  From a mathematical model that describes a complex chemical kinetic system of
$N$ species and $M$ elementrary reactions in a rapidly stirred vessel of size
$V$ as a Markov process, we show that a macroscopic chemical thermodynamics
emerges as $V\rightarrow\infty$. The theory is applicable to linear and
nonlinear reactions, closed systems reaching chemical equilibrium, or open,
driven systems approaching to nonequilibrium steady states. A generalized
mesoscopic free energy gives rise to a macroscopic chemical energy function
$\varphi^{ss}(\vx)$ where $\vx=(x_1,\cdots,x_N)$ are the concentrations of the
$N$ chemical species. The macroscopic chemical dynamics $\vx(t)$ satisfies two
emergent laws: (1) $(\rd/\rd t)\varphi^{ss}[\vx(t)]\le 0$, and (2)$(\rd/\rd
t)\varphi^{ss}[\vx(t)]=\text{cmf}(\vx)-\sigma(\vx)$ where entropy production
rate $\sigma\ge 0$ represents the sink for the chemical energy, and chemical
motive force $\text{cmf}\ge 0$ is non-zero if the system is driven under a
sustained nonequilibrium chemostat. For systems with detailed balance
$\text{cmf}=0$, and if one assumes the law of mass action,$\varphi^{ss}(\vx)$
is precisely the Gibbs' function $\sum_{i=1}^N x_i\big[\mu_i^o+\ln x_i\big]$
for ideal solutions. For a class of kinetic systems called complex balanced,
which include many nonlinear systems as well as many simple open, driven
chemical systems, the $\varphi^{ss}(\vx)$, with global minimum at $\vx^*$, has
the generic form $\sum_{i=1}^N x_i\big[\ln(x_i/x_i^*)-x_i+x_i^*\big]$,which has
been known in chemical kinetic literature.Macroscopic emergent "laws" are
independent of the details of the underlying kinetics. This theory provides a
concrete example from chemistry showing how a dynamic macroscopic law can
emerge from the kinetics at a level below.
