Problem 174 - Introductory Chemistry Atoms First

Question

It is possible to make two completely different buffers using the dihydrogen phosphate ion, \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) (a) In one buffer, \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) serves as the weak acid. What is the conjugate weak base? (b) Write the equations that show how the buffer in part (a) works when either \(\mathrm{H}_{3} \mathrm{O}^{+}\) or \(\mathrm{OH}^{-}\) is added. (c) In the other buffer, \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) serves as the weak base. What is the conjugate weak acid? (d) Write the equations that show how the buffer in part (c) works when either \(\mathrm{H}_{3} \mathrm{O}^{+}\) or \(\mathrm{OH}^{-}\) is added.

Step-by-Step Solution

Answer

(a) The conjugate weak base of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) is \(\mathrm{HPO}_{4}^{2-}\). (b) Equations for buffer with \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{OH}^{-}\) added: 1. \(\mathrm{HPO}_{4}^{2-} + \mathrm{H}_{3} \mathrm{O}^{+} \rightarrow \mathrm{H}_{2} \mathrm{PO}_{4}^{-} + \mathrm{H}_{2} \mathrm{O}\) 2. \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-} + \mathrm{OH}^{-} \rightarrow \mathrm{HPO}_{4}^{2-} + \mathrm{H}_{2} \mathrm{O}\) (c) The conjugate weak acid of \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) is \(\mathrm{H}_{3} \mathrm{PO}_{4}\). (d) Equations for buffer with \(\mathrm{H}_{3} \mathrm{O}^{+}\) and \(\mathrm{OH}^{-}\) added: 1. \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-} + \mathrm{H}_{3} \mathrm{O}^{+} \rightarrow \mathrm{H}_{3} \mathrm{PO}_{4} + \mathrm{H}_{2} \mathrm{O}\) 2. \(\mathrm{H}_{3} \mathrm{PO}_{4} + \mathrm{OH}^{-} \rightarrow \mathrm{H}_{2} \mathrm{PO}_{4}^{-} + \mathrm{H}_{2} \mathrm{O}\)

Step 1: (a) Identifying Conjugate Weak Base

The conjugate weak base of a weak acid is formed by removing a proton (H\(^{+}\)) from the acid. So, for \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\), the conjugate weak base will be: \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-} \rightarrow \mathrm{H}^{+} + \mathrm{HPO}_{4}^{2-}\) The conjugate weak base is \(\mathrm{HPO}_{4}^{2-}\).

Step 2: (b) Buffer Equations with H3O+ and OH- Added

When \(\mathrm{H}_{3} \mathrm{O}^{+}\) or \(\mathrm{OH}^{-}\) is added to a buffer containing \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{HPO}_{4}^{2-}\), the following equations can be written: 1. When \(\mathrm{H}_{3} \mathrm{O}^{+}\) is added: \(\mathrm{HPO}_{4}^{2-} + \mathrm{H}_{3} \mathrm{O}^{+} \rightarrow \mathrm{H}_{2} \mathrm{PO}_{4}^{-} + \mathrm{H}_{2} \mathrm{O}\) 2. When \(\mathrm{OH}^{-}\) is added: \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-} + \mathrm{OH}^{-} \rightarrow \mathrm{HPO}_{4}^{2-} + \mathrm{H}_{2} \mathrm{O}\)

Step 3: (c) Identifying Conjugate Weak Acid

The conjugate weak acid of a weak base is formed by adding a proton (H\(^{+}\)) to the base. So, for \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\), the conjugate weak acid will be: \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-} + \mathrm{H}^{+} \rightarrow \mathrm{H}_{3} \mathrm{PO}_{4}\) The conjugate weak acid is \(\mathrm{H}_{3} \mathrm{PO}_{4}\).

Step 4: (d) Buffer Equations with H3O+ and OH- Added

When \(\mathrm{H}_{3} \mathrm{O}^{+}\) or \(\mathrm{OH}^{-}\) is added to a buffer containing \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-}\) and \(\mathrm{H}_{3} \mathrm{PO}_{4}\), the following equations can be written: 1. When \(\mathrm{H}_{3} \mathrm{O}^{+}\) is added: \(\mathrm{H}_{2} \mathrm{PO}_{4}^{-} + \mathrm{H}_{3} \mathrm{O}^{+} \rightarrow \mathrm{H}_{3} \mathrm{PO}_{4} + \mathrm{H}_{2} \mathrm{O}\) 2. When \(\mathrm{OH}^{-}\) is added: \(\mathrm{H}_{3} \mathrm{PO}_{4} + \mathrm{OH}^{-} \rightarrow \mathrm{H}_{2} \mathrm{PO}_{4}^{-} + \mathrm{H}_{2} \mathrm{O}\)

Key Concepts

Acid-Base Chemistry

Acid-base chemistry is a fundamental concept in understanding chemical reactions that involve hydrogen ions, commonly known as protons. In this chemistry, acids donate protons, while bases accept protons.
One of the key features of acid-base reactions is the establishment of a balance between acids and bases in a solution. This balance is critical as it determines the pH level of the solution.

• Acids typically taste sour and can corrode metals. In solution, they release \( ext{H}^+ \) ions.
• Bases often feel slippery, can note the bitter taste, and tend to release hydroxide ions \( ext{OH}^- \) in solution.
• The strength of an acid or a base is determined by its ability to dissociate in water and the extent of that dissociation.

In acid-base chemistry, reactions often involve the transfer of protons between reactants, resulting in chemical species known as conjugate acids and bases.

Conjugate Acids and Bases

Conjugate acids and bases play a crucial role in buffer solutions. In every acid-base reaction, there is a pair of molecules or ions that differ by a single proton. This pair is called the conjugate acid-base pair.
For example, when \( ext{H}_2 ext{PO}_4^- \) acts as a weak acid, it donates a proton to become \( ext{HPO}_4^{2-} \), which is its conjugate base. Conversely, when \( ext{H}_2 ext{PO}_4^- \) acts as a base by accepting a proton, it becomes \( ext{H}_3 ext{PO}_4 \), its conjugate acid.

• A conjugate acid is formed when a base gains a proton while the conjugate base is formed when an acid loses a proton.
• This concept helps to understand how substances behave differently when they gain or lose protons, contributing to the stability and functionality of buffer solutions.

Recognizing these pairs is essential in understanding the underlying mechanisms that maintain pH levels within a narrow range in various environments.

pH Regulation

pH regulation is a critical aspect of many biological and chemical systems because even a small change in pH can significantly affect a system's functionality.
Buffers are the primary means by which pH is regulated in a solution. They consist of a weak acid and its conjugate base, or a weak base and its conjugate acid. They work by neutralizing added acids (\( ext{H}_3 ext{O}^+ \)) or bases (\( ext{OH}^- \)), ensuring that the pH remains relatively constant despite the addition of these substances.

• For example, in the buffer system containing \( ext{H}_2 ext{PO}_4^- \) and \( ext{HPO}_4^{2-} \), the weak acid \( ext{H}_2 ext{PO}_4^- \) neutralizes added bases, while the conjugate base \( ext{HPO}_4^{2-} \) neutralizes added acids.
• This dual action helps maintain pH near a target value, which is vital in numerous chemical processes and biological functions.

Understanding pH regulation through buffers is essential for grasping how many natural systems, including human bodies, maintain their required pH levels.