Write the balanced chemical equation for the reaction represented by the
equation below. The symbol K indicates an equilibrium constant. The subscript a after K indicates the equilibrium constant is an acid
dissociation constant. Acid dissociation constants are derived from the reaction of an acid with
water. For a given equilibrium, K is equal to the concentration of the products raised
to their stochiometric coefficients all multiplied together divided by the
equivalent for the reactants. Therefore, we know that the acetate anion and the hydronium ion are products in
this reaction. And acetic acid CH₃COOH is a reactant. Now, we can start constructing with chemical equation. Acetic acid is definitely one of the reactants. And since acid dissociation constants are always measured in water, water is
also one of the reactants. Equilibrium constants are only used for equilibria. Therefore, the reaction arrow is an equilibrium arrow. And the products are the acetate anion and the hydronium ion. The question asks for the balanced chemical equation. Therefore, we should check whether this equation is balanced. On both sides of the reaction equation, there are two equivalents of carbon,
six equivalents of hydrogen, and three equivalents of oxygen. The reaction equation is therefore balanced. Now, just to be safe, let’s work backwards from the chemical equation to see
whether the equilibrium constant makes sense. Starting off with the products, the top half of the equilibrium expression
looks fine. However, working just from the chemical equation, it looks like the bottom half
doesn’t quite match up. Water is not expressed in the original acid dissociation constant. It is removed because the acid dissociation constant is measured in water,
where water is the solvent. Its concentration is assumed to be constant. And therefore, it can be ignored.
So we’ve written the balanced chemical equation represented by the acid
dissociation constant and double-checked that it makes sense.