\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 ${H_{2}+D_{2} \leftrightarrow 2 HD}$,
given the masses $m_H, \, m_D$,
and the the vibrational frequency $\omega_0$ of the ${HD}$ bond.
Assume the temperature is high enough to allow
classical approximation of the rotational motion.
\Dn
(3) What is ${K(\infty)}$?
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