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\textbf{Understanding $\Delta G$} \\
version = 1.00 of deltag.tex 2012 jun 14
by Tom Schneider
\par
For a system open to exchanges with its surroundings,
a free energy change ($\Delta G$)
is related to an enthalpy change ($\Delta H$)
and to an entropy change ($\Delta S$):
\begin{equation}
\Delta G_{system}
= \Delta H_{system}
- T \Delta S_{system} .
\label{eqn.deltaG.def}
\end{equation}
But by definition
\begin{equation}
\Delta H_{system}
= - T \Delta S_{surroundings}
\label{eqn.deltaH.def}
\end{equation}
so
\begin{equation}
\Delta G_{system} =
- T \Delta S_{surroundings}
- T \Delta S_{system} .
\label{eqn.deltaG.deltaS}
\end{equation}
But
\begin{equation}
\Delta S_{surroundings}
+
\Delta S_{system}
= \Delta S_{total}
\label{eqn.deltaS.total}
\end{equation}
and therefore
\begin{equation}
\Delta G_{system} = - T \Delta S_{total} .
\label{eqn.deltaG.deltaStotal}
\end{equation}
So $\Delta G_{system}$
represents the \emph{total\/} entropy increase
(energy dissipation)
during a reaction.
\par
source: Darnell1986.
J.~Darnell, H.~Lodish, and D.~Baltimore.
\emph{Molecular Cell Biology}.
Scientific American Books, Inc., N. Y., 1986.
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