14. Billy, a neurotic fitness buff, decided to “flush the toxins from his body”

Question

14.   Billy, a neurotic fitness buff, decided to “flush the toxins from his body” by drinking 10 liters of distilled water in 20 minutes. Billy weighed 154 pounds and appeared to be a normally hydrated, healthy young man before he started. Assume that he experienced some brain swelling as a result of rapidly drinking the water (water intoxication). Assuming that his osmolarity was normal prior to drinking the water, what was his osmolarity after he finished?

   If you only had access to hypertonic sodium chloride solutions, how much 2.5% sodium chloride should you administer IV to return Billy’s osmolarity to 300 mOsm/L.

   ___________________

Explanation / Answer

Body weight = 154 pounds = 70 kg (approx.)

Gain = 10 L of water

Old TBW = 60% of the body weight = 42 L

Old TBW osmoles = 42 L x 300 mOsm/L = 12600 mOsm

New TBW = 42 L + 10 L = 52 L

New TBW osmolarity = 12600 mosmoles/52 L = 242.3 mOsm/L

1 L of 2.5% NaCl ((For NaCl, assume molecular weight is 58 g/m and osmotic coefficient is 2.0)

2.5 g/100 ml x 1000 ml ÷ 58 g/mole = 0.431 moles

0.431 moles x 2 = 0.862 osmoles = 862 mosmoles

Gain = 862 mosmoles and 1 L

New TBW osmolarity = 300 mOsm/L

Old TBW osmoles = 12600 mOsm

Old TBW volume = 52 L

So, the volume of 2.5% NaCl required to achieve 300mOsm/L

                        = [ (52 X 300) – 12600]/(862-300)

                        = 5.3 L (approx.)

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