A 70 kg man with poor access to water has serum sodium of 160 mEq/L. Using the free water deficit formula (deficit = 0.6 x body weight x [measured Na/140 minus 1]), what is his approximate free water deficit?
- A 12 litres
- B 9 litres
- C 6 litres ✓
- D 3 litres
Correct answer: C. 6 litres
Explanation
Deficit equals 0.6 x 70 x (160/140 minus 1) = 42 x 0.143, which is approximately 6 litres. The factor 0.6 represents total body water as a fraction of body weight in an adult man; 0.5 is conventionally used for women. Half the deficit is replaced over the first 24 hours to avoid cerebral oedema from overly rapid correction of chronic hypernatraemia.
Reference: Harrison's Principles of Internal Medicine, 21st ed.
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