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How does one derive $\Delta_\mathrm r G^\circ = -RT\ln(K)$? I don't see the connection mathematically or conceptually; how does Gibbs at all relate to the equilibrium constant of a reaction?

This was part one of a three part question which I've split into 3 individual questions as advised. I left this question as the one associated with the original title; the other one is here and I will edit the third in when my post cooldown allows me to post it, if anyone wishes to visit those as well now.

Vedvart1
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    @KarstenTheis The question has been split, as requested. – Vedvart1 May 01 '19 at 04:21
  • Related: https://chemistry.stackexchange.com/questions/104950/how-to-derive-the-relation-between-gibbs-energy-and-equilibrium-constant/104964#104964] – Karsten May 01 '19 at 18:35

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