Question

Equal molar quantities of acetic acid and sodium hydrogen phosphate \(\left(\mathrm{Na}_{2} \mathrm{HPO}_{4}\right)\) are mixed. (a) Write a balanced, net ionic equation for the acid-base reaction that can, in principle, occur. (b) Does the equilibrium lie to the right or left?

Short answer

(a) The net ionic equation is \( \text{CH}_3\text{COOH} + \text{HPO}_4^{2-} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}_2\text{PO}_4^- \). (b) The equilibrium lies to the left.

Step-by-step solution

Identify Reaction Participants

In this problem, we are mixing equimolar amounts of acetic acid (CH₃COOH), a weak acid, and sodium hydrogen phosphate (Na₂HPO₄), which can accept protons and act as a base. Na₂HPO₄ in solution forms HPO₄²⁻ ions.

Write the Initial Reaction

Since acetic acid is a weak acid and sodium hydrogen phosphate can act as a base, the acid-base reaction that occurs can be written as:\[ \text{CH}_3\text{COOH} + \text{HPO}_4^{2-} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}_2\text{PO}_4^- \]

Balance the Net Ionic Equation

This is a balanced equation as the number of atoms and charges are equal on both sides. The change involves acetic acid donating a proton to HPO₄²⁻, forming acetate (CH₃COO⁻) and dihydrogen phosphate (H₂PO₄⁻).

Determine the Direction of Equilibrium

Consider the acid dissociation constants (Ka values) to determine equilibrium direction. Acetic acid has a stronger tendency to hold onto its proton (lower Ka) than H₃PO₄. The conjugate base CH₃COO⁻ is weaker than H₂PO₄⁻, implying equilibrium will favor the left side, where weaker acids and bases reside.

Key concepts

Acetic Acid

Acetic acid, also known by its chemical formula \( \text{CH}_3\text{COOH} \), is a key component in vinegar, giving it its characteristic smell and taste. As a weak acid, it does not completely dissociate in water. This means that a significant portion of acetic acid molecules remain intact in solution. In chemical reactions, it tends to donate protons, but not as readily as strong acids like hydrochloric acid. This partial dissociation is denoted by its acid dissociation constant, \( K_a \), which helps us understand its acid strength.
When you lightly mix acetic acid in water, you get a solution containing mostly \( \text{CH}_3\text{COOH} \) molecules, with a small percentage breaking into \( \text{CH}_3\text{COO}^- \) and \( \text{H}^+ \) ions. This behavior is crucial in predicting how acetic acid behaves in acid-base reactions, especially when confronting basic substances in chemical equations.

Sodium Hydrogen Phosphate

Sodium hydrogen phosphate (\( \text{Na}_2\text{HPO}_4 \)) is a compound commonly used in laboratories and industry, especially as a buffer solution. In water, it dissolves to produce \( \text{HPO}_4^{2-} \) ions. This behavior classifies it as an amphoteric species, meaning it can react both as an acid and a base.
In the presence of strong acids, \( \text{HPO}_4^{2-} \) ions readily accept protons, acting as a basic species. Conversely, with strong bases, it can donate protons, behaving as an acidic species. The dual nature makes \( \text{Na}_2\text{HPO}_4 \) very versatile and an ideal component in pH regulation and buffer solutions. This ability directly influences the stability and direction of equilibrium in chemical reactions, especially with weak acids like acetic acid.

Net Ionic Equation

A net ionic equation captures the essence of chemical reactions in aqueous solutions, showing only the species that actively participate in the reaction. It provides a stripped-down version of the chemical equation, free from spectator ions that do not take part in the chemical change.
In the reaction between acetic acid and \( \text{HPO}_4^{2-} \), we can eliminate the spectator sodium ions since they do not participate in the proton transfer process. The net ionic equation becomes:\[ \text{CH}_3\text{COOH} + \text{HPO}_4^{2-} \rightleftharpoons \text{CH}_3\text{COO}^- + \text{H}_2\text{PO}_4^- \]
This equation illustrates the fundamental acid-base reaction occurring, emphasizing the transfer of a proton from acetic acid to the hydrogen phosphate ion, forming acetate and dihydrogen phosphate ions.

Equilibrium Direction

When predicting the direction of equilibrium for acid-base reactions, we take into account the relative strength of acids and bases involved. The dissociation constant, \( K_a \), of these substances provides valuable insight. Acetic acid, characterized by a relatively low \( K_a \), suggests it holds onto its protons more tightly compared to other acids like phosphoric acid (\( H_3PO_4 \)).
In our reaction between \( \text{CH}_3\text{COOH} \) and \( \text{HPO}_4^{2-} \), the equilibrium will favor the side with weaker acids and bases. Since \( \text{CH}_3\text{COOH} \) is weaker than the formed \( \text{H}_2\text{PO}_4^- \) (dihydrogen phosphate), the balance will lean towards the left, back towards the reactants. This backward tendency helps stabilize the system with weaker conjugates, illustrating the nature of acid-base equilibria in driving reactions to states of lowest potential energy.