In addition to serving as a foundational principle for the “Hydrogen Hypothesis”

Question

In addition to serving as a foundational principle for the “Hydrogen Hypothesis” model by Martin and Müller for eukaryotic cell evolution, interspecies hydrogen transfer occurs in various syntrophic environments. In anoxic freshwater ecosystems, propionate is converted to acetate, hydrogen and carbon dioxide. The accumulation of hydrogen gas from this process can make this conversion thermodynamically unfavorable; however, the consumption of hydrogen gas by methanoarchaeal species allow propionate consumption to continue. In this environment, propionate is fermented to acetate, H2 and CO2 as represented in this stoichiometric equation:

C3H5O2 + 3 H2O <--- ---> CH3COO- + HCO3 + H+ + H2 

The free energy change under standard state conditions (Go’) for this reaction is 20.0 kJ/mole. Concentrations of reactants and products in typical anoxic freshwater ecosystem are: propionate 1 mM; acetate 1 mM; HCO3 20 mM; H2 10^-4 M (atm). 

A.) What is the G for this reaction at 25oC under typical anoxic freshwater ecosystem conditions? Disregard water as a reactant and protons as products. (Hint: use molar quantities in your calculations) (SHOW WORK; R=80315 J/mole.K)

B.) At what H2 concentration does this reaction become thermodynamically unfavorable? (SHOW WORK)

Explanation / Answer

ANSWER:

The free energy change under standard state conditions.

Kc = concentration of product / concentration of reactant
= 0.02 *[H+]/ (0.001*0.001)
=20000 [H+]
I am considering [H+]= 10^-7 for freshwater
Kc = 0.002
use:
delta G = delta G0 + R*T*ln Kc
= 20,000 + 8.314*298*ln 0.002
= 4603 J

B)
Kc = 0.002 [H2]
delta G0 = - R*T*ln Kc
20000 = -8.314*298*ln (0.002 [H2])
0.002 [ H2] = 3.12*10^-4
[H2] = 0.156M
=156 mM

At concentration greater than 156 mM,its becomes unfavourable

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