Question

Which of the following solutions is a buffer? (a) A solution made by mixing \(100 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) and \(50 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{NaOH}\), (b) a solution made by mixing \(100 \mathrm{~mL}\). of \(0.100 \mathrm{M} \mathrm{CH}_{3} \mathrm{COOH}\) and \(500 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{NaOH}\), (c) \(\mathrm{A}\) solution made by mixing \(100 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{CH}, \mathrm{COOH}\) and \(50 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{HCl}\), (d) A solution made by mixing \(100 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{CH} \mathrm{CHOK}_{3}\) and \(50 \mathrm{~mL}\) of \(0.100 \mathrm{M} \mathrm{KCl}\).

Short answer

The only buffer solution among the given options is (a), as it contains acetic acid (a weak acid) and its conjugate base (the acetate ion) after the reaction with NaOH.

Step-by-step solution

Identify the species in each solution

In order to analyze if a solution is a buffer or not, we need to identify the species present in the solution. For this, we will write down which chemical compounds are present in each of the solutions given in the exercise. (a) \(0.100 M~CH_3COOH~(acetic~acid)~and~0.100M~NaOH\) (b) \(0.100 M~CH_3COOH~(acetic~acid)~and~0.100M~NaOH\) (c) \(0.100 M~CH_3COOH~(acetic~acid)~and~0.100M~HCl\) (d) \(0.100 M~CH_3CHOH K_3~and~0.100 M~KCl\)

Determine the chemical reactions for each solution

Next, let's analyze the chemical reactions happening in each solution. This will allow us to predict the resulting chemical species. (a) \(CH_3COOH~+~NaOH~\rightarrow~CH_3COONa~+~H_2O\) (the acetic acid reacts with the NaOH) (b) \(CH_3COOH~+~NaOH~\rightarrow~CH_3COONa~+~H_2O\) (the acetic acid reacts with the NaOH) (c) \(CH_3COOH~+~HCl~\rightarrow~CH_3COOH \cdot HCl\) (the acetic acid reacts with the HCl) (d) \(CH_3CHOHK_3~\rightarrow~CH_3CHOH~+~K_3\) (no reaction happens with KCl)

Check if the solutions fulfill the buffer conditions

Now, we will verify if the resulting chemical species in each solution fulfill the conditions for a buffer solution, which consists of a weak acid and its conjugate base, or a weak base and its conjugate acid. (a) In this solution, we have acetic acid (a weak acid) and its conjugate base (the acetate ion). It's a buffer solution. (b) In this solution, we have acetic acid and an excess of NaOH. Since there's a large amount of strong base (NaOH), it will not act as a buffer solution. (c) In this solution, we have acetic acid and a strong acid (HCl). The presence of a strong acid won't allow the solution to act as a buffer. (d) In this solution, we have CH3CHOHK3 and KCl. There's no weak acid/base and its conjugate present in this solution, so it's not a buffer solution.

Conclusion

After evaluating the chemical species present in each solution and the reactions happening in them, we can conclude that the solution (a) is a buffer solution since it fulfills the buffer conditions by containing a weak acid and its conjugate base.

Key concepts

Acid-Base Reactions

Acid-base reactions are fundamental chemical processes where acids and bases interact. Acids like acetic acid (\(CH_3COOH\)), donate protons (H\(^+\)) in these reactions, while bases like sodium hydroxide (\(NaOH\)) accept protons.

An acid-base reaction typically results in the formation of water and a salt. For example, in our buffer solution example, acetic acid reacts with NaOH to form water and sodium acetate (\(CH_3COONa\)):

• \(CH_3COOH + NaOH \rightarrow CH_3COONa + H_2O\)

This formation of sodium acetate is important, as it acts as a conjugate base, helping to maintain the buffer capacity of the solution.

Understanding these interactions is crucial for analyzing whether a given mixture will behave as a buffer, as seen in exercises involving buffer solutions.

Chemical Equilibrium

Chemical equilibrium refers to a state where the rate of the forward reaction equals the rate of the reverse reaction. This concept is essential for buffers, as both components—the weak acid and its conjugate base—must be present in substantial concentrations.

In a buffer solution made of acetic acid and sodium acetate, the equilibrium involves this reaction:

• \(CH_3COOH \rightleftharpoons CH_3COO^- + H^+\)

Here, acetic acid dissociates into acetate ions and hydrogen ions, while in reverse, acetate ions combine with hydrogen ions to form acetic acid.

The concentrations of these species determine the buffer's pH and its ability to resist changes when small amounts of acids or bases are added. Mastery of equilibrium concepts helps students comprehend how buffer solutions maintain their pH stability in various chemical processes.

Conjugate Acids and Bases

Conjugate acids and bases are vital concepts in understanding buffer solutions. They arise from acid-base reactions where an acid and a base form their conjugate counterparts.

When an acid donates a proton, it forms its conjugate base. Ex: Acetic acid becomes acetate ion (\(CH_3COO^-\)) after losing a proton. Similarly, a base accepting a proton forms a conjugate acid. This relationship helps to understand the resilience of buffer solutions.

In buffer systems, the presence of both a weak acid and its conjugate base is key to its function. They work together to neutralize any added acid or base, thus maintaining a stable pH.

• A weak acid forms its conjugate base upon donating a proton.
• A weak base forms its conjugate acid upon accepting a proton.

These pairs are essential players in the buffer solution's ability to resist pH changes, highlighting their indispensability in chemical equilibrium and reaction studies.