A 52-year-old man is brought to the emergency department by ambulance after being found ob… — USMLE Step 2 CK

A 52-year-old man is brought to the emergency department by ambulance after being found obtunded in his garage. His medical history is significant for major depressive disorder and alcohol use disorder. He is unresponsive to verbal stimuli but localizes to pain. Vital signs are within normal limits except for a respiratory rate of $24/\text{min}$ . Laboratory evaluation reveals the following:

Test	Result
Sodium ( $Na^+$ )	$138 \text{ mEq/L}$
Potassium ( $K^+$ )	$4.5 \text{ mEq/L}$
Chloride ( $Cl^-$ )	$100 \text{ mEq/L}$
Bicarbonate ( $HCO_3^-$ )	$12 \text{ mEq/L}$
Blood urea nitrogen (BUN)	$28 \text{ mg/dL}$
Creatinine	$1.4 \text{ mg/dL}$
Glucose	$144 \text{ mg/dL}$
Serum ethanol	Undetectable
Measured serum osmolality	$320 \text{ mOsm/kg}$

Arterial blood gas on room air shows a pH of $7.22$ , $PCO_2$ of $26 \text{ mm Hg}$ , and $PO_2$ of $92 \text{ mm Hg}$ .

Based on these laboratory results, what is the patient's calculated serum osmolar gap?

Answer: 26 mOsm/kg

Answer

The patient's osmolar gap is

26 \text{ mOsm/kg}

. This is calculated by taking the measured osmolality (

320 \text{ mOsm/kg}

) and subtracting the calculated osmolality (

294 \text{ mOsm/kg}

). The formula for calculated osmolality is

(2 \times Na^+) + (\text{Glucose}/18) + (\text{BUN}/2.8)

. This elevated gap, alongside a high anion gap metabolic acidosis (

138 - (100 + 12) = 26

), strongly suggests toxic alcohol ingestion, such as methanol or ethylene glycol, given the clinical context of obtundation and negative ethanol levels.

Step-by-Step Solution

Calculate the expected serum osmolality.

Calculated osmolality =

294 \text{ mOsm/kg}

The calculated osmolality requires serum sodium, glucose, and BUN. The formula is

2[Na^+] + \frac{\text{Glucose}}{18} + \frac{\text{BUN}}{2.8}

Calculate the osmolar gap.

Osmolar gap =

26 \text{ mOsm/kg}

The osmolar gap is the difference between the measured serum osmolality (

320 \text{ mOsm/kg}

) and the calculated serum osmolality (

294 \text{ mOsm/kg}

Key Concept

The serum osmolar gap is used to detect the presence of unmeasured osmotically active substances (such as toxic alcohols). It is calculated by subtracting the calculated serum osmolality from the measured serum osmolality.

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