The conversion of fumarate dianion to the malate dianion by the addition of wate

Question

The conversion of fumarate dianion to the malate dianion by the addition of water to the olefinic group is essential to the operation of the carboxylic acid cycle in the tissues both of humans and of the frog. When this reaction was studied in the lab at 25 degree C and at the physiological pH, delta, G degree was found to be - 3.68 kJ mol^-1 and delta, H degree was14.90 kJ mol^-1. Assuming that delta H degree is independent of temperature, calculate the equilibrium constant K for this reaction (i) in humans at 37 degree C, and (ii) in a frog at 7 degree C.

Explanation / Answer

deltaGo= -RTlnK

lnK= -deltaGO/RT=3.68*1000/(8.314*298)

K= 4.42 = Equilibrium cosntant at 25 deg.c

from Van't Hoff equation

ln (K2/K)= (deltaH/R)*(1/T- 1/T2)

for T2= 37+273= 310K, K2= equilibrum constnat

ln( K2/K)= (14.9*1000/8.314)*(1/298-1/310)

K2/K= 1.26 and K2= 1.26*4.42= 5.57

at 5 deg.c T3= 5+273= 278

ln (K3/K)= (14.9*1000/8.314)*(1/298-1/278)

K3/K= 0.65

K3= 4.42*0.65= 2.873

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