91Ó°ÊÓ

In chemical equilibrium, reactions reach a point where the forward and reverse reactions occur at the same rate. This is when concentrations of the reactants and products remain constant. The equilibrium constant (\( K_c \)) provides a quantitative representation of this balance. It is a ratio, comparing the concentration of the products to the reactants, all raised to the power of their respective stoichiometric coefficients from the balanced chemical equation.

For our reaction, \( 2 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_{2}(g) + \mathrm{O}_{2}(g) \), the equilibrium expression is:\( K_c = \frac{[\mathrm{N}_2][\mathrm{O}_2]}{[\mathrm{NO}]^2} \).

You can see that \( K_c = 2.4 \times 10^3 \) at \(2000^{\circ} \mathrm{C} \). The large value of \( K_c \) indicates that at equilibrium, the product concentrations are favored over the reactant concentrations, meaning the reaction proceeds significantly towards the right under these conditions.

• Important: A higher \( K_c \) favors product formation.
• It provides insight into which side of the reaction is favored dynamically.

The ICE table is a systematic way of keeping track of the concentrations of reactants and products through Initial, Change, and Equilibrium states. This method helps us simplify the understanding of what happens to substances during the shift towards equilibrium.

In our context, it starts with:

• **I**nitial concentrations: Here, only \( [\mathrm{NO}]_0 = 0.250 \, \mathrm{M} \), with \( [\mathrm{N}_2]_0 = 0 \, \mathrm{M} \) and \( [\mathrm{O}_2]_0 = 0 \, \mathrm{M} \).
• **C**hange in concentrations: As the reaction moves towards equilibrium, let changes be represented as \( -2x \) for \( \mathrm{NO} \), \( +x \) for \( \mathrm{N}_2 \), and \( +x \) for \( \mathrm{O}_2 \).
• **E**quilibrium concentrations: These are derived as \( [\mathrm{NO}] = 0.250 - 2x \), \( [\mathrm{N}_2] = x \), and \( [\mathrm{O}_2] = x \).

The equations reflect the stoichiometry of the reaction, showing that every two moles of \( \mathrm{NO} \) that decompose form one mole each of \( \mathrm{N}_2 \) and \( \mathrm{O}_2 \). This method systematically sets up the values needed to solve for \( x \), which represents the change in concentration from the initial state to the equilibrium state.

Stoichiometry plays a crucial role in understanding how the substances in a chemical reaction are related based on their balanced chemical equation.

In this reaction, \( 2 \mathrm{NO}(g) \rightleftharpoons \mathrm{N}_2(g) + \mathrm{O}_2(g) \), stoichiometry tells us the relationship between \( \mathrm{NO} \) and the products, \( \mathrm{N}_2 \) and \( \mathrm{O}_2 \).

• The balanced equation indicates every 2 moles of \( \mathrm{NO} \) yield 1 mole each of \( \mathrm{N}_2 \) and \( \mathrm{O}_2 \).
• This is represented in the Change row of the ICE table as \( -2x \) for \( \mathrm{NO} \) which aligns with the stoichiometric coefficients in the reaction.

Since stoichiometry is based on the law of conservation of mass, it allows chemists to predict the quantities of reactants consumed and products formed. It's essential for solving for equilibrium concentrations once the value of \( x \) is obtained. In practical applications, it provides a roadmap for balancing equations and understanding how molecules relate to each other quantitatively, ensuring calculations remain accurate.