In the last reaction of the citric acid cycle, malate is dehydrogenated to regen

Question

In the last reaction of the citric acid cycle, malate is dehydrogenated to regenerate oxaloacetate: L - Malate + Nad^+ rightarrow oxaloacetate + NADH + H ^+ DeltaG_0' = 29.7 kJ/ mol Calculate the equilibrium constant for this reaction at 25degree C. Because DeltaG_0' assumes a standard pH of 7, the equilibrium constant calculated in (a) corresponds to K_eq = [oxaloacetate [NADH]/[L - Malate][NAD^+] The measured concentration of L-malate in rat liver mitochondria is about 0.20 mM when [NAD^+]/[NADH] is 10. Calculate the concentration of oxaloacetate in these mitochondria. To appreciate the magnitude of the mitochondrial oxaloacetate concentration, calculate the number of oxaloacetate molecules in a single rat liver mitochondrion. Assume the mitochondrion is a sphere of diameter 2.0 mum.

Explanation / Answer

a)
delta Go = 29.7 KJ/mol = 29700 J/mol
T = 25 oC = (25 + 273) K = 298 K
use:
delta Go = -R*T*ln Kc
29700 = -8.314*298 * ln Kc
ln Kc = -11.99
Kc = 6.2*10^-6
Answer: 6.2*10^-6

b)
Keq = [oxaloacetate] [NaDH] / {[L-malate] [NAD+]}
6.2*10^-6 = [oxaloacetate]/{(0.2*10^-3)*10}
[oxaloacetate] = 1.2*10^-8 M
Answer: 1.2*10^-8 M

c)
molar mass of oxaloacetate = 132 g/mol
r = 2 *10^-6 m / 2 =1*10^-6 m
Volume = 4/3*pi*r^3
   = 4/3 * pi* (1*10^-6)^3
   = 4.19*10^-18 m^3
   = 4.19*10^-15 L

use:
[oxaloacetate] = number of moles / volume
1.2*10^-8 = number of moles / (4.19*10^-15)
number of moles = 5.03*10^-23 mol

number of molecules = number of moles * 6.022*10^23
   = 5.03*10^-23 * 6.022*10^23
    = 30
Answer: 30

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