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Oct 15, 2022 at 23:22 history edited Karsten CC BY-SA 4.0
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Oct 15, 2022 at 23:20 comment added Karsten @Andrew Your right, of course. I guess I was confused.
Oct 15, 2022 at 21:57 comment added Andrew I don't think brackets generally indicate equilibrium concentrations. My understanding is that brackets just denote concentration and that when you are solving for the equilibrium condition, you can either use the subscript (which is rare) or preface the solution with, "At equilibrium. . . ". For example, you could split equation 3 into the first equality (with d[A]/dt), which is true for all concentrations, and then explicitly state the condition of equilibrium results in the second equality (to 0), and with that condition stated, you don't need the eq subscript.
Oct 15, 2022 at 19:42 comment added Karsten @Andrew Now I explicitly defined the brackets and left out the inconsistent "eq" subscript. I'm still interested whether there is a convention about the meaning of brackets, though.
Oct 15, 2022 at 19:41 history edited Karsten CC BY-SA 4.0
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Oct 15, 2022 at 19:39 comment added Andrew It is a bit confusing that you use the eq subscript in equations 3a and 3b, but not in equations 3 or 6, both of which also are true only for equilibrium concentrations. Nonetheless, you've nicely shown that the expressions derived from the two methods are equivalent.
Oct 15, 2022 at 17:55 comment added Karsten I'm not saying the usage is logical. For rate laws, the values have units, for the equilibrium constant, they don't, so the usage is a bit of a mess.
Oct 15, 2022 at 17:54 comment added Karsten @andselisk I was not aware of that convention. Do you have a source for that? I have seen brackets (always square) for defining the reaction quotient as well. Of course, this is always an approximation, using concentration divided by standard state concentration instead of activities. I have also seen brackets used to define rate laws (where concentrations are typically not a equilibrium.
Oct 15, 2022 at 16:19 comment added andselisk The 'eq' subscripts seem excessive as square brackets already imply equilibrium concentration. Any other amount-of-substance concentration is denoted with $c$ anyways.
Oct 15, 2022 at 15:30 comment added Karsten To troubleshoot the answers, I set the kinetic constants to 5, 6, 7, 10, 1, 21, so that $$5 * 6* 7 = 10 * 1 * 21$$. This made it easier for me to quickly check whether expressions are correct or not, and how to factor out $$\frac{k_{-3}}{k_3}$$ in the last bit of the answer.
Oct 15, 2022 at 15:21 history edited Karsten CC BY-SA 4.0
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Oct 15, 2022 at 15:09 history answered Karsten CC BY-SA 4.0