\sect{Baruch's A52.}
\begin{itemize}
\item [(a)]
Consider ideal gases of atoms ${A}$, atoms ${B}$ and atoms ${C}$
undergoing the reaction
${\nu C \leftrightarrow A+B}$ (${\nu}$ is an integer).
If ${n_{A}, n_{B}}$ and ${n_{C}}$ denote the respective densities
show that in equilibrium
\[\frac{(n_{C})^{\nu}}{ n_{A}n_{B} } =V^{2-\nu}\frac{(f_{C})^{\nu}}{ f_{A}f_{B} }
= K\left(T\right)\mbox{(law of mass action).}\]
Here ${V}$ is the volume while the $f$'s are the respective single
particle partition functions.
The quantity ${K\left(T\right)}$ is known as the \emph{equilibrium constant} of the reaction.
\item [(b)]
Derive the equilibrium constant of the reaction
${H_{2}+D_{2}\leftrightarrow 2 HD}$ in
terms of the masses $m_H, \, m_D$ and $\omega_0$ the vibrational
frequency of ${HD}$. Assume temperature is high enough to allow
classical approximation for the rotational motion. Show that
$K(\infty) = 4$.\\
\end{itemize}
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