Question

You have a patient that has 14 L of fluid in his ECF compartment and 28 L of fluid in his ICF compartment. The concentration of nonpenetrating solutes in his blood is 300 mosmol/L, and the concentration of nonpenetrating solutes in his cells is 300 mosmol/L. Following the IV infusion of 1L of a 100 mosmol/L NaCl solution, what will be the volume of the ECF compartment? Assume that there is not sufficient time for water or solutes to be eliminated from the body.

Answer 1

Initially

Volume of ECF =14 L

Concentration of solutes =300 mOsm/L

So number of solutes = 14 *300 =4200 mOsm

Volume of ICF =28 L

Number of solutes = 28*300 =8400 moms

Then 1 L of 100 mOsm/L NaCl is added to ECF.

Volume of ECF = 14+1 =15 L

So number of solutes in ECF =4200 +100 =4300 mOsm

Let x Litre of water flows from ECF to ICF.

So osmolarity of ICF = 8400 / (28+x)

Osmolarity of ICF = 4200 /(15-x)

Both should be equal.

Solving, x =666.7 ml

Volume of ECF = 15 L- 0.67 L =14.33 L