Question

Two solutions are made containing the same concentrations of solutes. One solution is composed of \(\mathrm{NH}_{3}\) and \(\mathrm{NH}_{4} \mathrm{NO}_{3},\) while the other is composed of \(\mathrm{H}_{2} \mathrm{SO}_{4}\) and \(\mathrm{Na}_{2} \mathrm{SO}_{4}\). Which solution should have the larger capacity as a buffer?

Short answer

The solution with \\( NH_3\\ ) and \\( NH_4NO_3\\ ) has a larger buffer capacity.

Step-by-step solution

Understanding Buffer Solutions

Buffer solutions resist changes in pH when small amounts of acids or bases are added. They typically consist of a weak acid and its conjugate base, or a weak base and its conjugate acid.

Identifying Buffer Components

The first solution contains \(NH_3\), a weak base, and \(NH_4NO_3\), which provides \(NH_4^+\), a weak acid that is the conjugate acid of \(NH_3\). This combination makes the first solution a buffer system.The second solution contains \(H_2SO_4\), a strong acid, and \(Na_2SO_4\), a neutral salt. This solution lacks a conjugate base of a weak acid and therefore does not act as an effective buffer.

Comparing Buffer Capacities

The buffer capacity of a solution depends on the component concentrations and their ability to neutralize added acids or bases. \(NH_3\) and \(NH_4NO_3\) together form a system capable of neutralizing added acid \(NH_3 + H^+ ightarrow NH_4^+\) and added base \(NH_4^+ + OH^- ightarrow NH_3 + H_2O\). The second solution, lacking a weak acid-base pair, cannot act similarly.

Key concepts

Weak Acids and Bases

Weak acids and bases are the unsung heroes in the world of chemistry. They only partially dissociate in solution, which means they don't release all their hydrogen ions or hydroxide ions. For a weak acid, an example would be acetic acid (CH₃COOH). When dissolved, it releases some hydrogen ions, but not all. Because of this unique behavior, weak acids don't dramatically change the pH of a solution. This incomplete ionization allows them to act gently in chemical reactions.
On the other hand, weak bases, like ammonia (NH₃), work similarly, only partially accepting protons (H⁺) when dissolved in water. As a result, both weak acids and bases offer more stable pH levels, making them excellent for buffer solutions.
Here's why they are important:

• Weak acids and bases offer control over pH without drastic changes.
• They act as the main components in buffer solutions, helping maintain consistent pH levels.
• This property is crucial in many biological and chemical processes where pH balance is essential.

Conjugate Acid-Base Pairs

In the world of acids and bases, conjugate acid-base pairs are like dance partners. When an acid donates a proton (H⁺), it transforms into its conjugate base. Conversely, when a base accepts a proton, it becomes its conjugate acid. Consider the ammonia and ammonium ion duo: NH₃ and NH₄⁺. When NH₃ (the base) accepts a proton, it converts into NH₄⁺ (the conjugate acid).
Such pairs are vital for buffer systems because they enable reversible reactions that help resist pH changes. They work in tandem, with each partner ready to counteract sudden shifts in acidity or alkalinity. Let's see how they function:

• Conjugates allow reversible reactions that absorb or release H⁺ ions.
• They form the backbone of buffer systems, adjusting pH levels as needed.
• Their interplay is key in biological systems, sustaining life-supporting conditions.
• They convert quickly between acid and base forms, making them dynamic components in buffer solutions.

Buffer Capacity

Buffer capacity is a measure of the resilience of a buffer solution — how well it can resist changes in pH when a small amount of acid or base is introduced. Imagine a buffer as a sponge for hydrogen ions: the more sponges (buffers), the more capacity to absorb changes. Two main things determine buffer capacity: the concentrations of the acid and base pair, and their respective ionization constants.
The higher the concentration of the buffer components, the greater the capacity. For instance, our solution containing NH₃ and NH₄NO₃ has a greater buffer capacity compared to the non-buffer system of H₂SO₄ and Na₂SO₄. This is because it contains both a weak base (NH₃) and its conjugate acid (NH₄⁺).
More insights on buffer capacity:

• Buffer capacity depends on the absolute concentrations of the buffering agents.
• The ideal ratio in a buffer system is equal concentrations of acid and base for optimal capacity.
• Near the pKa of the weak acid, the buffer capacity is at its maximum.
• This property allows systems to stabilize pH, critical in processes such as metabolic pathways and industrial applications.