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Chemical equilibrium occurs when the forward and reverse reactions happen at equal rates. It results in constant concentrations of reactants and products over time. This doesn't mean the amounts are equal, but that their ratios remain unchanged. In this example, the formation of ammonia (\( \mathrm{N}_2 + 3\mathrm{H}_2 \rightleftharpoons 2\mathrm{NH}_3\) ) reaches equilibrium at a certain pressure and temperature. Once equilibrium is established, the concentrations of nitrogen, hydrogen, and ammonia remain stable.

Understanding equilibrium in chemical reactions helps explain many natural phenomena. It's essential in optimizing industrial processes, like ammonia production via the Haber process. Recognizing when a reaction reaches equilibrium allows chemists to control conditions for maximum yield.

Mole fraction is a way of expressing the composition of a mixture using ratios. It represents the ratio of the number of moles of a component to the total moles in the mixture. In mathematical terms, the mole fraction, denoted as \( y_i \), is calculated using: \[y_i = \frac{n_i}{n_{\text{total}}}\]where \( n_i \) is the moles of the component, and \( n_{\text{total}} \) is the total moles of all components in the system.

For the given problem, the mole fraction of ammonia was provided as 0.21. This means that for every mole of mixed gases present at equilibrium, 0.21 moles are ammonia. Understanding and calculating mole fractions are crucial for determining partial pressures and applying equilibrium constant expressions. In essence, it gives a snapshot of the composition of a mixture at equilibrium.

The equilibrium constant expression is a mathematical formula that represents the relationship between the concentrations (or pressures) of reactants and products in an equilibrium state. For reactions involving gases, we often use the equilibrium constant \( K_p \), which is based on partial pressures rather than concentrations. For the reaction \( \mathrm{N}_2 + 3\mathrm{H}_2 \rightleftharpoons 2\mathrm{NH}_3 \), the equilibrium constant expression is:\[K_p = \frac{(P_{\mathrm{NH}_3})^2}{P_{\mathrm{N}_2}(P_{\mathrm{H}_2})^3}\]Here, \( P_{\mathrm{NH}_3} \), \( P_{\mathrm{N}_2} \), and \( P_{\mathrm{H}_2} \) represent the partial pressures of ammonia, nitrogen, and hydrogen, respectively.

The given \( K_p \) value helps determine how pressures at equilibrium relate to each other, guiding adjustments to system conditions and predicting shifts in the equilibrium position. It’s a crucial part of solving equilibrium problems in chemistry.

Partial pressure refers to the pressure exerted by a single gas in a mixture of gases. Each gas contributes to the total pressure in proportion to its mole fraction. The relationship between the mole fraction and partial pressure is given by:\[P_i = y_i \times P_{\text{total}}\]where \( P_i \) is the partial pressure of gas \( i \), \( y_i \) is its mole fraction, and \( P_{\text{total}} \) is the total pressure of the system.

In the equilibrium system, knowing the mole fractions allows us to calculate the partial pressures of nitrogen, hydrogen, and ammonia. These partial pressures are essential when plugging values into the equilibrium constant expression. Calculating partial pressures helps in understanding how each component affects the overall system pressure and achieving a meaningful interpretation of equilibrium conditions.