The following equilibrium constants have been determined for oxalic acid at \(25^{\circ} \mathrm{C}\) : $$\begin{array}{l}\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q) \rightleftharpoons \mathrm{H}^{+}(a q)+\mathrm{HC}_{2} \mathrm{O}_{4}^{-}(a q) \\\\\qquad \begin{array}{r}K_{\mathrm{c}}^{\prime}=6.5 \times 10^{-2} \\\\\mathrm{HC}_{2} \mathrm{O}_{4}^{-}(a q) \Longrightarrow \mathrm{H}^{+}(a q)+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q) \\\K_{\mathrm{c}}^{\prime \prime}=6.1 \times 10^{-5}\end{array}\end{array}$$ Calculate the equilibrium constant for the following reaction at the same temperature: $$\mathrm{H}_{2} \mathrm{C}_{2} \mathrm{O}_{4}(a q) \rightleftharpoons 2 \mathrm{H}^{+}(a q)+\mathrm{C}_{2} \mathrm{O}_{4}^{2-}(a q)$$

Chemical equilibrium is a state in a chemical reaction where the rates of the forward and reverse reactions are equal, leading to no overall change in the concentrations of the reactants and products over time. This concept is fundamental in understanding how reactions proceed and how concentrations of substances are regulated in a closed system. At equilibrium, the reaction has reached a state of balance, but it's essential to note that both reactions are still occurring, just at the same rate.

One can represent equilibrium using an equilibrium constant \( K_c \), characteristic of a particular reaction at a given temperature. The equilibrium constant is a ratio of the concentration of the products raised to their stoichiometric coefficients to the concentration of the reactants raised to their coefficients. If the value of \( K_c \) is high, it means that at equilibrium, the reaction mixture is mostly products. Conversely, a low \( K_c \) value indicates that the reactants are favored.

The acid dissociation constant, also known as \( K_a \), is a special type of equilibrium constant that measures the strength of an acid in solution. It specifically refers to the equilibrium established when an acid donates a proton (\( H^+ \) ion) to water, forming its conjugate base and a hydronium ion \( H_3O^+ \). For a weak acid undergoing dissociation, \( HA \) represents the acid, and \( A^- \) represents the conjugate base.

The acid dissociation constant is described by the equation \( K_a = [H^+][A^-] / [HA] \), where the square brackets denote concentration. A larger \( K_a \) implies that the acid is stronger, meaning it donates protons more effectively. In the exercise, we're handling a two-step dissociation process for oxalic acid, which involves calculating two separate constants, \( K_c' \) and \( K_c'' \) before determining the total \( K_c \) for the overall reaction.

Reaction stoichiometry involves the quantitative relationship between reactants and products in a chemical reaction. It's based on the balanced chemical equation and the principle of the conservation of mass, which states that matter cannot be created or destroyed during a chemical reaction. Therefore, the amount of products and reactants must remain constant over time.

In the context of calculating an equilibrium constant, reaction stoichiometry determines how changes to the coefficients in a chemical reaction will affect the value of the equilibrium constant. The math underlying these relationships can be quite complex, involving exponents based on reaction coefficients and products of individual reaction constants when multiple steps are involved. As demonstrated in the exercise solution, knowing how to combine reaction steps and stoichiometric coefficients correctly can help us find the overall \( K_c \) for the entire reaction sequence.