Question

Q2. A healthy male presents with altered mental status and this was attributed to his [Na+ ] being 108 mEq/L. To return the patient to normal Na+ levels, how much of a 5 wt% NaCl solution must be administered? (Normal plasma Na+ concentration = 140 mEq/L; molecular weight of NaCl is 58; 5 wt% NaCl = 5g/100mL)

Total Body Water = 42L

Extracellular Fluid = 14L

Osmolarity = 300mOsmoles/L

Intracellular Fluid = 28L

Answer 1

parameters are given

we have to go from Na+ =108meq/l to achieve Na+=140meq/l

by using 5% NaCl

total body water x [Na+] = 42 x 108 = 4536 meq. total Na + caoncentration required for body

TBW [Na]= 4536

Normal saline has 154meq/l Na+  

so in 5% Nacl has = 5 x NS = 5 x 154/0.9 =855.55 meq/l

TBW [Na] we want to achieve is 140 meq/l

TBW [Na]= total body sodium required + 5% Na+ X amount divided by TBW+ amount

140    = )

140 ( 42 + amount ) = 4536 + 855 x amount

5880 + 140 x amount = 4536 + 855x amount

5880 - 4536 = (855 -140 ) x amount

1344 = 715 x amount  

amount of 5% Nacl required to achieve 140 meq/l [Na] = 1344/715 = 1.88 L

5% Nacl amount is 1.88L