I have calculated $\Delta_\text{r} G^o$ two different ways and got completely different results. Why? What assumptions have I made incorrectly, particularly in the first calculation shown below?
Okay, so everyone knows that liquid Hydrochloric acid is a strong acid so it completely dissociates in water according to the following chemical equation:
$\ce{HCl (l) + H2O (l) -> H3O+ (aq) + Cl- (aq)}$
If I used tabulated values of Standard State Gibbs Free Energy of formation $\Delta_\text{f} G^o$ to calculate $\Delta_\text{r} G^o$, standard State Gibbs Free Energy formation change of the reaction.
Standard State Gibbs Free Energies of formation:
$\begin{array}{lr}
\ce{HCl (l)} & \pu{-131.17 kJ mol^{-1}}\\
\ce{H2O (l)} & \pu{-237.19 kJ mol^{-1}}\\
\ce{H3O+(aq)} & \pu{-237.19 kJ mol^{-1}}\\
\ce{Cl-} & \pu{-131.17 kJ mol^{-1}}
\end{array}$
Source (I used this one because I couldn't find any that listed $\ce{HCl}$ as a liquid and not a gas): http://www.vias.org/genchem/standard_ent...
Then, if you have one mole of each constituent according to the chemical equation, the standard state Gibbs Free Energy of the reaction = 0 kJ
by means of calculating ΔGoreaction = ΣΔGoformation of products - ΣΔGoformation of reactants
So ΔGoreaction should be less than zero if the reaction is favorable! But we know that HCl completely dissociates in water into Chloride ion and hydronium. What is going on here!?
If I calculate the standard state Gibbs Free Energy of the chemical reaction a different way. That is that
$\Delta G^\circ_\text{reaction} = -R \cdot T \cdot \ln(\ce{Keq})$ at equilibrium, where
for the acid $\ce{HCl}$, $\ce{Keq = Ka} = \pu{1.3e6}$,
Then the Gibbs Free Energy change of the chemical reaction at standard state
$\Delta G^\circ_\text{reaction} = (\pu{-8.314 J K-1 mole-1}) \cdot (\pu{1 mole}) \cdot (\pu{298 K}) \cdot \ln(\pu{1.3e6})$
$= \pu{-34.88 kJ}$,
which is less than zero; therefore, the reaction is favorable. What is going on!? See the difference in the calculations!?
It seems that the Ka of strong acids like HCl is usually assumed to be too large for most websites to even bother displaying. But, I found a table of Ka's of strong acids here: http://depts.washington.edu/eooptic/links/acidstrength.html