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(B) For a buffer solution,the $pH$ is given by the Henderson-Hasselbalch equation: $pH = pK_a + \log \frac{[	ext{salt}]}{[	ext{acid}]}$. Since the c

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$I$ and $III$

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(B) For a buffer solution,the $pH$ is given by the Henderson-Hasselbalch equation: $pH = pK_a + \log \frac{[	ext{salt}]}{[	ext{acid}]}$. Since the concentration of the acid and salt are proportional to their volumes (as molarity is the same),the $pH$ is lowest when the ratio $\frac{[	ext{salt}]}{[	ext{acid}]}$ is the smallest. Calculating the ratio $\frac{V_{	ext{salt}}}{V_{	ext{acid}}}$ for each: $I: \frac{4.0}{4.0} = 1.0$ $II: \frac{40.0}{4.0} = 10.0$ $III: \frac{4.0}{40.0} = 0.1$ $IV: \frac{10.0}{0.1} = 100.0$ Comparing the ratios,$III$ $(0.1)$ and $I$ $(1.0)$ have the lowest values. However,looking at the options provided,we re-evaluate the question. The $pH$ is lowest when the acid concentration is highest relative to the salt. Comparing the ratio $\frac{[	ext{acid}]}{[	ext{salt}]}$,the highest ratio corresponds to the lowest $pH$. $I: \frac{4}{4} = 1$ $II: \frac{4}{40} = 0.1$ $III: \frac{40}{4} = 10$ $IV: \frac{0.1}{10} = 0.01$ The lowest $pH$ occurs for the solutions with the highest acid-to-salt ratio,which are $III$ and $I$. Given the options,$III$ and $IV$ is not correct,but $III$ and $I$ is not an option. Re-checking the question: the lowest $pH$ occurs when the ratio $\frac{[	ext{salt}]}{[	ext{acid}]}$ is minimum. The values are $III$ $(0.1)$ and $I$ $(1.0)$. If we look for the lowest $pH$ among the sets,$III$ is the lowest. The question asks for a set. Based on the ratio $\frac{[	ext{salt}]}{[	ext{acid}]}$,$III$ and $I$ are the lowest. Since $I$ and $III$ is option $B$,that is the correct choice.

Buffer Solution	Volume of $0.1 \ M$ Weak Acid (mL)	Volume of $0.1 \ M$ Sodium Salt (mL)
$I$	$4.0$	$4.0$
$II$	$4.0$	$40.0$
$III$	$40.0$	$4.0$
$IV$	$0.1$	$10.0$

Buffer Solution Volume of $0.1 \ M$ Weak Acid (mL) Volume of $0.1 \ M$ Sodium Salt (mL)

$I$ $4.0$ $4.0$

$II$ $4.0$ $40.0$

$III$ $40.0$ $4.0$

$IV$ $0.1$ $10.0$

Which of the two sets of buffer solutions have the least $pH$?

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Buffer Solution Volume of $0.1 \ M$ Weak Acid (mL) Volume of $0.1 \ M$ Sodium Salt (mL) $I$ $4.0$ $4.0$ $II$ $4.0$ $40.0$ $III$ $40.0$ $4.0$ $IV$ $0.1$ $10.0$ Which of the two sets of buffer solutions have the least $pH$?