\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 ${K(\infty)}$? %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%