(Solved): The equilibrium constant, Kc, is calculated using molar concentrations. For gaseous reactions an ...

The equilibrium constant, $K_{\mathrm{c}}$, is calculated using molar concentrations. For gaseous reactions another form of the equilibrium constant, $K_{\mathrm{p}}$, is calculated from partial pressures instead of concentrations. These two equilibrium constants are related by the equation $K_{\mathrm{p}}=K_{\mathrm{c}}(RT{)}^{?n}$ where $R=0.08206\mathrm{L}?\mathrm{atm}/(\mathrm{K}?\mathrm{mol}),T$ is the absolute temperature, and $?n$ is the change in the number of moles of gas (sum moles products - sum moles reactants). For example, consider the reaction ${\mathrm{N}}_2(\mathrm{g})+3{\mathrm{H}}_2(\mathrm{g})?2{\mathrm{NH}}_3(\mathrm{g})$ for which $?n=2?(1+3)=?2$. For the reaction $\mathrm{X}(\mathrm{g})+3\mathrm{Y}(\mathrm{g})?2\mathrm{Z}(\mathrm{g})$ $K_{\mathrm{p}}=1.76\times 10^{?2}$ at a temperature of $205^{?}\mathrm{C}$. Calculate the value of $K_c$. Express your answer numerically. For the reaction $2\mathrm{A}(\mathrm{g})+3\mathrm{B}(\mathrm{g})?\mathrm{C}(\mathrm{g})$ $K_{\mathrm{C}}=82.8$ at a temperature of $373^{?}\mathrm{C}$. Calculate the value of $K_{\mathrm{p}}$. Express your answer numerically.