\sect{The law of mass action for C==A+B}

Consider ideal gases of atoms ${A}$, atoms ${B}$ and atoms ${C}$
undergoing the reaction ${\nu C \leftrightarrow A+B}$, where ${\nu}$ is an integer.
$n_{A}$, and $n_{B}$ and $n_{C}$ are the respective densities of the atoms.
The law of mass action states that 

\[n^{a}_{A}n^{b}_{B}n^{c}_{C} \ = \ K(T)\]

\Dn

(1) Determine what are the exponents ${a,b}$ and ${c}$, 
and the equilibrium constant $K(T)$.

\Dn

(2) Write explicit expression for ${K(T)}$ 
for the reaction ${H_{2}+D_{2} \leftrightarrow  2 HD}$.

\Dn

(3) What is ${K(\infty)}$? 

\Dn

In item (2) the masses of the hydrogen atoms are $\mass_H$ and $\mass_D$.
The Deuterium has spin~1. The length of the molecule is~$a$, 
the binding energy is $-\varepsilon_0$, and the vibrational frequency 
of the ${HD}$ bond is~$\omega_0$.  
Assume that the vibration amplitude is much smaller compared with~$a$, 
and that the temperature~$T$ is high enough to allow
a classical approximation for the rotational motion.

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