Analysis of an equilibrium mixture in which the following equilibrium exists gave \(\left[\mathrm{OH}^{-}\right]=\left[\mathrm{HCO}_{3}^{-}\right]=3.2 \times 10^{-3} .\) $$\mathrm{HCO}_{3}^{-}(a q)+\mathrm{OH}^{-}(a q) \rightleftarrows \mathrm{CO}_{3}^{2-}(a q)+\mathrm{H}_{2} \mathrm{O}(l)$$ The equilibrium constant is \(4.7 \times 10^{3} .\) What is the concentration of the carbonate ion?

Understanding the concept of chemical equilibrium is fundamental to solving exercises involving calculation of ion concentrations. At its core, chemical equilibrium represents a state in which a chemical reaction and its reverse reaction occur at equal rates. In this state, the concentration of reactants and products remains constant over time, although both reactions continue to happen.

In practical terms, when a system reaches equilibrium, the forward and reverse reactions balance each other out, and no net change in the concentrations of the substances involved occurs. This does not mean the reactants and products are at equal concentrations but that their ratios are fixed and defined by the equilibrium constant for the reaction, symbolized by 'K'. The larger the value of 'K', the more product is favored in the equilibrium position.

For ionic reactions in aqueous solutions, like the example given, the equilibrium constant (K) expression is written in terms of the molar concentrations of the ions involved. This value of 'K' is crucial as it allows us to compute unknown concentrations at equilibrium, providing a quantitative understanding of the system's balance.

The bicarbonate (\(HCO_3^-\)) and carbonate (\(CO_3^{2-}\)) ions play a vital role in many chemical equilibria, especially in biological and environmental systems. They are part of the bicarbonate buffering system, which regulates the pH levels in blood and keeps it within the narrow range necessary for life.

The bicarbonate ion is a weak base and acts as a buffer, while the carbonate ion is a stronger base and can function as a buffer at higher pH levels. These ions can interconvert through chemical reactions with water or hydrogen ions, which is why they are often found in equilibrium with each other and with hydroxide ions.In the exercise, hydroxide ions react with bicarbonate ions to form carbonate ions and water. This reaction is reversible, and so these ions will reach a particular equilibrium state in given conditions, as described by the equilibrium constant. By understanding the dynamics between these ions, you can predict the behavior of solutions in response to change and calculate ion concentrations at equilibrium.

Hydroxide ion (\(OH^-)\) concentration in a solution is a direct measure of its basicity or alkalinity. The hydroxide ions originate from the dissociation of bases in water and play a critical role in the equilibrium of acid-base reactions. A higher concentration of hydroxide ions indicates a higher pH and thus a more basic solution.

In the context of the exercise, the concentration of hydroxide ions is in dynamic equilibrium with bicarbonate and carbonate ions. To solve for the carbonate ion concentration, you must understand that the hydroxide ion concentration affects the position of the equilibrium and, consequently, the concentration of all other ions in the system. The equilibrium constant expression incorporates the hydroxide ion concentration, and changes in this value can shift the equilibrium towards or away from the formation of carbonate ions.

By analyzing tissue at equilibrium and knowing the concentration of hydroxide and bicarbonate ions, we can deduce the concentration of carbonate ions using the equilibrium constant. This is an excellent example of the practical application of hydroxide ion concentration to understand chemical equilibrium in aqueous solutions.