# How to find entropy of chemical network reaction?

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?

• 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? – Greg Jun 27 '20 at 10:35
• 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. – Dari Obukhova Jun 27 '20 at 10:55
• 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. – Greg Jun 27 '20 at 15:47