At \(25^{\circ} \mathrm{C}, K_{\mathrm{p}} \approx 1 \times 10^{-31}\) for the reaction $$ \mathrm{N}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{NO}(g) $$ a. Calculate the concentration of \(\mathrm{NO}\), in molecules \(/ \mathrm{cm}^{3}\), that can exist in equilibrium in air at \(25^{\circ} \mathrm{C}\). In air, \(P_{\mathrm{N}_{2}}=0.8 \mathrm{~atm}\) and \(P_{\mathrm{O}_{2}}=0.2 \mathrm{~atm}\) b. Typical concentrations of \(\mathrm{NO}\) in relatively pristine environments range from \(10^{8}\) to \(10^{10}\) molecules \(/ \mathrm{cm}^{3}\). Why is there a discrepancy between these values and your answer to part a?

For the given reaction: N2 (g) + O2 (g) ⇌ 2 NO (g) The expression for the equilibrium constant (Kp) can be written as: \[K_{p} = \frac{(P_{\mathrm{NO}})^{2}}{P_{\mathrm{N_{2}}}\times P_{\mathrm{O_{2}}}}\] Where \(P_{\mathrm{NO}}\), \(P_{\mathrm{N_{2}}}\), and \(P_{\mathrm{O_{2}}}\) represent the partial pressures of the respective gases at equilibrium.

Let x be the change in pressure due to the reaction, then at equilibrium: - \(P_{\mathrm{N_{2}}} = 0.8 - x\) - \(P_{\mathrm{O_{2}}} = 0.2 - x\) - \(P_{\mathrm{NO}} = 2x\)

Substituting the values into the expression for Kp: \[{1 \times 10 ^{-31}} = \frac{(2x)^2}{(0.8-x)(0.2-x)}\]

Now solving the equation for x: \[x \approx 1.09 \times 10 ^{-11} \mathrm{~atm}\] Now, using the ideal gas law (PV=nRT) and the definition of concentration, we can find the concentration of NO at equilibrium in molecules/cm³: \[C_{\mathrm{NO}} = \frac{n_{\mathrm{NO}}}{V} = \frac{P_{\mathrm{NO}}}{RT} \times N_{\mathrm{A}}\] Where R is the ideal gas constant (0.0821 L atm/mol K), T is the temperature (25°C = 298 K), and NA is Avogadro's number (\(6.02214076 \times 10^{23}\) molecules/mol). Plugging in the values: \[C_{\mathrm{NO}} = \frac{(2)(1.09 \times 10^{-11}\mathrm{~atm})}{(0.0821 \mathrm{~L~atm/mol~K})(298\mathrm{~K})} \times 6.02214076 \times 10^{23}\mathrm{~molecules/mol}\] \[C_{\mathrm{NO}} \approx 5.4 \times 10^6 \mathrm{~molecules/cm^3}\]

The equilibrium concentration of nitrogen monoxide calculated in part a is approximately 5.4 × 10^6 molecules/cm³, which is significantly lower than the typical concentrations found in relatively pristine environments, ranging from 10^8 to 10^10 molecules/cm³. This discrepancy could be due to various reasons, including the presence of other reactions involving nitrogen and oxygen species in the atmosphere that can contribute to the formation of NO, as well as the fact that real environmental systems may not be at perfect equilibrium. Additionally, human activities and natural processes such as combustion, lightning, and microbial activity can also lead to NO formation, thus leading to higher concentrations in the environment than what is predicted at chemical equilibrium.