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A buffer solution is a solution that can resist significant pH changes when a small amount of acid or base is added to it. Buffers are typically composed of a weak acid or base and its conjugate base or acid, respectively. The components should be present in roughly equal amounts. When a strong acid or base is added to the buffer solution, the weak acid or base and its conjugate will react to neutralize the added acid/base, thus minimizing the pH change.

The first mixture is composed of acetic acid (\(\mathrm{CH}_{3} \mathrm{COOH}\)), which is a weak acid, and sodium acetate (\(\mathrm{CH}_{3} \mathrm{COONa}\)), which is the salt of the conjugate base (acetate ion, \(\mathrm{CH}_{3} \mathrm{COO}^{-}\)) of acetic acid. The acetic acid can donate a proton (\(\mathrm{H}^{+}\)) to the solution, and the acetate ion from sodium acetate can accept a proton. This equilibrium allows the solution to resist pH changes when small amounts of strong acids or bases are added, making this mixture a buffer.

The second mixture is composed of hydrochloric acid (\(\mathrm{HCl}\)) and sodium chloride (\(\mathrm{NaCl}\)). Hydrochloric acid is a strong acid that fully dissociates in water, and its conjugate base, the chloride ion (\(\mathrm{Cl}^{-}\)), is a very weak base. Sodium chloride is a salt that dissociates into sodium (\(\mathrm{Na}^{+}\)) and chloride (\(\mathrm{Cl}^{-}\)) ions in water. Both components do not have the ability to neutralize a significant amount of added acid or base because there is no equilibrium between a weak acid/base and its conjugate base/acid. Therefore, this mixture cannot act as a buffer. In conclusion, a mixture of \(\mathrm{CH}_{3} \mathrm{COOH}\) and \(\mathrm{CH}_{3} \mathrm{COONa}\) can act as a buffer because it has an equilibrium between a weak acid and its conjugate base, while a mixture of \(\mathrm{HCl}\) and \(\mathrm{NaCl}\) cannot act as a buffer because both components are fully dissociated and cannot neutralize added strong acids/bases.