Please provide complete correct and detailed mathematical solution. This is all

Question

Please provide complete correct and detailed mathematical solution. This is all the information provided. Thank you.

Alcohol (A) is converted to acetaldehyde (DE) by alcohol dehydrogenase (ADH) which is degraded to acetic acid (AOOH) by aldehyde dehydrogenase (ALDH). Acetic acid is then quickly degraded and excreted. Acetaldehyde is a toxic substance that can form radicals and damage body tissue and is responsible for much of the long-term damage caused by drinking. Looking at the degradation of ethanol in more detail, this reaction is aided by cofactor nicotinamide adenine dinucleotide (NAD+) which is converted to NADH, and proceeds by the following elementary steps: Derive a rate expression for the rate of A consumption. where B_i are constants and C_A and C_DE are A and DE concentrations, respectively .Assume that step (2) is rate limiting and that steps (1) and (3) are quasi-equilibrated. You will need to make an additional assumption about the concentration of water, which requires your justification.

Explanation / Answer

Since step 2 is rate limiting the overall reaction will depend on the rate of this reaction. Implying the overall rate contanst which is critical is the one f2or the second step. This has an equilibrium step with rate constants k2 and k-2

Rate of second step =k[C2H5OH.ADH]

Since second step is in equilibrium k2[C2H5OH.ADH] = k-2[CH3CHO.ADH][H2O]. Since these reactions are happening in the body where the composition of water is very high the concentartion term for water is constant and hence it can be taken as part of the constant k-2.

[C2H5OH.ADH] = k2/k-2 [CH3CHO.ADH]

sugbstituing for the rate of second reaction = k(k2/k-2) [CH3CHO.ADH]. SInce all the constants can be combined as K we get

overall rate of the reaction is equal to the rate of the second reaction that is = K [CH3CHO.ADH]. The overall reaction is actually.

C2H5OH + ADH -------> CH3CHO + ADH.

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