For the reaction; \(\mathrm{N}_{2 \mathrm{k} \mathrm{g}}+3 \mathrm{H}_{2(\mathrm{~g})} \rightleftharpoons 2 \mathrm{NH}_{3(\mathrm{~g})}\) At \(400 \mathrm{~K}, K_{\mathrm{p}}=41 \mathrm{~atm}^{-2}\). Find the value of \(K_{\mathrm{p}}\) for each of the following reactions at the same temperature: (i) \(2 \mathrm{NH}_{3(\mathrm{~g})} \Longrightarrow \mathrm{N}_{2(\mathrm{~g})}+3 \mathrm{H}_{2(\mathrm{~g})}\) (ii) \({ }_{2} \mathrm{~N}_{2(\mathrm{~g})}+\frac{3}{2} \mathrm{H}_{2(g)} \Longrightarrow \mathrm{NH}_{3(\mathrm{~g})}\); (iii) \(2 \mathrm{~N}_{2(\mathrm{~g})}+6 \mathrm{H}_{2(\mathrm{~g})} \rightleftharpoons 4 \mathrm{NH}_{3(\mathrm{~g})}\)

The equilibrium constant, represented as Kp, is a crucial concept in understanding the balance that exists in chemical reactions that occur in the gaseous phase. It helps us quantify the concentration of reactants and products at equilibrium. Kp is specifically used when dealing with partial pressures of gases.

For a general reaction of the form \(aA(g) + bB(g) \rightleftharpoons cC(g) + dD(g)\), Kp is defined by the equation \[ K_p = \frac{(P_C)^c \cdot (P_D)^d}{(P_A)^a \cdot (P_B)^b} \] where \(P_X\) represents the partial pressure of the substance X, and the lowercase letters (a, b, c, d) are the stoichiometric coefficients from the balanced chemical equation. If the reaction is reversed, Kp becomes its reciprocal, and if the stoichiometry is changed, Kp is raised to the power corresponding to the change.

In the given exercise, to find the Kp for different variations of the reaction, we manipulated the original Kp according to these rules. For instance, we reversed the reaction in (i) yielding a Kp of \(1/41 \, atm^2\), reflecting the dynamic nature of chemical equilibrium.

Le Chatelier's principle is a fantastic tool for predicting how a system at equilibrium reacts to external changes. It states that if an external condition (such as concentration, temperature, or pressure) is altered, the system will adjust to minimize that change.

For example, if the pressure is increased by decreasing the volume of the container for a gaseous reaction at equilibrium, the system will shift in the direction that produces fewer moles of gas, thus lowering the pressure. Similarly, if the temperature is changed, the system shifts in a direction to absorb or release heat, depending on whether the temperature is increased or decreased.

This principle is valuable for understanding how changes can affect the position of equilibrium and is indirectly linked to the Kp by dictating how equilibrium shifts in response to changes, although it does not change the value of Kp itself.

Chemical reaction reversibility is an inherent aspect of many chemical processes where the reactants form products, which in turn can recreate the original reactants. At equilibrium, the rate of the forward reaction is equal to the rate of the reverse reaction, meaning the concentration of reactants and products remains constant over time, though not necessarily equal.

It's important to understand that not all reactions are reversible in practical terms. A reversible reaction is one that can reach equilibrium, and it is these reactions we describe using the equilibrium constant Kp. This concept was demonstrated in the exercise when the direction of the equation was reversed, significantly affecting the Kp value.

Stoichiometry in chemical reactions deals with the quantitative relationships between the reactants and products. The coefficients in a balanced equation tell us in what ratios the substances react and are formed.

In terms of equilibrium, the stoichiometric coefficients directly influence the equilibrium constant's exponents as highlighted in our calculations. Doubling the coefficients in reaction (iii) required us to square the original Kp value. Understanding the stoichiometry is essential for accurate calculations and predicting how the system responds to changes, a concept closely tied to Le Chatelier's Principle.

By comprehending stoichiometry, students can improve their understanding of chemical concepts significantly, enabling them to solve equilibrium problems and predict the outcome of chemical reactions more effectively.