Problem 11 - General Chemistry: Principles and Modern Applications

Question

Indicate which of the following aqueous solutions are buffer solutions, and explain your reasoning. (a) \(0.100 \mathrm{M} \mathrm{NaCl}\) (b) \(0.100 \mathrm{M} \mathrm{NaCl}-0.100 \mathrm{M} \mathrm{NH}_{4} \mathrm{Cl}\) (c) \(0.100 \mathrm{M} \mathrm{CH}_{3} \mathrm{NH}_{2}-0.150 \mathrm{M} \mathrm{CH}_{3} \mathrm{NH}_{3}^{+} \mathrm{Cl}^{-}\) (d) \(0.100 \mathrm{M} \mathrm{HCl}-0.050 \mathrm{M} \mathrm{NaNO}_{2}\) (e) \(0.100 \mathrm{M} \mathrm{HCl}-0.200 \mathrm{M} \mathrm{NaCH}_{3} \mathrm{COO}\) (f) \(0.100 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}-0.125 \mathrm{M} \mathrm{NaCH}_{3} \mathrm{CH}_{2} \mathrm{COO}\)

Step-by-Step Solution

Answer

The buffer solutions are b, c, and f.

Step 1: Identifying buffer solution a

Solution a only contains \(0.100 \mathrm{M} \mathrm{NaCl}\), a salt. Since there is no weak acid or base present in the solution, it cannot act as a buffer. Hence, it is not a buffer solution.

Step 2: Identifying buffer solution b

A buffer solution consists of a weak base or acid and its conjugate. Looking at solution b, it contains \(0.100 \mathrm{M} \mathrm{NaCl}\) and \(0.100 \mathrm{M} \mathrm{NH}_{4}\mathrm{Cl}\). Here, \(\mathrm{NH}_{4}\) is a weak acid and \(\mathrm{Cl}^{-}\) is its conjugate base. Hence, it is a buffer solution.

Step 3: Identifying buffer solution c

Solution c consist of \(0.100 \mathrm{M} \mathrm{CH}_{3} \mathrm{NH}_{2}\) and \(0.150 \mathrm{M} \mathrm{CH}_{3} \mathrm{NH}_{3}^{+} \mathrm{Cl}^{-}\). The \(\mathrm{CH}_{3} \mathrm{NH}_{2}\) is a weak base and \(\mathrm{CH}_{3} \mathrm{NH}_{3}^{+}\) is its conjugate acid. Hence, it is a buffer solution.

Step 4: Identifying buffer solution d

Solution d contains \(0.100 \mathrm{M} \mathrm{HCl}\) and \(0.050 \mathrm{M} \mathrm{NaNO}_{2}\). Here, \(\mathrm{HCl}\) is a strong acid and not a weak one, so it cannot form a buffer with its salt, hence it is not a buffer solution.

Step 5: Identifying buffer solution e

Solution e contains \(0.100 \mathrm{M} \mathrm{HCl}\) and \(0.200 \mathrm{M} \mathrm{NaCH}_{3} \mathrm{COO}\). The \(\mathrm{HCl}\) is still a strong acid and hence, like in the previous solution, even though \(\mathrm{CH}_{3} \mathrm{COO}^{-}\) is a conjugate base, this solution cannot act as a buffer. Hence, it is not a buffer solution.

Step 6: Identifying buffer solution f

Lastly, solution f consists of \(0.100 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) and \(0.125 \mathrm{M} \mathrm{NaCH}_{3} \mathrm{CH}_{2} \mathrm{COO}\). Here, \(\mathrm{CH}_{3} \mathrm{COOH}\) is a weak acid and \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COO}^{-}\) is its conjugate base. Hence, it is a buffer solution.

Key Concepts

weak acids

Weak acids are substances that partially dissociate into ions in solution. This means that when they dissolve in water, they do not release all of their hydrogen ions at once, unlike strong acids. Instead, a significant portion of the weak acid remains undissolved in the molecular form. This partial dissociation is represented by a reversible reaction of the form:
\[ HA (aq) \rightleftharpoons H^+ (aq) + A^- (aq) \]Here, \( HA \) stands for the weak acid, \( H^+ \) is the hydrogen ion, and \( A^- \) is the conjugate base.

• Examples include acetic acid (\( CH_3COOH \)), formic acid, and citric acid.
• Weak acids typically have a higher pH than strong acids at the same concentration.
• In buffer solutions, weak acids together with their conjugate bases help resist pH changes.

Understanding the nature of weak acids is crucial in recognizing their role in buffer solutions.

conjugate base

A conjugate base is the species that remains after a weak acid has donated a hydrogen ion. It is basically the acid minus one proton. The concept of a conjugate base is important because it pairs with the weak acid in both chemical reactions and buffer solutions. For example:
- When acetic acid (\( CH_3COOH \)) donates a hydrogen ion, it becomes acetate (\( CH_3COO^- \)), its conjugate base.
This concept comes into play significantly in buffer systems:

• A buffer contains a weak acid and its conjugate base, like \( CH_3COOH \) and \( CH_3COO^- \).
• Conjugate bases act to neutralize small amounts of added acids in solutions, maintaining stability in pH.
• The strength and availability of the conjugate base depend on its parent weak acid.

Understanding the relationship between weak acids and their conjugate bases is vital in grasping how buffers work and maintain equilibrium in a solution.

weak bases

Weak bases are the counterparts of weak acids. They partially accept protons (\( H^+ \)) when dissolved in water. Unlike strong bases, which dissociate completely, weak bases only react partially to form their protons in chemical solutions, according to a reversible reaction:
\[ B(aq) + H_2O(l) \rightleftharpoons BH^+(aq) + OH^-(aq) \]Here, \( B \) represents the weak base, \( BH^+ \) stands for the conjugate acid, and \( OH^- \) is the hydroxide ion.

• Examples of weak bases include ammonia (\( NH_3 \)) and methylamine (\( CH_3NH_2 \)).
• They usually result in a solution with a lower pH compared to strong bases at the same concentration.
• In buffer systems, weak bases work with their conjugate acids to maintain pH balance.

Recognizing weak bases and understanding their properties is essential for identifying buffer solutions, especially as they work in tandem with their conjugate acids.

pH stability

pH stability is a vital concept often associated with buffer solutions. A buffer solution is designed to resist changes in pH upon the addition of small amounts of acid or base. This is particularly important in many scientific and biological contexts where pH levels must remain constant for proper functioning.
Buffers maintain pH stability via the acid-base equilibrium:

• When an acid is added, the conjugate base present in the buffer will neutralize it, limiting the change in pH.
• Conversely, if a base is added, the weak acid in the buffer will react to stabilize the pH.
• Optimal buffering occurs when there are equal concentrations of weak acid and conjugate base.

This buffering capacity is usually expressed around the pKa of the weak acid or pKb of the weak base. Understanding the mechanisms of pH stability helps us to see why buffers are crucial in chemistry, biology, and environmental systems.