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I have the following system of reactions:

$$ \begin{aligned} \ce{X_1 + Y_1 &<=>[$k_{21}$][$k_{12}$] X_2} \\ \ce{X_2 &<=>[$k_{32}$][$k_{23}$] X_3} \\ \ce{X_3 &<=>[$k_{13}$][$k_{31}$] X_1 + Y_2} \\ \ce{X_2 + Y_3 &<=>[$k_{42}$][$k_{24}$] X_4} \\ \ce{X_4 &<=>[$k_{34}$][$k_{43}$] X_3 + Y_4} \end{aligned} $$

Here $\ce{X_1},\ldots,\ce{X_4}$ represent the state of the molecule that catalyzes the reaction, and $\ce{Y_1},\dots,\ce{Y_4}$ represent a reactant or a product that is consumed or produced by the reaction.

I need to find the free energy flow $J_G$ with respect to $\ce{Y}$ and the entropy generation $R_S$ with respect to $\ce{X}.$

Could anyone recommend the approach to this problem?

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  • $\begingroup$ First, you should clear up the basics: the network is not in line with your description of X and Y you gave. Second, if you share how far you got it helps us give a meaningful answer. Have you tried to apply Hess's law? $\endgroup$ – Greg Jun 27 '20 at 10:35
  • $\begingroup$ Dear Greg, thanks for your comment. I made a mistake with the indexes for X and Y, corrected it. Does it make sense now? Everything I provided here is all the information I have for this task. I need to find J_in and J_out to get the free energy flow and then find entropy. I think that they must match in this reaction network but I am a bit lost. $\endgroup$ – Dari Obukhova Jun 27 '20 at 10:55
  • $\begingroup$ OK, so have you tried to apply the Hess's law to the reactions? I do not know what do you mean by the free energy flow for the whole network, but for if you need it for the X1 --> X4 reaction, that would be just the straight application of Hess's law. $\endgroup$ – Greg Jun 27 '20 at 15:47

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