Question

Which of the following mixtures would result in a buffered solution when \(1.0 \mathrm{~L}\) of each of the two solutions are mixed? a. \(0.2 \mathrm{M} \mathrm{HNO}_{\mathrm{z}}\) and \(0.4 \mathrm{M} \mathrm{NaNO}_{3}\) b. \(0.2 \mathrm{M} \mathrm{HNO}_{3}\) and \(0.4 \mathrm{M} \mathrm{HF}\) c. \(0.2 \mathrm{M} \mathrm{HNO}_{3}\) and \(0.4 \mathrm{M} \mathrm{NaF}\) d. \(0.2 \mathrm{M} \mathrm{HNO}_{3}\) and \(0.4 \mathrm{M} \mathrm{NaOH}\)

Short answer

The correct answer is option c: \(0.2 M HNO_3\) and \(0.4 M NaF\) produce a buffered solution. This mixture forms a weak acid/conjugate base pair, which will result in a buffered solution.

Step-by-step solution

Identify Weak Acids and Bases and Their Conjugates

First, it is crucial to recognize the weak acids and bases and their respective conjugate pairs. This will assist in determining if the pairs are suitable for creating a buffered solution. \(HNO_3\) is a strong acid, and \(NO_3^-\) is its conjugate base. \(HF\) is a weak acid, and \(F^-\) is its conjugate base. \(NaNO_3\) is the sodium salt of a strong acid, \(HNO_3\), and will produce \(Na^+\) and \(NO_3^-\) in water. \(NaF\) is the sodium salt of a weak acid, \(HF\), and will produce \(Na^+\) and \(F^-\) in water. \(NaOH\) is a strong base, and \(OH^-\) is its conjugate base.

Evaluate the Given Mixtures

Next, examine each of the provided mixtures to see if they can create a buffered solution by forming a weak acid and its conjugate base or a weak base and its conjugate acid. a. \(0.2 M HNO_3\) and \(0.4 M NaNO_3\): The mixture contains a strong acid and its conjugate base. Therefore, it cannot form a buffered solution. b. \(0.2 M HNO_3\) and \(0.4 M HF\): This mixture contains a strong acid and an unrelated weak acid. No weak acid/conjugate base pair is present in this mixture, so it cannot form a buffered solution. c. \(0.2 M HNO_3\) and \(0.4 M NaF\): In this mixture, the \(HNO_3\) is a strong acid, and the \(NaF\) dissociates into \(Na^+\) and its conjugate base \(F^-\). The \(F^-\) can react with the \(HNO_3\) to produce the weak acid, \(HF\), and its conjugate base \(NO_3^-\). Therefore, this mixture forms a weak acid/conjugate base pair and can result in a buffered solution. d. \(0.2 M HNO_3\) and \(0.4 M NaOH\): The mixture comprises a strong acid and a strong base, which will neutralize each other. This mixture cannot form a buffered solution.

Choose the Buffered Solution

Based on the analysis of the given mixtures: a. Not buffered (strong acid and its conjugate base) b. Not buffered (strong acid and unrelated weak acid) c. Buffered (forms a weak acid and its conjugate base pair) d. Not buffered (strong acid and strong base) The correct answer is option c: \(0.2 M HNO_3\) and \(0.4 M NaF\) produce a buffered solution.

Key concepts

Weak Acids and Bases

Understanding weak acids and bases is fundamental to grasping the concept of buffered solutions. Unlike their strong counterparts that fully dissociate in water, weak acids and bases only partially dissociate. This partial dissociation leads to an equilibrium between the non-dissociated molecules and the ions produced. An example of a weak acid is hydrofluoric acid (HF), which dissociates into its ions only to a limited extent in water.

It is important to note that the strength of an acid or a base is not about its pH level but about its ability to dissociate. Thus, a weak acid can actually have a low pH if it is highly concentrated, and similarly, a weak base can have a high pH if highly concentrated. In the context of the exercise, this understanding is crucial to identify which compounds can contribute to buffer formation.

Conjugate Acid-Base Pairs

A conjugate acid-base pair consists of molecules or ions that differ by the presence of one hydrogen ion (H+). When an acid donates a hydrogen ion, the remaining species is its conjugate base. Similarly, when a base accepts a hydrogen ion, it forms its conjugate acid. The concept of conjugate acid-base pairs is tied in with Brønsted-Lowry acid-base theory, which defines an acid as a proton donor and a base as a proton acceptor.

In our textbook example, hydrofluoric acid (HF) and its ion (F-) form a conjugate acid-base pair. When choosing components for a buffered solution, it's important to pair a weak acid with its conjugate base or a weak base with its conjugate acid. This pairing is essential because it provides resistance to pH changes when adding small amounts of acid or base to the solution, maintaining equilibrium.

Buffer Systems in Chemistry

A buffer system is a solution that resists changes in pH when small amounts of acid or base are added. It typically consists of a weak acid and its conjugate base or a weak base and its conjugate acid. This resistance is essential for maintaining stable pH levels in many biological and chemical systems.

Buffer systems work through the neutralization reaction that occurs when the acid or base is added to the solution. If an acid is added, it will be neutralized by the conjugate base present in the buffer. Conversely, if a base is added, the weak acid neutralizes it. This back-and-forth process occurs at the equilibrium point of the weak acid or base's dissociation in water.

For a buffer to effectively maintain pH, both components of the conjugate pair must be present in sufficient quantities. This is highlighted in the textbook exercise, where the buffered solution contained a weak acid and its conjugate base, allowing it to resist significant pH changes upon the addition of other substances.