\sect{Baruch's  A51.}

\begin{itemize}
\item [(a)]
Evaluate the chemical potential of a classical ideal gas in two
dimensions in terms of the temperature and the density per unit
area.

\item [(b)]
An ${H_{2}}$ molecule decomposes into ${H}$ atoms when it is absorbed
upon a certain metallic surface with an energy gain ${\epsilon}$
per ${H}$ atom due to binding on the surface. (This binding is not
to a particular site on the surface, i.e. the ${H}$ atoms are free
to move parallel to the surface). Consider ${H_{2}}$ as an ideal
gas with mass ${2\mathsf{m}_{H}}$ and derive the density adsorbed
per unit area as function of ${\epsilon}$, temperature and the
${H_{2}}$ pressure.

[Hint: Chemical equilibrium is obtained by minimizing the total
free energy with respect to one of the densities.]

\end{itemize}

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