient's Δ-Δ ratio is 2.5, confirming the coexistence of a metabolic alkalosis. The clinical scenario most likely responsible for this complex acid-base disorder is salicylate toxicity with central hyperventilation from the salicylate, anion gap metabolic acidosis from the salicylate, and metabolic alkalosis from gastritis and vomiting.