Question

The kinetics of ethanol absorption in the human body followed by the metabolic oxidation of ethanol by the enzyme LADH (Liver Alcohol Dehydrogenase) can be mathematically described in terms of a consecutive reaction sequence of the type: A--k₁-->B--k₂-->C

where the absorption step exhibits first order kinetics with a rate constant k₁ and the metabolic oxidation exhibits zero order kinetics with a rate constant k₂. Write down the rate equations for the time rate of decay of reactant A and the rate of formation of species B and C. Integrate these expressions using the assumption that at zero time [A] = [A]₀ ,[B] = [C] = 0 , and show that the time variation for the species concentrations are given by:

[A]_t=[A]_o exp[-k₁t] and [B]_t=[A]_o(1-exp[-k₁t])-k₂t and [C]_t=k₂t

Show that the intermediate species B will exhibit a maximum concentration at a time given by t_m=(1/k₁)(ln((k₁*[A]_o)/k₂) , and determine the value of the maximum concentration [B]_m at this time.

Answer 1