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Entropy is a fundamental concept in thermodynamics that measures the degree of randomness or disorder in a system. It is denoted by the symbol \(S\). In chemistry, entropy changes, represented by \(\Delta S\), occur during chemical reactions and can indicate how the disorder of a system changes when reactants become products.

In a reaction where the number of gas molecules increases, like the conversion of \(\mathrm{Cl}_2(g)\) to \(2\mathrm{Cl}(g)\), entropy increases. This is because more particles are free to move, thus increasing randomness. On the other hand, in reactions where gases form more ordered states, such as when a gas reacts to form a solid, entropy decreases, as seen in the reaction \(\mathrm{CO}_2(g) + \mathrm{CaO}(s) \rightarrow \mathrm{CaCO}_3(s)\).

Understanding entropy helps predict whether a reaction is favorable. An increase in entropy \((\Delta S^{\circ} > 0)\) often means greater feasibility, especially at higher temperatures. However, entropy must be considered alongside enthalpy to determine the overall spontaneity of a reaction.

Enthalpy is a measure of the total energy of a thermodynamic system, usually focused on heat changes during a reaction. It is represented by the symbol \(H\), and changes in enthalpy are denoted as \(\Delta H\).

Reactions can either release heat and be exothermic \((\Delta H^{\circ} < 0)\) or absorb heat and be endothermic \((\Delta H^{\circ} > 0)\). For example, reaction (i) \(2\mathrm{Fe}(s) + \mathrm{O}_2(g) \rightarrow 2\mathrm{FeO}(s)\) is exothermic since energy is released as new bonds are formed. Meanwhile, reaction (iii) \(\mathrm{NH}_4\mathrm{Cl}(s) \rightarrow \mathrm{NH}_3(g) + \mathrm{HCl}(g)\) is endothermic as energy is needed to sublimate the solid into gases.

The sign and magnitude of \(\Delta H\) help in determining the favorability of a reaction at different temperatures. Exothermic reactions, which release energy, are usually more spontaneous at lower temperatures, while endothermic reactions become more feasible as the temperature increases.

Chemical equilibrium occurs when the rates of the forward and reverse reactions are equal, and the concentrations of reactants and products remain stable over time. This balance is described by the equilibrium constant \(K\).

For example, in the reaction \(2\mathrm{Fe}(s) + \mathrm{O}_2(g) \rightleftharpoons 2\mathrm{FeO}(s)\), the reaction is exothermic and has a lower entropy, leading to \(K > 1\) at room temperature, meaning the products are favored.

The value of \(K\) also varies with temperature changes due to the relationship between enthalpy and equilibrium, often described by the van 't Hoff equation. For exothermic reactions, \(K\) decreases with an increase in temperature because the reverse reaction becomes more favorable. Conversely, for endothermic reactions, such as the sublimation of \(\mathrm{NH}_4\mathrm{Cl}\), \(K\) increases with temperature, favoring product formation as the temperature is raised.

Understanding chemical equilibrium and its dependence on temperature is crucial for predicting how changes in conditions will affect the direction and extent of a chemical reaction.