Why are Kc and Kp interchangeable in the free energy-equilibrium equation? [duplicate]








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[Thermodynamics and equilibrium constant [duplicate]](/questions/7717/thermodynamics-and-equilibrium-constant)

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In this equation that relates Standard free energy and the equilibrium constant:


$\Delta Gº=-RT \ln K\_{eq}$


My textbook (and my teacher) say both $K\_p$ (constant related to pressure) and $K\_c$ (constant related to concentration) can be used in the place of $K\_{eq}$.


When using the equation that relates $K\_p$ with $K\_c$


$K\_p=K\_c(RT)^{\Delta n}$


We would get two different $\Delta Gº$ values, which shouldn't be possible.


My question is, why can we use both constants if their values are different?




The equilibrium constant is defined by activities:


[![enter image description here](https://i.stack.imgur.com/RQCP2.png)](https://i.stack.imgur.com/RQCP2.png)


The activity of a species in a liquid solution can be approximated to: $a=c/c^0$ where c is the concentration of the species and $c^o$ is the standard concentration ($1M$). This approximation leads to $K\_{eq}=K\_c$. The activity of gasses is called fugacity and it can be approximated to: $f=p/p^0$ where p is the pressure of the gas and $p^0$ is the standard pressure ($1$ $bar$). This leads to $K\_{eq}=K\_p$. Therefore, if a reaction takes place in e.g. water, one should use $K\_c$, but if the reaction takes place in the gaseous state, $K\_p$ should be used when calculating $dG$.


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