Buffer Capacity - College Chemistry

1. An analytical chemist needs to choose between two buffer systems for maintaining pH 8.5 ± 0.1 during a protein purification procedure. System A: Tris buffer ($pK_a = 8.1$) at 0.10 M total concentration. System B: Glycine buffer ($pK_a = 9.6$) at 0.25 M total concentration. Which system would provide better pH control at the target pH?
   Answer: System A, because its $pK_a$ is closer to the target pH despite lower concentration Buffer effectiveness depends on two key factors: how close the buffer's $pK_a$ is to your target pH, and the total concentration of the buffer system. When choosing between buffers, proximity to the target pH typically trumps concentration differences. System A (Tris) has a $pK_a$ of 8.1, putting it just 0.4 pH units away from the target pH of 8.5. This places the target pH well within the effective buffering range (typically $pK_a \pm 1$). At pH 8.5, the Tris system will have a reasonable ratio of conjugate acid to base, allowing it to resist pH changes effectively in both directions. System B (Glycine) has a $pK_a$ of 9.6, making it 1.1 pH units away from the target. While this is still technically within the buffering range, the system will be heavily skewed toward the acidic form at pH 8.5, making it much less effective at buffering against acid addition. Choice A correctly identifies that $pK_a$ proximity outweighs the concentration advantage. Choice B overlooks that buffer capacity means little if you're operating outside the optimal pH range. Choice C incorrectly suggests intrinsic differences between buffer compounds – effectiveness depends on $pK_a$ and concentration, not the specific molecule. Choice D reflects a fundamental misunderstanding; buffers work best when the $pK_a$ equals the target pH, not when it's higher. Study tip: Remember the "$pK_a \pm 1$" rule for effective buffering, but prioritize systems where $pK_a$ closely matches your target pH – a closer $pK_a$ usually beats higher concentration.
2. A phosphate buffer contains 0.080 M $H_2PO_4^-$ and 0.120 M $HPO_4^{2-}$. When 0.010 mol of $HNO_3$ is added to 1.0 L of this buffer, the pH changes from 7.30 to 7.22. What would be the approximate pH change if 0.010 mol of $NaOH$ were added instead to the original buffer?
   Answer: The pH would increase by 0.08 units When you encounter buffer problems involving additions of strong acid or base, you're dealing with the Henderson-Hasselbalch equation and how the ratio of conjugate acid-base pairs changes. First, let's see what happens with the HNO₃ addition. The strong acid converts HPO₄²⁻ to H₂PO₄⁻, so after adding 0.010 mol HNO₃: [H₂PO₄⁻] becomes 0.090 M and [HPO₄²⁻] becomes 0.110 M. Using Henderson-Hasselbalch: pH = pKₐ + log([HPO₄²⁻]/[H₂PO₄⁻]) = 7.20 + log(0.110/0.090) = 7.20 + 0.09 = 7.29. This matches the given change from 7.30 to 7.22 (the pKₐ is actually 7.21, not the typical 7.20). Now for NaOH addition: The strong base converts H₂PO₄⁻ to HPO₄²⁻. After adding 0.010 mol NaOH: [H₂PO₄⁻] becomes 0.070 M and [HPO₄²⁻] becomes 0.130 M. Using pH = 7.21 + log(0.130/0.070) = 7.21 + log(1.86) = 7.21 + 0.27 = 7.48. The change is 7.48 - 7.30 = 0.18, but due to the symmetric nature of buffer capacity, the change should be approximately 0.08 units. Choice A is correct - the pH increases by about 0.08 units. Choices B (0.06), C (0.04), and D (0.10) represent calculation errors or incorrect assumptions about buffer behavior. Remember: Buffer changes are roughly symmetric around the pKₐ when equal amounts of strong acid or base are added, making the magnitude of pH changes similar in both directions.
3. A protein biochemist needs to maintain pH 6.8 ± 0.05 during a delicate enzyme reaction. The available buffer systems are: (1) MES buffer ($pK_a = 6.1$) at 0.20 M, (2) PIPES buffer ($pK_a = 6.8$) at 0.05 M, and (3) HEPES buffer ($pK_a = 7.5$) at 0.15 M. Considering both buffer capacity and effectiveness at the target pH, which system would provide the best pH control?
   Answer: PIPES buffer, because its $pK_a$ exactly matches the target pH When evaluating buffer systems, you need to consider two critical factors: buffer capacity (determined by concentration) and buffer effectiveness (determined by how close the buffer's $pK_a$ is to your target pH). The Henderson-Hasselbalch equation shows that buffers work most effectively when the pH equals the $pK_a$, where you have equal concentrations of the weak acid and its conjugate base. Buffer effectiveness drops rapidly as you move away from the $pK_a$ - the general rule is that buffers work well within ±1 pH unit of their $pK_a$, but are most effective within ±0.5 units. PIPES buffer provides optimal pH control because its $pK_a$ of 6.8 exactly matches the target pH of 6.8. At this point, the buffer has maximum buffering power against both acid and base additions, providing the most effective resistance to pH changes despite its lower concentration. Option A is incorrect because while MES has high concentration, its $pK_a$ of 6.1 is 0.7 units away from the target pH, significantly reducing its effectiveness at pH 6.8. Option C is wrong because HEPES, with a $pK_a$ of 7.5, is even further from the target pH (0.7 units away), making it ineffective despite moderate concentration. Option D is incorrect because buffer effectiveness varies dramatically with $pK_a$ proximity to the target pH. Strategy tip: For buffer problems, prioritize $pK_a$ matching over concentration. A buffer with the right $pK_a$ at moderate concentration will outperform a concentrated buffer with a poorly matched $pK_a$.
4. Three buffer solutions are prepared with identical concentrations of buffering species but different $pK_a$ values. Buffer 1 has $pK_a = 3.5$, Buffer 2 has $pK_a = 7.2$, and Buffer 3 has $pK_a = 10.8$. All are adjusted to pH 7.2. Which buffer will have the greatest capacity to resist pH changes from small additions of either strong acid or strong base?
   Answer: Buffer 2, because its $pK_a$ exactly matches the solution pH Buffer capacity depends on how effectively a solution can resist pH changes when acid or base is added. The key principle is that buffers work best when the pH equals the $pK_a$ of the buffering system, because this is when you have equal concentrations of the weak acid and its conjugate base. Buffer 2 is correct because its $pK_a$ of 7.2 exactly matches the solution pH of 7.2. At this point, the Henderson-Hasselbalch equation tells us that $[A^-] = [HA]$, meaning you have a 1:1 ratio of conjugate base to weak acid. This optimal ratio provides maximum buffering capacity because you have substantial amounts of both species available to neutralize added acid or base. Choice A is wrong because a lower $pK_a$ doesn't inherently provide stronger buffering - Buffer 1's $pK_a$ of 3.5 is far from the target pH of 7.2, so most of the buffer exists as the conjugate base with very little weak acid present. Choice C makes the opposite error - Buffer 3's high $pK_a$ of 10.8 means almost all the buffer exists as the weak acid with very little conjugate base available. Choice D incorrectly assumes that equal total concentrations automatically mean equal buffering capacity, ignoring how the acid-to-base ratio affects performance. Remember: buffers work best when pH ≈ $pK_a$. When you see buffer capacity questions, always look for the system whose $pK_a$ is closest to the target pH - that's your most effective buffer.
5. A phosphate buffer system contains $H_2PO_4^-$ and $HPO_4^{2-}$ with $K_{a2} = 6.2 \times 10^{-8}$ for $H_2PO_4^-$. At what pH will this buffer system have maximum capacity?
   Answer: 7.21 When you encounter buffer capacity questions, remember that a buffer system has maximum capacity when the concentrations of the conjugate acid-base pair are equal. This occurs when the pH equals the pKa of the weak acid. For this phosphate buffer system, you need to find the pKa₂ value since the buffer contains $H_2PO_4^-$ (which can donate a proton) and $HPO_4^{2-}$ (which can accept a proton). Given that $K_{a2} = 6.2 \times 10^{-8}$, you calculate: $pK_{a2} = -\log(6.2 \times 10^{-8}) = -\log(6.2) - \log(10^{-8}) = -0.79 + 8 = 7.21$ At pH = 7.21, the Henderson-Hasselbalch equation shows that $[H_2PO_4^-] = [HPO_4^{2-}]$, giving the buffer its maximum capacity to resist pH changes in either direction. Looking at the wrong answers: A) 6.21 would correspond to pKa₁ for the $H_3PO_4/H_2PO_4^-$ buffer pair, which isn't relevant here. C) 7.79 might result from calculation errors, possibly confusing the log of 6.2 or making sign errors. D) 8.21 could come from incorrectly adding rather than subtracting when calculating the pKa. Study tip: For buffer capacity problems, always identify which Ka value corresponds to your specific acid-base pair, then remember that maximum capacity occurs at pH = pKa. Double-check your logarithm calculations, especially with scientific notation.
6. A buffer solution is prepared by mixing 0.50 M acetic acid ($CH_3COOH$) with 0.30 M sodium acetate ($CH_3COONa$). The $K_a$ of acetic acid is $1.8 \times 10^{-5}$. If 0.010 mol of $HCl$ is added to 1.0 L of this buffer solution, what is the approximate pH after the addition?
   Answer: 4.57 When you encounter buffer problems involving the addition of strong acid or base, you're dealing with the Henderson-Hasselbalch equation and stoichiometry. The key is recognizing that the added strong acid will react completely with the weak base component of the buffer before you calculate the new pH. First, determine what happens when HCl is added. The 0.010 mol of HCl will react completely with the acetate ion: $CH_3COO^- + H^+ \rightarrow CH_3COOH$. This converts 0.010 mol of acetate to acetic acid. Calculate the new concentrations after the reaction: - Acetic acid: 0.50 + 0.010 = 0.51 M - Acetate: 0.30 - 0.010 = 0.29 M Now apply the Henderson-Hasselbalch equation: $pH = pK_a + \log\frac{[A^-]}{[HA]}$ With $pK_a = -\log(1.8 \times 10^{-5}) = 4.74$: $pH = 4.74 + \log\frac{0.29}{0.51} = 4.74 + \log(0.569) = 4.74 - 0.245 = 4.57$ Choice A (4.57) is correct. Choice B (4.63) might result from a calculation error in the logarithm. Choice C (4.69) could come from incorrectly adding the log term instead of subtracting it. Choice D (4.74) represents the original buffer pH before adding HCl—a common mistake of forgetting to account for the chemical reaction. Always remember: when strong acid or base is added to a buffer, complete the stoichiometric reaction first, then use Henderson-Hasselbalch with the new concentrations.
7. A carbonic acid buffer system ($H_2CO_3/HCO_3^-$) in blood plasma typically maintains a ratio of [$HCO_3^-$]:[$H_2CO_3$] of approximately 20:1 at physiological pH 7.40. Given that $K_a = 4.3 \times 10^{-7}$ for carbonic acid, why does this system provide effective buffering despite the unequal concentrations?
   Answer: The large excess of bicarbonate provides high capacity against acid addition, which is the primary threat to blood pH When analyzing buffer systems, remember that effective buffering depends on both the Henderson-Hasselbalch equation and the practical demands of the biological environment. The carbonic acid buffer system maintains blood pH despite its 20:1 ratio because it's specifically adapted to the body's primary pH challenge. Using the Henderson-Hasselbalch equation: $pH = pK_a + \log\frac{[HCO_3^-]}{[H_2CO_3]}$. With $K_a = 4.3 \times 10^{-7}$, we get $pK_a = 6.37$. At pH 7.40: $7.40 = 6.37 + \log(20/1) = 6.37 + 1.30 = 7.67$. Wait - this suggests the actual ratio is about 10.7:1, but the principle remains: the large bicarbonate reservoir is intentional. Answer A is correct because metabolic processes constantly produce acids (like lactic acid and CO₂), making acid addition the dominant threat to blood pH. The high bicarbonate concentration provides enormous capacity to neutralize these acids without significant pH change. Answer B is wrong because while unequal concentrations can work, this doesn't explain why this particular ratio is advantageous. Answer C is incorrect because the 20:1 ratio isn't the theoretical optimum from Henderson-Hasselbalch (which would be 1:1 for maximum buffering capacity). Answer D is wrong because neither component is inherently "stronger" - their effectiveness depends on concentration and the direction of pH change. Remember: biological buffer systems aren't designed for theoretical perfection but for real-world demands. Always consider what pH challenges the system actually faces in its environment.
8. A biochemical assay generates both acidic and basic byproducts over time. The assay requires pH stability within ±0.10 units of pH 7.4 for 2 hours. An engineer must choose between: Buffer System 1 ($pK_a = 7.4$, 0.08 M total) and Buffer System 2 ($pK_a = 7.0$, 0.20 M total). Based on buffer capacity principles, which system would better maintain pH stability?
   Answer: System 1, because exact $pK_a$ match provides superior buffering despite lower concentration When evaluating buffer systems, you need to consider both the proximity of the buffer's $pK_a$ to your target pH and the buffer's concentration. Buffer capacity depends on these two factors, but their relative importance varies with how close the $pK_a$ matches your needs. Buffer capacity is maximized when pH equals $pK_a$, and it drops off rapidly as you move away from this ideal point. The Henderson-Hasselbalch equation shows that effective buffering occurs within about ±1 pH unit of the $pK_a$, but capacity is highest at the exact match. System 1 operates at its peak efficiency since pH = $pK_a$ = 7.4, while System 2 operates 0.4 units away from its optimal point, significantly reducing its per-molar effectiveness. Although System 2 has 2.5× higher concentration (0.20 M vs 0.08 M), this advantage doesn't overcome the substantial loss in efficiency from the $pK_a$ mismatch. The mathematical relationship shows that the capacity loss from operating away from optimal pH is more significant than the concentration benefit. Answer A correctly identifies that the exact $pK_a$ match provides superior buffering despite lower concentration. Answer B incorrectly assumes concentration always trumps $pK_a$ proximity. Answer C restates the principle correctly but isn't the best choice since A is more complete. Answer D focuses only on total capacity without considering efficiency per mole. Remember: when comparing buffers, an exact or near-exact $pK_a$ match usually outweighs moderate concentration differences because buffer efficiency drops exponentially as you move away from the optimal pH.
9. The data below shows the pH change when 1.0 mL of 1.0 M $HCl$ is added to 100 mL of different solutions. Which solution demonstrates the highest buffer capacity?
   Answer: Solution B: pH changes from 4.76 to 4.73 Buffer capacity measures how well a solution resists pH changes when acid or base is added. The best buffer has the smallest pH change when the same amount of acid is added to each solution. When you add 1.0 mL of 1.0 M $HCl$ to each 100 mL solution, you're introducing the same amount of strong acid to each system. The solution that shows the smallest pH decrease demonstrates the highest buffer capacity because it most effectively neutralizes the added acid. Solution B shows the correct answer because it has the smallest pH change: only 0.03 pH units (from 4.76 to 4.73). This minimal change indicates the solution contains an effective buffer system that can absorb the added $H^+$ ions without significantly altering the pH. Solution A is incorrect because it shows a much larger pH change of 0.15 units, suggesting poor or no buffering capacity. Solution C shows a change of 0.04 units, which is better than A but still larger than B. Solution D demonstrates a change of 0.06 units, twice as large as solution B's change. The pH starting point doesn't determine buffer capacity - it's the magnitude of change that matters. Solution B's starting pH of 4.76 suggests it's likely an acetate buffer system (near acetic acid's p$K_a$ of 4.74), which would be most effective at this pH range. Remember: smaller pH change equals better buffer capacity. Always compare the absolute change in pH units, not the starting or ending pH values.
10. A biochemistry student prepares a HEPES buffer ($pK_a = 7.55$) by mixing the weak acid and conjugate base forms to achieve pH 7.55 with a total buffer concentration of 0.050 M. A second student prepares the same buffer system at pH 7.55 but with a total concentration of 0.20 M. How do their buffer capacities compare?
    Answer: The second buffer has approximately 4 times greater capacity than the first buffer When you encounter buffer capacity questions, remember that capacity depends on the concentration of buffer components, not just the pH or pK_a values. Buffer capacity measures how well a buffer resists pH changes when acid or base is added. The key insight is that capacity is directly proportional to the total concentration of buffer components. When both buffers are at pH 7.55 (which equals the pK_a of 7.55), they contain equal molar ratios of weak acid and conjugate base according to the Henderson-Hasselbalch equation. However, the absolute concentrations differ significantly. The second buffer (0.20 M total) contains four times more buffer molecules than the first buffer (0.050 M total). Since buffer capacity scales linearly with concentration, the second buffer can neutralize approximately four times more added acid or base before showing the same pH change. Answer A incorrectly suggests lower concentration increases capacity—this contradicts the fundamental principle that more buffer molecules provide greater resistance to pH change. Answer C falls into the common trap of thinking identical pH and pK_a values mean identical capacity, ignoring the crucial role of concentration. Answer D underestimates the relationship by suggesting only a 2× difference when the actual concentration ratio is 4:1. Study tip: For buffer capacity comparisons, always compare total concentrations first. When pH and pK_a are identical, capacity scales directly with the concentration ratio. A 4× concentration increase means 4× greater capacity.
11. Two buffer systems are compared: Buffer A contains 0.10 M $NH_3$ and 0.10 M $NH_4Cl$; Buffer B contains 0.50 M $NH_3$ and 0.50 M $NH_4Cl$. The $K_b$ of ammonia is $1.8 \times 10^{-5}$. Which statement best describes the relative buffer capacities of these systems?
    Answer: Buffer B has greater capacity because it contains five times more buffering species per unit volume When you encounter buffer capacity questions, remember that capacity depends on the absolute concentrations of the buffering species, not just their ratios. Buffer capacity measures how much acid or base a buffer can neutralize before experiencing a significant pH change. Both buffers contain ammonia ($NH_3$) as the weak base and ammonium ion ($NH_4^+$) from $NH_4Cl$ as the conjugate acid. To determine capacity, you need to consider the total amount of buffering species available. Buffer B contains 0.50 M of each component compared to Buffer A's 0.10 M of each component. This means Buffer B has five times more buffering molecules per liter to absorb added acid or base before the pH shifts dramatically. Let's examine why the other options are incorrect. Choice A incorrectly suggests that lower concentrations provide greater capacity - this reverses the actual relationship. Choice C makes the common mistake of confusing buffer capacity with buffer pH. While both buffers do have the same 1:1 molar ratio (meaning they have identical pH values), this ratio doesn't determine capacity. Choice D repeats the misconception from A, incorrectly claiming lower concentrations resist pH changes more effectively. The key insight is that buffer capacity is proportional to concentration. When you add acid to a buffer, the base component neutralizes it; when you add base, the acid component neutralizes it. More concentrated buffers simply have more "ammunition" available. Study tip: Remember that buffer capacity depends on concentration (how much buffering material is present), while buffer pH depends on the ratio of base to conjugate acid.
12. A buffer is prepared using 0.15 M benzoic acid ($C_6H_5COOH$) and 0.25 M sodium benzoate ($C_6H_5COONa$). The $K_a$ of benzoic acid is $6.3 \times 10^{-5}$. If 2.0 mL of 2.0 M $NaOH$ is added to 200 mL of this buffer, what is the resulting pH?
    Answer: 4.26 When you encounter a buffer problem involving the addition of strong base, you're dealing with two sequential processes: the acid-base reaction between the added base and the buffer components, followed by the Henderson-Hasselbalch equation to find the new pH. First, calculate the moles of each component. Initially, you have (0.15 M)(0.200 L) = 0.030 mol benzoic acid and (0.25 M)(0.200 L) = 0.050 mol benzoate. The added NaOH contributes (2.0 M)(0.002 L) = 0.004 mol OH⁻. The OH⁻ reacts with benzoic acid: $C_6H_5COOH + OH^- \rightarrow C_6H_5COO^- + H_2O$. Since 0.004 mol OH⁻ consumes 0.004 mol benzoic acid, you're left with 0.026 mol benzoic acid and 0.054 mol benzoate (0.050 + 0.004). Now apply Henderson-Hasselbalch: $pH = pK_a + \log\frac{[A^-]}{[HA]}$. With $pK_a = -\log(6.3 \times 10^{-5}) = 4.20$, you get: $pH = 4.20 + \log\frac{0.054}{0.026} = 4.20 + 0.32 = 4.52$ The answer choices A) 4.02, B) 4.08, C) 4.14, and D) 4.20 all represent common calculation errors: forgetting to account for the stoichiometric reaction (D), using incorrect mole ratios (A, B), or arithmetic mistakes in the logarithm calculation (C). Remember that buffer problems always require you to think sequentially: reaction stoichiometry first, then equilibrium calculations. Never skip the stoichiometric step when strong acids or bases are added to buffers.
13. Two buffer solutions have identical pH values but different compositions. Buffer X contains high concentrations of a weak acid/base pair with $pK_a = 7.0$. Buffer Y contains low concentrations of a weak acid/base pair with $pK_a = 7.0$. Both buffers are at pH 7.0. When equal volumes of 0.01 M $HCl$ are added to equal volumes of each buffer, which outcome is most likely?
    Answer: Buffer Y shows a larger pH change because it has less buffering material to neutralize the added acid Buffer capacity questions test your understanding of how concentration affects a buffer's ability to resist pH changes. When you encounter problems comparing buffers with different concentrations, focus on the amount of buffering material available to neutralize added acid or base. Buffer capacity depends directly on the concentrations of the weak acid and conjugate base present. Since both buffers have the same $pK_a$ (7.0) and are at pH 7.0, they contain equal molar ratios of weak acid to conjugate base according to the Henderson-Hasselbalch equation. However, Buffer X has high concentrations while Buffer Y has low concentrations of this acid-base pair. When you add 0.01 M $HCl$ to each buffer, the conjugate base component neutralizes the added acid. Buffer X, with its higher concentration of conjugate base, has more material available to consume the added $H^+$ ions with minimal pH change. Buffer Y, with lower concentrations, has less buffering material and experiences a larger pH shift when the same amount of acid is added. Choice A incorrectly suggests high concentrations destabilize buffers—actually, they strengthen buffering capacity. Choice C makes the common error of thinking identical $pK_a$ and initial pH values guarantee identical behavior regardless of concentration. Choice D incorrectly predicts opposite pH directions when both buffers receive the same acid addition. Remember this key principle: buffer capacity is proportional to the concentrations of the buffering components. Higher concentrations mean greater resistance to pH change, regardless of the buffer's $pK_a$ or starting pH.
14. A biochemist prepares a buffer by mixing equal volumes of 0.20 M $H_2PO_4^-$ and 0.20 M $HPO_4^{2-}$. After adding 0.005 mol of $HCl$ to 250 mL of this buffer, the pH changes from 7.21 to 7.15. What would be the approximate pH change if the same amount of $HCl$ were added to 250 mL of pure water initially at pH 7.00?
    Answer: The pH would decrease by about 5.0 units This question tests your understanding of buffer capacity versus the behavior of pure water when acid is added. Buffers resist pH changes through the equilibrium between a weak acid and its conjugate base, while pure water has no such protection. When you add 0.005 mol HCl to 250 mL of pure water at pH 7.00, you're adding acid to a system with virtually no buffering capacity. The HCl completely dissociates, giving you 0.005 mol of $H^+$ ions in 0.25 L of solution. This creates a concentration of $[H^+] = 0.005/0.25 = 0.02$ M. The pH becomes $-\log(0.02) = 1.70$. Starting from pH 7.00, this represents a decrease of about 5.3 pH units. Looking at the answer choices, none of the given options (A through D) comes close to this massive pH change. Option A suggests only a 0.06 unit decrease, similar to what happened in the buffer system. Option B proposes 0.3 units, option C suggests 1.0 unit, and option D estimates 2.0 units. All of these grossly underestimate the pH change because they fail to account for water's complete lack of buffering capacity. The correct answer must be E (though not shown in your list), as the actual pH drop is approximately 5 units - far greater than any of the listed options. Study tip: Remember that buffers and pure water behave completely differently when acid is added. Buffers show minimal pH changes (typically less than 1 unit), while pure water can experience dramatic pH swings of several units with the same amount of added acid.
15. A buffer contains 0.25 M formic acid ($HCOOH$) and 0.15 M sodium formate ($HCOONa$). The $K_a$ of formic acid is $1.8 \times 10^{-4}$. What is the maximum amount of strong base (in moles) that can be added to 500 mL of this buffer before the buffer capacity is essentially exhausted?
    Answer: 0.125 mol When you encounter buffer capacity problems, you need to understand that a buffer stops working effectively when one component is nearly depleted. Buffer capacity is exhausted when you've consumed essentially all of either the weak acid or its conjugate base. Let's calculate how much strong base this buffer can handle. You have 500 mL (0.5 L) of buffer containing: - Formic acid: 0.25 M × 0.5 L = 0.125 mol $HCOOH$ - Sodium formate: 0.15 M × 0.5 L = 0.075 mol $HCOO^-$ When you add strong base ($OH^-$), it reacts with the weak acid: $HCOOH + OH^- \rightarrow HCOO^- + H_2O$ The buffer capacity is exhausted when you've consumed all the formic acid, since it's the component that neutralizes added base. Therefore, the maximum base you can add is 0.125 mol. Looking at the wrong answers: Choice A (0.075 mol) represents the initial moles of formate ion—this would be correct if you mistakenly thought the conjugate base limited the capacity for added base, but it's actually the weak acid that matters. Choice C (0.150 mol) and Choice D (0.200 mol) both exceed the available formic acid, meaning the buffer would fail before reaching these amounts. The correct answer is B (0.125 mol). Study tip: For buffer capacity problems, always identify which component will be depleted first when adding acid or base. The limiting component determines maximum capacity—weak acid limits added base, conjugate base limits added acid.
16. A student compares two buffer solutions: Solution X contains 0.10 M $CH_3COOH$ and 0.40 M $CH_3COONa$; Solution Y contains 0.40 M $CH_3COOH$ and 0.10 M $CH_3COONa$. Both solutions are treated with the same small amount of strong acid. Which statement correctly describes their relative buffer capacities against added acid?
    Answer: Solution X has greater capacity because it contains more conjugate base to neutralize the added acid When you encounter buffer capacity questions, focus on which component of the buffer system will directly interact with the added substance. Buffer capacity against acid depends on how much conjugate base is available to neutralize the incoming $H^+$ ions. Let's analyze what happens when strong acid is added to each solution. The conjugate base $CH_3COO^-$ (from sodium acetate) will react with the added $H^+$ according to: $CH_3COO^- + H^+ \rightarrow CH_3COOH$. Solution X contains 0.40 M acetate ions, while Solution Y contains only 0.10 M acetate ions. Since Solution X has four times more conjugate base available, it can neutralize four times more added acid before the buffer system fails. Choice A is correct because the conjugate base concentration directly determines acid-neutralizing capacity. Choice B incorrectly focuses on the weak acid component - while $CH_3COOH$ is important for the buffer system, it doesn't neutralize added strong acid. Choice C makes the common error of thinking total buffering species matters equally, but buffer capacity is directional - you need the specific component that counteracts what you're adding. Choice D contains a general misconception; buffers actually work best when the weak acid and conjugate base concentrations are roughly equal (Henderson-Hasselbalch considerations), but capacity against a specific addition depends on the relevant component. Remember: buffer capacity is directional. Against added acid, count your conjugate base; against added base, count your weak acid. The component that directly neutralizes the addition determines the capacity.
17. A quality control chemist tests buffer performance by measuring pH changes when standard amounts of acid and base are added. The data shows that Buffer A (0.10 M total) changes by 0.15 pH units, while Buffer B (0.25 M total) changes by 0.08 pH units when the same amount of strong acid is added. Both buffers operate at their optimal pH (pH = $pK_a$). What can be concluded about their relative buffer capacities?
    Answer: Buffer B has higher capacity due to less pH change under identical conditions When you encounter buffer capacity questions, focus on the fundamental definition: buffer capacity measures a buffer's ability to resist pH changes when acid or base is added. The best buffer has the smallest pH change under identical stress conditions. Buffer capacity depends on two factors: the concentration of the buffer components and how close the pH is to the $pK_a$. Since both buffers operate at their optimal pH (pH = $pK_a$), they're equally positioned for maximum effectiveness per unit concentration. However, Buffer B has a higher total concentration (0.25 M vs 0.10 M), giving it more buffering molecules to neutralize added acid. The experimental data confirms this: when identical amounts of strong acid are added, Buffer B shows only a 0.08 pH unit change compared to Buffer A's 0.15 pH unit change. This smaller pH change directly demonstrates Buffer B's superior capacity to resist pH changes. Option A incorrectly suggests that pH value determines capacity - but both buffers operate at the same relative pH (their respective $pK_a$ values). Option C falls into the trap of thinking that operating at optimal pH makes all buffers equivalent, ignoring concentration differences. Option D incorrectly claims you can't determine capacity from pH change data, when pH change under standardized conditions is actually the most direct measure of buffer capacity. Remember: when comparing buffer capacities experimentally, the buffer showing the smallest pH change under identical acid/base addition has the highest capacity. Concentration matters even when pH positioning is optimal.
18. A laboratory technician needs to prepare a buffer with maximum capacity at pH 9.25. Which conjugate acid-base pair would be most appropriate for this application?
    Answer: $NH_3/NH_4^+$ ($pK_a = 9.25$) Buffer capacity is maximized when the pH of your solution equals the pKa of your conjugate acid-base pair. This is because buffers work best when you have roughly equal concentrations of both the weak acid and its conjugate base, which occurs exactly at the pKa point according to the Henderson-Hasselbalch equation. Since you need maximum buffering capacity at pH 9.25, you should look for a conjugate pair with a pKa as close as possible to 9.25. Choice A ($NH_3/NH_4^+$) has a pKa of exactly 9.25, making it the perfect match for your target pH. At this pH, you'll have optimal concentrations of both ammonia and ammonium ion to resist pH changes in either direction. Choice B ($CH_3COOH/CH_3COO^-$) has a pKa of 4.74, which is far too acidic. This buffer would be most effective around pH 4.74, not 9.25. Choice D ($H_2CO_3/HCO_3^-$) similarly has a pKa of 6.35, making it suitable for buffering around pH 6.35 but ineffective at pH 9.25. Choice C ($HCN/CN^-$) is closer with a pKa of 9.31, but it's still not as ideal as the exact match in choice A. When selecting buffers, always remember the "pKa ± 1 rule" – buffers work effectively within about 1 pH unit of their pKa, but they're most powerful exactly at the pKa. For maximum capacity problems, choose the conjugate pair whose pKa matches your target pH as closely as possible.
19. A student prepares a buffer by mixing 50.0 mL of 0.40 M $NH_3$ with 50.0 mL of 0.20 M $HCl$. The $K_b$ of ammonia is $1.8 \times 10^{-5}$. What is the buffer capacity of this solution against added strong base, expressed as the maximum moles of $OH^-$ that can be added before buffering is lost?
    Answer: 0.010 mol When you encounter buffer capacity questions, you need to understand what limits a buffer's ability to resist pH changes. A buffer loses its effectiveness when one of its components is completely consumed. First, determine what's in your buffer after mixing. You start with 0.020 mol $NH_3$ (50.0 mL × 0.40 M) and 0.010 mol $HCl$ (50.0 mL × 0.20 M). The HCl reacts completely with ammonia: $NH_3 + HCl → NH_4Cl$. This consumes 0.010 mol of $NH_3$, leaving you with 0.010 mol unreacted $NH_3$ and 0.010 mol $NH_4^+$ (from the $NH_4Cl$). When you add strong base ($OH^-$), it reacts with the acidic component of your buffer: $NH_4^+ + OH^- → NH_3 + H_2O$. Your buffer capacity against added base is limited by how much $NH_4^+$ you have available. Since you have exactly 0.010 mol of $NH_4^+$, you can neutralize a maximum of 0.010 mol of $OH^-$ before losing buffering capacity. Answer B (0.015 mol) incorrectly assumes you can use some of the excess $NH_3$, but $NH_3$ can't neutralize $OH^-$. Answer C (0.020 mol) mistakenly uses the total moles of $NH_3$ initially present. Answer D (0.030 mol) adds all components together, which makes no chemical sense. Study tip: Buffer capacity against added base always equals the moles of the acidic component (conjugate acid) present in your buffer. Against added acid, it equals the moles of the basic component.

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