Endothelial cells contain a surface enzyme that converts a toxin A into a harmle

Question

Endothelial cells contain a surface enzyme that converts a toxin A into a harmless species at a rate that is proportional to the perfused surface area and the toxin concentration squared (conversion rate 1?4 k00ScA2), where k00 1?4 9 105 cm4 mol 1 min 1 and S 1?4 60 cm2. Blood flow to the organ segment is 6 ml/min. Find the toxin concentration at the outlet of the organ segment if the inlet concentration is 0.01 mol/L. Assume the toxin distributes equally in plasma and red cells, and that the blood volume in the organ segment is well-mixed.

13.11.8 Steady-State Removal of a Toxin Endothelial cells contain a surface enzyme that converts a toxin A into a harm- less species at a rate that is proportional to the perfused surface area and the toxin concentration squared (conversion rate=k"SCA2), where k"=9 × 105 cm4 mol-1 min-1 and S = 60 cm2. Blood flow to the organ segment is 6 ml/min. Find the toxin concentration at the outlet of the organ segment if the inlet 986 13 Macroscopic Approach to Biomass Transpont concentration is 0.01 mol/L. Assume the toxin distributes equally in plasma and red cells, and that the blood volume in the organ segment is well-mixed.

Explanation / Answer

As the given system is well mixed, Mixed flow reactor equation can be applied.

FA0 -FA = (-rA)S    -- eq (1)

Here FA0 = v0CA0,   FA = v0CA and (-rA)S = K"SCA2

So eq (1) reduced to

v0(CA0 - CA) = K"SCA2    -- eq (2)

6(ml.min)*(0.001-CA)(mol/L)=9*105(cm4/mol.min)*60(cm2)*CA2(mol/L)2

Unit conversion (1ml = 1 cm3 =0.001L)

0.001-CA (mol/L) = 9000*CA2(mol/L)2

Solving above quadratic equation results in CA = 0.001 mol/L

CA = 0.001 mol/L(90% conversion)

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