please explain in detail. You are investigating the biosynthesis of an unusual n

Question

please explain in detail.

You are investigating the biosynthesis of an unusual natural product called "curesallofum" (CAOU) that is produced in a rare Antarctic night blooming daylily by a two step reaction. First, "curesnoneofum" (CNOU) is used to produce "curessomeofum" (CSOU). CSOU is the precursor to CAOU. In your laboratory, you have determined that CNOU CSOU has a G°,--10 kcal/mol and CAOU CSOU has the following rate constants, k1=0.01 mol/min and k2=1 mol/min. Furthermore, you have measured the quantity of each compound in this plant during the daytime growing period as follows. CNOU = 10 nM. CSOU = 100 nM, and CAOU = 1 nM. Under these conditions, is biosynthesis of CAOU a favorable or unfavorable reaction with respect to free energy. You must explain how you arrived at this answer

Explanation / Answer

We know,

Equilibrium constant K= [Conc of product]/[Conc of reactant] = Forward rate const/Reverse rate const

For reaction1,

K = [CSOU]/[CNOU] = 10

Also, G = -RT lnK

Thus, -10 = -RT ln(10) or constant RT = 4.343 kcal/mol

For the other reaction CAOU to CSOU, equilibrium constant is calculated from rate constants

K= k1/k2 = 0.02

G = -RT lnK = - 4.343 kcal/mol x ln(0.01) = 20 kcal/mol

Thus, net Gibbs energy change = G1 + G2 = 10 kcal/mol > 0

Since Gibbs energy change is positive, the net reaction is not feasible at given conditions

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