Write the balanced chemical equation for the equilibrium that is taking place between acetic acid and sodium acetate in the buffer solution.

I don't know what buffer problem you have but the two equilibria involved are as follows:

CH3COOH ==> CH3COO^- + H^+

CH3COO^- + H^+ ==> CH3COOH

To write the balanced chemical equation for the equilibrium between acetic acid (CH3COOH) and sodium acetate (CH3COONa) in a buffer solution, we need to consider the dissociation of both compounds.

The dissociation of acetic acid is as follows:
CH3COOH (aq) ⇌ CH3COO- (aq) + H+ (aq)

The dissociation of sodium acetate is as follows:
CH3COONa (aq) → CH3COO- (aq) + Na+ (aq)

In a buffer solution, these reactions occur simultaneously and establish an equilibrium. The balanced chemical equation for this equilibrium can be written as follows:

CH3COOH (aq) + CH3COONa (aq) ⇌ CH3COO- (aq) + CH3COOH (aq)

Here, the reactants are acetic acid and sodium acetate, and the products are acetate ion (CH3COO-) and acetic acid. The double arrows indicate that the reaction can proceed in both directions, indicating the equilibrium state.

It's important to note that in a buffer solution, the primary purpose is to maintain a stable pH. Acetic acid and sodium acetate work together to resist changes in the pH of the solution, as they can both accept and donate protons. The reaction equilibrium between them helps to maintain the buffer's effectiveness.