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Chemical equilibrium is a state in a reversible chemical reaction where the rates of the forward and reverse reactions are equal. This balance means that the concentrations of reactants and products remain constant over time. At equilibrium, no net change is observed in the concentration of either reactants or products.
In the reaction \[ \text{N}_2\text{O}_4(g) \leftrightharpoons 2\text{NO}_2(g) \]N\(_2\)O\(_4\) breaks down into NO\(_2\), and NO\(_2\) combines to form N\(_2\)O\(_4\). At equilibrium, these processes occur at the same rate, resulting in stable concentrations of both gases.
Equilibrium constants are used to describe this balance. The concentration-based equilibrium constant \(K_c\) is derived from the concentrations of reactants and products at equilibrium. For the given reaction, \[K_c = \frac{[\text{NO}_2]^2}{[\text{N}_2\text{O}_4]} = 0.20 \, \text{M}\]indicates the ratio of the concentrations of NO\(_2\) and N\(_2\)O\(_4\) when the system is at equilibrium.

The ideal gas law is a fundamental equation in chemistry that relates the pressure, volume, temperature, and amount of gas. It is represented by:\[ PV = nRT \]where \(P\) is pressure, \(V\) is volume, \(n\) is the number of moles, \(R\) is the ideal gas constant \(0.08314 \text{ L} \cdot \text{bar} \cdot \text{mol}^{-1} \cdot \text{K}^{-1}\), and \(T\) is temperature in Kelvin.
In equilibrium calculations involving gases, it's often necessary to link concentration-based equilibrium constants \(K_c\) and pressure-based constants \(K_p\) using the ideal gas law. This adaptation accounts for the changes in the number of moles of gas during a reaction.
The relationship is given by:\[ K_p = K_c (RT)^{\Delta n} \]where \(\Delta n\) is the change in moles of gas between reactants and products. This equation helps convert the concentrations into pressures, maintaining the consistency of the data for gaseous reactions.

Reaction stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction based on the balanced equation. It ensures that all the atoms are conserved and provides insight into the ratio of molecules participating in the reaction.
For the reaction \( \text{N}_2\text{O}_4(g) \leftrightharpoons 2\text{NO}_2(g) \), the stoichiometry tells us:- One molecule of \( \text{N}_2\text{O}_4 \) splits into two molecules of \( \text{NO}_2 \).- The stoichiometric coefficients are 1 for \( \text{N}_2\text{O}_4 \) and 2 for \( \text{NO}_2 \).
These coefficients are crucial for calculating \(\Delta n\), which represents the change in the number of moles of gases during the reaction. Here, \(\Delta n\) is calculated as:\[ \Delta n = 2 - 1 = 1 \]This value is then used in the equation relating \(K_c\) and \(K_p\), enabling the computation of \(K_p\) for different conditions, such as temperature or pressure.