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Chemical equilibrium is a state in a chemical reaction where the concentrations of reactants and products remain constant over time. This does not mean that the reactions have stopped; rather, the rate of the forward reaction equals the rate of the reverse reaction. Think of it like a busy office where email is constantly sent and received at an equal rate, resulting in a consistent inbox size.
At equilibrium, the system has reached a balance. For our example with the reaction \( \mathrm{AB}_2(\mathrm{~g}) \rightleftharpoons \mathrm{A}(\mathrm{g})+\mathrm{B}_2(\mathrm{~g}) \), once equilibrium is established, the amounts of \( \mathrm{A} \), \( \mathrm{B}_2 \), and \( \mathrm{AB}_2 \) will not change as long as conditions such as temperature and pressure remain constant.

The equilibrium constant, often denoted as \( K \), is a value that expresses the relationship between the concentrations or pressures (for reactions involving gases) of the products and reactants at equilibrium. It is specific to a particular reaction at a given temperature.
For our reaction, the equilibrium constant in terms of pressure, \( K_p \), is given by:\[ K_p = \frac{P_{A} \cdot P_{B_2}}{P_{AB_2}} \]
This equation tells us that higher equilibrium constant values indicate a greater extent of reaction towards the products, while lower values suggest the reactants are favored. The equilibrium constant is crucial because it helps predict how a change in conditions (like pressure or temperature) might affect the position of equilibrium.

Partial pressure is the contribution each gas in a mixture makes to the total pressure. It is an essential concept in understanding chemical equilibrium in gaseous reactions. Each gas in a mixture exerts a pressure as if it were the only gas present.
In the case of the decomposition of \( \mathrm{AB}_2 \), the partial pressures \( P_A \) and \( P_{B_2} \) correspond to the pressures that \( \mathrm{A} \) and \( \mathrm{B}_2 \) exert independently in the system. At equilibrium, these can be calculated from the degree of dissociation \( \alpha \), as shown:

• \( P_{AB_2} = P(1-\alpha) \)
• \( P_A = P_{B_2} = P \alpha \)

This concept helps in deriving the equilibrium constant expression where these partial pressures are a crucial part of the equation.

A decomposition reaction is a type of chemical reaction where one compound breaks down into two or more simpler substances. It's like a big Lego block breaking into smaller pieces. In the given reaction \( \mathrm{AB}_2(\mathrm{~g}) \rightleftharpoons \mathrm{A}(\mathrm{g})+\mathrm{B}_2(\mathrm{~g}) \), \( \mathrm{AB}_2 \) decomposes into \( \mathrm{A} \) and \( \mathrm{B}_2 \).
Decomposition reactions often require energy input in the form of heat, light, or electricity. They are crucial in understanding equilibrium because the extent to which a compound decomposes can be quantitatively described by the degree of dissociation, \( \alpha \). In equilibrium systems, the decomposition is balanced by the reverse reaction, where \( \mathrm{A} \) and \( \mathrm{B}_2 \) combine to reform \( \mathrm{AB}_2 \), thus maintaining equilibrium conditions.