Write the mathematical expression for the reaction quotient, \(Q_{c}\) for each of the following reactions: (a) \(\mathrm{CH}_{4}(\mathrm{g})+\mathrm{C}_{2}(\mathrm{g})=\mathrm{CH}_{3} \mathrm{Cl}(\mathrm{g})+\mathrm{HCl}(g)\) (b) \(\mathrm{N}_{2}(g)+\mathrm{O}_{2}(g)=2 \mathrm{NO}(g)\) (c) \(2 \mathrm{SO}_{2}(g)+\mathrm{O}_{2}(g) \rightleftharpoons 2 \mathrm{SO}_{3}(g)\) (d) \(\operatorname{BaSO}_{3}(s)=\operatorname{BaO}(s)+\operatorname{SO}_{2}(g)\) (e) \(\mathrm{P}_{4}(g)+5 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{P}_{4} \mathrm{O}_{10}(s)\) (f) \(\operatorname{Br}_{2}(g)=2 \operatorname{Br}(g)\) (g) \(\mathrm{CH}_{4}(g)+2 \mathrm{O}_{2}(g) \rightleftharpoons \mathrm{CO}_{2}(g)+2 \mathrm{H}_{2} \mathrm{O}(I)\) (h) \(\operatorname{CuSO}_{4} \cdot 5 \mathrm{H}_{2} \mathrm{O}(s)=\mathrm{CuSO}_{4}(s)+5 \mathrm{H}_{2} \mathrm{O}(g)\)

Chemical equilibrium occurs when a chemical reaction and its reverse reaction proceed at the same rate, leading to constant concentrations of the reactants and products. It's a state where the forward and reverse reactions are happening continually, but because they are equally fast, no overall concentration change is observed.

At equilibrium, the rate at which the products are formed from the reactants equals the rate at which the reactants are formed from the products. This can occur in both closed systems, where no reactants or products are added or removed, and open systems where external influences might come into play.

An important aspect of understanding chemical equilibrium is the concept of dynamic equilibrium. Despite the reaction appearing to be at rest because concentrations remain constant, both the reactants and products are being produced and consumed continually. This is different from static equilibrium, where no reactions are occurring at all.

The stoichiometric coefficients in a chemical equation reflect the number of moles of each substance that participates in the reaction. These coefficients serve as multipliers for the molecules or formula units involved in the reaction, and they are crucial in predicting the amounts of reactants and products involved in chemical reactions.

When calculating the reaction quotient, Qc, or the equilibrium constant, it's the stoichiometric coefficients that determine the exponents to which each species' concentration is raised in the expression. For instance, in the reaction \(N_2(g) + O_2(g) = 2NO(g)\), the coefficient of \(NO\) is 2, indicating that two moles of \(NO\) are produced for every one mole of \(N_2\) and \(O_2\) consumed. Hence, the square of the concentration of NO appears in the reaction quotient expression for this reaction.

In the context of Qc, the reaction quotient, we consider the concentrations of gaseous and aqueous species because their concentrations vary and have a meaningful impact on the reaction dynamics. On the contrary, pure solids and liquids, which have fixed densities and do not have varying concentrations in a given reaction environment, are not included when calculating Qc.

Concentrations are typically measured in moles per liter (Molarity, M) in the case of gases and aqueous solutions. When we refer to concentration, symbolized by square brackets, such as \( [NO] \), we mean the molarity of the nitrogen monoxide gas in the reaction mixture.

For example, in the equilibrium expression for the formation of sulfur trioxide \(2SO_2(g) + O_2(g) \rightleftharpoons 2SO_3(g)\), the concentrations of the gaseous reactants \(SO_2\) and \(O_2\), and the product \(SO_3\) are included in the reaction quotient. In contrast, if there were solid sulfur or liquid water involved, these would not appear in the Qc expression.