# Derivation of Enthaply of reaction as function of equilibrium constant

1. Feb 6, 2010

### kthouz

Can someone help me and tell me where does the equation of enthalpy as function of reduced Gibbs energy and equilibrium constant (patial pressure) come from? From which thermodynamic law does it come?
For an equation aA+bB=cC+dD
where A,B,C and D are molecules in a reaction balanced by stochiometric coefficients a,b,c and d.
The equation of enthalpy of rection is given as

$$\Delta_{rxn}$$$$H^{o}$$=T[$$\Delta_{rxn}$$$$\Phi^{o}$$ - Rln($$K_{p}$$)] ... (1)

where T is teh temperature, R the ideal gas constant, $$K_{p}$$ is the equilibrium constant and $$\Delta_{r}$$$$\Phi^{o}$$ is the reduced Gibbs free energy and is given by

$$\Delta_{rxn}$$$$\Phi^{o}$$= {a$$\Phi^{o}$$(C)+d$$\Phi^{o}$$(D)-[a$$\Phi^{o}$$(A)+b$$\Phi^{o}$$(B)]}.

Can someone tell me where equation come from? please