4 compounds in equilibrium with one another - determine their equilibrium concentrations
In case anyone else travels this road...

Using $\mathrm{\Delta G~=~-RTlnK_{eq}}$ and the 3 $\mathrm{\Delta G's}$ supplied above, we find that
\begin{aligned}
\mathrm{K^{1/4}_{eq}}~&amp;=~0.003\\
\mathrm{K^{3/1}_{eq}}~&amp;=~40.749\\
\mathrm{K^{2/3}_{eq}}~&amp;=~2.163\\
\end{aligned}
We also know that the concentrations of the 4 species must total to 1

$${[1] + [2] + [3] + [4] = 1}$$

so we have the following 4 equations and 4 unknowns
\begin{aligned}%
[1]~ &amp;=~~~ 0.003 ~[4]\\
[3]~ &amp;=~ 40.749 ~[1]\\
[2]~ &amp;=~~~ 2.163 ~[3]\\
[1] + [2] + [3] + [4]~ &amp;=~ 1\\
\end{aligned}
solving for the 4 concentrations yields
\begin{aligned}%
[1]~ &amp;=~~~ 0.23\%\\
[2]~ &amp;=~ 20.27\%\\
[3]~ &amp;=~~~ 9.37\%\\
[4]~ &amp;=~ 70.13\%\\
\end{aligned}