Write an equilibrium constant, \(K_{\mathrm{p}},\) for the formation from its gaseous elements of (a) 1 mol \(\mathrm{NOCl}(\mathrm{g})\) (b) \(2 \mathrm{mol} \mathrm{ClNO}_{2}(\mathrm{g}) ;\) (c) \(1 \mathrm{mol} \mathrm{N}_{2} \mathrm{H}_{4}(\mathrm{g}) ;\) (d) \(1 \mathrm{mol}\) \(\mathrm{NH}_{4} \mathrm{Cl}(\mathrm{s})\)

Start by writing the reactions for the formation of each compound from its elements in gaseous state. Every compound forms from its components in their basic states:\n\n(a) \(\mathrm{NOCl(g)}\) forms from half a mole \(\mathrm{N}_{2}\) and \(\mathrm{Cl}_{2}\) and \(\mathrm{O}_{2}\):\n\[\(\begin{equation} \frac{1}{2}N_2(g) + \frac{1}{2}O_2(g) + Cl_2(g) \longrightarrow NOCl(g) \end{equation}\)\n(b) \(\mathrm{ClNO}_2(g)\) forms from \(\mathrm{N}_{2}\), \(\mathrm{Cl}_{2}\), and \(\mathrm{O}_{2}\):\n\[\(\begin{equation} N_2(g) + Cl_2(g) + 2O_2(g) \longrightarrow 2ClNO_2(g) \end{equation}\)\n(c) \(\mathrm{N}_{2}\mathrm{H}_{4}\) forms from \(\mathrm{N}_{2}\) and \(\mathrm{H}_{2}\):\n\[\(\begin{equation} N_2(g) + 2H_2(g) \longrightarrow N_2H_4(g) \end{equation}\)\n(d) \(\mathrm{NH}_{4}\mathrm{Cl(s)}\) forms from \(\mathrm{NH}_{3}\) and \(\mathrm{HCl}\):\n\[\(\begin{equation} NH_3(g) + HCl(g) \longrightarrow NH_4Cl(s) \end{equation}\)

For each reaction, \(K_p\) is the ratio of the partial pressure of the product over the partial pressure of the reactants, each raised to their coefficients as power.\n\n(a) For \(\mathrm{NOCl}\):\n\[\(\begin{equation} K_p = \frac{P_{NOCl}}{P_{N2}^{0.5} \times P_{O2}^{0.5} \times P_{Cl2}} \end{equation}\)\n(B) For \(\mathrm{ClNO}_{2}\):\n\[\(\begin{equation} K_p = \frac{P_{ClNO2}^2}{P_{N2} \times P_{O2}^2 \times P_{Cl2}} \end{equation}\)\n(c) For \(\mathrm{N}_{2}\mathrm{H}_{4}):\n\[\(\begin{equation} K_p = \frac{P_{N2H4}}{P_{N2} \times P_{H2}^2} \end{equation}\)\n(d) For \(\mathrm{NH}_{4}\mathrm{Cl}\) (don't include solids in \(K_p\)):\n\[\(\begin{equation} K_p = P_{NH4Cl} \end{equation}\)

If given values, this step would involve filling out the pressures and calculating \(K_p\). However, in this problem, we are not given any pressures and are asked to write the expression only. Thus, this step is not needed in this problem.