Which of the following solutions is a buffer? (a) \(0.20 \mathrm{M}\) for\(\operatorname{mic}\) acid \((\mathrm{HCOOH}),(\mathbf{b}) 0.20 M\) formic acid \((\mathrm{HCOOH})\) and \(0.20 \mathrm{M}\) sodium formate \((\mathrm{HCOONa}),(\mathbf{c}) 0.20 \mathrm{Mnitric}\) acid \(\left(\mathrm{HNO}_{3}\right)\) and \(0.20 \mathrm{M}\) sodium nitrate \(\left(\mathrm{NaNO}_{3}\right)\) (d) both b and \(\mathrm{c},(\mathbf{e})\) all of \(\mathrm{a}, \mathrm{b},\) and \(\mathrm{c}\).

In this step, we will identify the weak acids and their conjugate bases (or weak bases and their conjugate acids) in each given solution: (a) \(0.20 \mathrm{M}\) formic acid \((\mathrm{HCOOH})\): This solution has only a weak acid, and its conjugate base is not present. (b) \(0.20 \mathrm{M}\) formic acid \((\mathrm{HCOOH})\) and \(0.20 \mathrm{M}\) sodium formate \((\mathrm{HCOONa})\): This solution has both a weak acid and its conjugate base present. (c) \(0.20 \mathrm{M}\) nitric acid \(\left(\mathrm{HNO}_{3}\right)\) and \(0.20 \mathrm{M}\) sodium nitrate \(\left(\mathrm{NaNO}_{3}\right)\): Nitric acid (\(\mathrm{HNO}_{3}\)) is a strong acid, so this solution does not contain a weak acid and its conjugate base.

Based on our analysis in Step 1, we can now identify the buffer solution(s) from the given options: (a) \(0.20 \mathrm{M}\) formic acid \((\mathrm{HCOOH})\): Not a buffer solution. (b) \(0.20 \mathrm{M}\) formic acid \((\mathrm{HCOOH})\) and \(0.20 \mathrm{M}\) sodium formate \((\mathrm{HCOONa})\): This is a buffer solution because it contains both a weak acid and its conjugate base. (c) \(0.20 \mathrm{M}\) nitric acid \(\left(\mathrm{HNO}_{3}\right)\) and \(0.20 \mathrm{M}\) sodium nitrate \(\left(\mathrm{NaNO}_{3}\right)\): Not a buffer solution. (d) Both b and c: Not valid since option (c) is not a buffer solution. (e) All of a, b, and c: Not valid since options (a) and (c) are not buffer solutions. From our evaluation, we can conclude that the correct answer is (b) \(0.20 \mathrm{M}\) formic acid \((\mathrm{HCOOH})\) and \(0.20 \mathrm{M}\) sodium formate \((\mathrm{HCOONa})\), as this is the buffer solution among the given options.