A 50-year-old male with acute pancreatitis has measured serum osmolality 315 mOsm/kg, Na+ 138 mEq/L, glucose 180 mg/dL, and BUN 28 mg/dL. What is his calculated serum osmolality and osmolar gap?

Answer and explanation

Correct answer: D. Calculated osmolality 296 mOsm/kg; Osmolar gap 19 mOsm/kg

  1. Step 1: Calculated Serum Osmolality = 2 x Na+ + [Glucose (mg/dL) / 18] + [BUN (mg/dL) / 2.8].
  2. Step 2: Calculated Osmolality = 2(138) + (180 / 18) + (28 / 2.8) = 276 + 10 + 10 = 296 mOsm/kg.
  3. Step 3: Osmolar Gap = Measured Osmolality - Calculated Osmolality = 315 - 296 = 19 mOsm/kg. An osmolar gap > 10 mOsm/kg suggests the presence of unmeasured exogenous osmotically active substances (such as toxic alcohols).
Answer
Calculated osmolality 296 mOsm/kg; Osmolar gap 19 mOsm/kg (suggesting unmeasured solute).
Why not the others: 310 mOsm/kg incorrectly omits the glucose divisor; 284 mOsm/kg omits BUN calculation; 302 mOsm/kg uses BUN divided by 6.

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