Problem 16 - Chemistry Matter and Change

Question

Challenge Write an equation for a base equilibrium in which the base in the forward reaction is \(\mathrm{PO}_{4}^{3-}\) and the base in the reverse reaction is \(\mathrm{OH}^{-} .\)

Step-by-Step Solution

Answer

The base equilibrium involving the bases \(\mathrm{PO}_{4}^{3-}\) and \(\mathrm{OH}^{-}\), along with their conjugate acids, is represented by the balanced chemical equation: \[\mathrm{PO}_{4}^{3-} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{HPO}_{4}^{2-} + \mathrm{OH}^{-}\]

Step 1: Identify the Acid-Base Pairs

We are given two bases: \(\mathrm{PO}_{4}^{3-}\) and \(\mathrm{OH}^{-}\). For each base, we can identify its associated acid. For \(\mathrm{PO}_{4}^{3-}\), adding a proton (H\(^+\)) will result in the conjugate acid, which is \(\mathrm{HPO}_{4}^{2-}\). For \(\mathrm{OH}^{-}\), adding a proton (H\(^+\)) will result in the conjugate acid, which is \(\mathrm{H}_{2}\mathrm{O}\).

Step 2: Write the Balanced Chemical Equation

Now that we have identified the acid-base pairs, we can write the balanced chemical equation for the base equilibrium: \[\mathrm{PO}_{4}^{3-} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{HPO}_{4}^{2-} + \mathrm{OH}^{-}\] The double arrows indicate the equilibrium between the forward and reverse reactions, with the forward reaction involving the base \(\mathrm{PO}_{4}^{3-}\) and its conjugate acid \(\mathrm{HPO}_{4}^{2-}\), and the reverse reaction involving the base \(\mathrm{OH}^{-}\) and its conjugate acid \(\mathrm{H}_{2}\mathrm{O}\).

Key Concepts

Acid-Base Pairs

In chemistry, acids and bases interact in specific pairs known as acid-base pairs. An acid-base pair entails an acid that can donate a proton (H\(^+\)) and a base that can accept a proton. These sets are vital to understanding how reactions proceed and are often found on opposite sides of a chemical equation.

In an acid-base pair, when the base forms a conjugate acid by accepting a proton, the acid simultaneously forms a conjugate base by donating it. This dual association is key to many chemical reactions, including equilibrium reactions, where substances can change back and forth, maintaining a balance.

• For instance, in the given exercise, the phosphate ion \(\mathrm{PO}_{4}^{3-}\) serves as a base. The chemical reaction shows its pair, which involves \(\mathrm{HPO}_{4}^{2-}\) as its conjugate acid.
• In the reverse reaction, the hydroxide ion \(\mathrm{OH}^{-}\) acts as the base, with water \(\mathrm{H}_{2}\mathrm{O}\) being its conjugate acid.

Understanding acid-base pairs is a cornerstone for predicting the direction and products of chemical reactions.

Conjugate Acid

A conjugate acid is what we get when a base gains a proton. Think of it as the base's plus-one. During a chemical reaction, when a base accepts a hydrogen ion (H\(^+\)), it transforms into its conjugate acid. Knowing this relationship helps predict the chemical behavior of a substance when it participates in a reaction.

For example, in the provided exercise, the phosphate ion \(\mathrm{PO}_{4}^{3-}\) is the base in the forward reaction. By gaining a proton, it forms \(\mathrm{HPO}_{4}^{2-}\), which is its conjugate acid. This transformation is crucial to understanding how equilibrium is reached in a reaction.

• The conjugate acid \(\mathrm{HPO}_{4}^{2-}\) is now capable of donating a proton in the reverse reaction, highlighting how reversible reactions can be dynamic yet balanced.
• On the other hand, the hydroxide ion \(\mathrm{OH}^{-}\) becomes water, \(\mathrm{H}_{2}\mathrm{O}\), which is its conjugate acid in the reverse reaction.

The concept of conjugate acids helps illustrate how a system at equilibrium can shift in response to changes in proton concentration either way.

Chemical Equation

A chemical equation succinctly represents a chemical reaction using symbols and formulas. It provides information on the reactants that are consumed and the products that are formed, as well as their relative quantities. The equation helps chemists understand the details of how interactions proceed and predict outcomes.

In the given exercise, the chemical equation illustrates the equilibrium between the reaction participants:

\[\mathrm{PO}_{4}^{3-} + \mathrm{H}_{2}\mathrm{O} \rightleftharpoons \mathrm{HPO}_{4}^{2-} + \mathrm{OH}^{-}\]

• The double arrow (\(\rightleftharpoons\)) used in the equation signifies that the reaction is reversible, meaning it can proceed in both the forward and reverse directions.
• In the forward direction, the base \(\mathrm{PO}_{4}^{3-}\) reacts with water, forming \(\mathrm{HPO}_{4}^{2-}\) and \(\mathrm{OH}^{-}\).
• Conversely, in the reverse reaction, \(\mathrm{OH}^{-}\) acts as the base, accepting a proton from \(\mathrm{HPO}_{4}^{2-}\) to reform \(\mathrm{PO}_{4}^{3-}\) and \(\mathrm{H}_{2}\mathrm{O}\).

The chemical equation is a powerful tool for visualizing reactions, assessing equilibrium conditions, and discerning the direction of chemical processes.