4. You are studying the behavior of a perfluorocarbon-based O2 carrier as an emergency treatment for hypoxemia. It has an approximate molecular radius of 2 nm. Consider ultrafiltration through the kidney (glomerular membrane pore radius 4 nm, length 800 nm). Assuming a therapeutic dose in the blood of 22 mM and 2 mM in the filtrate, determine the electrochemical potential across glomerular membrane.

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Explanation:

The molecular radius of the perflurocarbon-based O2 carrier suggests that it passes through the Bowman's capsule during ultrafiltration. Initial levels of the O2 carrier in blood are 22mM and concentration of the O2 carrier in the final glomerular filtrate is 2mM. Electrochemical potential is the driving source of energy required for the transport of a solute across the membrane. It is also known as the Gibbs free energy G. ΔG'o is the free energy change under standard conditions. Standard free energy change is directly related to the equilibrium constant (K'eq). Equilibrium is the state of the reaction where the concentration of the reactants equals the concentration of the products.

K'eq = [final concentration]/[initial concentration]

K'eq = 2mM/22mM = 0.09

ΔG'o = - RT ln K'eq; R (gas constant) = 8.315 J/mol. K

T (temperature) = 298 K

ΔG'o = - (8.315 x 298) ln 0.09 = + 5.96 kJ/mol

The separation of small molecules and ions from large molecules and cells in the blood is termed as ultrafiltration. The filtered out fluid is known as glomerular filtrate, capsular filtrate or ultrafiltrate. A nephron is a single unit of structure and function in a kidney.