# How would you define the concept of equilibrium in terms of free energy and entropy?

##### 1 Answer

Well, we could start from this equation:

#color(green)(DeltaG = DeltaG^@ + RTlnQ)# where:

#DeltaG# is theGibbs' free energy.#DeltaG^@# is theGibbs' free energyat#25^@ "C"# and#"1 bar"# (or, depending on your book, older books say#"1 atm"# , where#"1 atm = 1.01325 bar"# ).#R# is theuniversal gas constant#"8.314472 J/mol"cdot"K"# .#T# is thetemperaturein#"K"# .#Q# is thereaction quotient, i.e. the not-yet-equilibrium constant.

When we are at equilibrium,

#color(blue)(DeltaG^@ = -RTlnK)# where

#Q = K# at equilibrium.#K# may or may not be#1# .

*So, at equilibrium, you can use the standard Gibbs' free energy (which is tabulated in many if not all textbooks in an appendix) to solve for the equilibrium constant for the particular reaction.*

Furthermore, since

#color(green)(DeltaG = DeltaH - TDeltaS)# ,where

and recognize that now we have:

#0 = DeltaH - TDeltaS#

#TDeltaS = DeltaH#

#color(blue)(DeltaS = (DeltaH)/T)#

One example where this description of entropy at equilibrium is true is for **phase changes**. That is a constant-temperature *phase-phase equilibrium*.

*So at equilibrium, you could determine the entropy from knowing the enthalpy and the current temperature.*