Acid–Base Titrations - College Chemistry

Which indicator would be most appropriate for the titration of a weak acid ( $K_a = 2.0 \times 10^{-5}$ ) with a strong base, given that the equivalence point pH is approximately 8.7?
Answer: Phenolphthalein (transition range: pH 8.2-10.0) for its alkaline transition range. When selecting an indicator for acid-base titrations, you need to match the indicator's transition range with the equivalence point pH. The key principle is that the indicator should change color at approximately the same pH where equivalence occurs. For a weak acid-strong base titration, the equivalence point is always basic (pH > 7) because the conjugate base of the weak acid hydrolyzes water, producing OH⁻ ions. With an equivalence point pH of 8.7, you need an indicator that transitions in the basic range. Phenolphthalein (option C) is perfect here because its transition range of pH 8.2-10.0 encompasses the equivalence point at pH 8.7. The indicator will change color right around the equivalence point, giving you a sharp, accurate endpoint. Option A (methyl orange) transitions far too early at pH 3.1-4.4, well before reaching equivalence. You'd get a false endpoint in the acidic region. Option B (bromothymol blue) changes color in the neutral range (pH 6.0-7.6), which occurs before the actual equivalence point at pH 8.7, again giving a premature endpoint. Option D (methyl red) also transitions too early at pH 4.8-6.0, despite the mention of "weak acid systems" - the transition range, not the acid type, determines suitability. Study tip: For weak acid-strong base titrations, always choose indicators that transition in the basic range (pH > 7). Phenolphthalein is typically your best choice for these titrations, while methyl orange works best for strong acid-weak base titrations where the equivalence point is acidic.
A laboratory technician prepares a standardized NaOH solution and finds that 23.7 mL of this NaOH solution neutralizes 1.25 g of potassium hydrogen phthalate (KHP, molar mass = 204.2 g/mol). What is the molarity of the NaOH solution?
Answer: 0.259 M When you see a standardization problem involving acid-base neutralization, you're working with stoichiometry and molarity calculations. The key is recognizing that KHP (potassium hydrogen phthalate) is a monoprotic acid that reacts 1:1 with NaOH. Start by finding the moles of KHP: $\text{moles KHP} = \frac{1.25 \text{ g}}{204.2 \text{ g/mol}} = 0.00612 \text{ mol}$ Since the reaction is KHP + NaOH → NaKP + H₂O, the molar ratio is 1:1, so 0.00612 mol of NaOH was used. Now calculate molarity: $\text{Molarity} = \frac{0.00612 \text{ mol}}{0.0237 \text{ L}} = 0.258 \text{ M}$ Rounding to three significant figures gives 0.259 M, which is answer B. Looking at the wrong answers: A) 0.204 M results from using the mass of KHP (1.25) directly divided by the volume in mL (23.7) without proper unit conversion or molar mass consideration. C) 0.315 M likely comes from an error in the molar mass calculation or volume conversion. D) 0.421 M suggests a significant calculation error, possibly confusing the stoichiometry or making multiple unit conversion mistakes. Remember that standardization problems always follow the same pattern: convert mass to moles using molar mass, use stoichiometry to find moles of the unknown solution, then divide by volume in liters to get molarity. Always check that your units cancel properly and that you're using the correct molar ratios from the balanced equation.
During the titration of a weak acid with a strong base, which statement best describes the region before the equivalence point?
Answer: The solution contains a buffer system of the weak acid and its conjugate base formed from neutralization. When analyzing weak acid-strong base titrations, focus on what chemical species are present in solution at different stages and how they interact. Before the equivalence point, you've added some strong base, but not enough to neutralize all the weak acid. This creates a crucial situation: the added $OH^-$ ions react with the weak acid ( $HA$ ) to form its conjugate base ( $A^-$ ) and water. So you now have both unreacted weak acid and newly formed conjugate base coexisting in solution - this is the definition of a buffer system. Answer B correctly identifies this buffer composition. The weak acid and its conjugate base work together to resist dramatic pH changes as you continue adding base, though the pH does gradually increase. Answer A misses the key point that base addition creates the conjugate base species. You're no longer dealing with just weak acid equilibrium - the neutralization reaction has introduced a second component. Answer C contains a common misconception. While the solution does have buffer capacity, the pH doesn't remain constant. Buffers resist pH change but don't prevent it entirely. The pH gradually increases throughout this region. Answer D incorrectly suggests complete neutralization is occurring. In reality, weak acids don't behave like strong acids even when partially neutralized. The system maintains its weak acid character through the buffer equilibrium. Study tip: Remember the sequence - titration creates the buffer before destroying it. Before equivalence = buffer zone (weak acid + conjugate base). At equivalence = salt solution. This pattern appears frequently on chemistry exams.
A titration requires 18.6 mL of 0.0985 M Ba(OH)₂ to neutralize 25.0 mL of HCl solution. What is the molarity of the HCl solution?
Answer: 0.147 M Acid-base titrations involve determining the concentration of an unknown solution by reacting it with a known solution. The key insight here is recognizing that Ba(OH)₂ is a diprotic base, meaning each molecule provides two OH⁻ ions that can neutralize acid. Start with the balanced chemical equation: $\text{Ba(OH)}_2 + 2\text{HCl} \rightarrow \text{BaCl}_2 + 2\text{H}_2\text{O}$ . Notice the 1:2 molar ratio—one mole of Ba(OH)₂ neutralizes two moles of HCl. First, calculate moles of Ba(OH)₂: $0.0186 \text{ L} \times 0.0985 \text{ M} = 0.00183 \text{ mol Ba(OH)}_2$ Using stoichiometry, find moles of HCl: $0.00183 \text{ mol Ba(OH)}_2 \times \frac{2 \text{ mol HCl}}{1 \text{ mol Ba(OH)}_2} = 0.00366 \text{ mol HCl}$ Finally, calculate HCl molarity: $\frac{0.00366 \text{ mol}}{0.0250 \text{ L}} = 0.147 \text{ M}$ Choice A (0.0733 M) results from forgetting the 1:2 stoichiometry and treating Ba(OH)₂ as monoprotic. Choice C (0.184 M) comes from calculation errors, likely in unit conversion. Choice D (0.294 M) suggests using incorrect volume relationships or mathematical mistakes in the stoichiometric conversion. Remember that polyprotic acids and bases always require careful attention to stoichiometry. Count the number of H⁺ or OH⁻ ions each molecule provides, write the balanced equation, and use those coefficients as conversion factors. Many titration errors stem from ignoring this crucial stoichiometric relationship.
A titration curve shows the following data points: at 0 mL titrant added, pH = 11.8; at 20.0 mL titrant added, pH = 9.3; at 40.0 mL titrant added, pH = 2.1. This curve is most consistent with:
Answer: Weak base being titrated with strong acid, showing buffer region then sharp drop. When analyzing titration curves, you need to identify both the starting pH and the pattern of pH change to determine what's being titrated with what. The key clues are the initial pH (which tells you about the analyte) and how the pH changes as titrant is added. The starting pH of 11.8 indicates a basic solution, so we're titrating either a strong or weak base. The dramatic pH drop from 9.3 to 2.1 between 20.0 and 40.0 mL suggests we've hit the equivalence point, where the titrant (an acid) has neutralized the base. The final pH of 2.1 is quite acidic, confirming the titrant is a strong acid. The moderate pH drop from 11.8 to 9.3 in the first 20 mL indicates buffering behavior - the weak base and its conjugate acid are resisting pH change. This is characteristic of a weak base being titrated. Answer D correctly identifies this as a weak base titrated with strong acid, showing the expected buffer region followed by a sharp pH drop at equivalence. Answer A is wrong because we start basic (pH 11.8), not acidic. Answer B is incorrect because we begin with a base, not an acid - the high starting pH rules this out. Answer C suggests a strong base, but a strong base would start at a higher pH (closer to 13-14) and wouldn't show the gradual buffering behavior seen in the first portion. Remember: always check the starting pH first to identify your analyte, then look for buffering behavior to distinguish strong from weak species.
When phenolphthalein indicator is added to the titration of a strong acid with a strong base, the endpoint occurs at approximately pH 8.7, while the true equivalence point is at pH 7.0. This discrepancy represents:
Answer: A negligible difference because the steep titration curve means very little extra base was added. When evaluating indicator endpoints in acid-base titrations, you need to understand the relationship between the titration curve's steepness and the practical impact of small pH differences. In a strong acid-strong base titration, the equivalence point occurs at pH 7.0, but the titration curve is extremely steep in this region. This means that adding just a few drops of titrant causes a dramatic pH change—often jumping from around pH 4 to pH 10 within 0.1 mL of base addition. Phenolphthalein changes color around pH 8.7, which falls within this steep region. The correct answer is B because the steep titration curve means that reaching pH 8.7 instead of pH 7.0 requires only a tiny additional volume of titrant—typically less than one drop. This minimal volume difference translates to a negligible error in your concentration calculations, usually less than 0.1%. Answer A is incorrect because systematic errors that "significantly affect" calculations would involve much larger volume discrepancies than what occurs here. Answer C misunderstands the situation—both the acid and base are indeed strong electrolytes; the steep curve actually confirms this. The gradual transitions seen with weak electrolytes would make indicator choice much more critical. Answer D incorrectly assumes there's a problem with the indicator itself. Phenolphthalein is functioning exactly as expected; its transition range simply doesn't coincide perfectly with the equivalence point. Remember: In strong acid-strong base titrations, indicator choice is forgiving because the steep curve minimizes endpoint errors. Focus on choosing indicators whose transition ranges fall anywhere within the steep portion of the curve.
During a weak acid-strong base titration, a student observes that the pH changes from 4.5 to 4.7 when 5.0 mL of base is added, but changes from 8.2 to 11.8 when the next 0.5 mL is added. This observation indicates:
Answer: The first addition occurred in the buffer region, while the second occurred past the equivalence point. When you encounter a weak acid-strong base titration question with dramatic pH changes, focus on identifying which regions of the titration curve you're observing. The key is recognizing that different parts of the curve show vastly different rates of pH change. The first observation—pH changing only 0.2 units (4.5 to 4.7) with 5.0 mL of base—indicates you're in the buffer region. Here, the weak acid and its conjugate base are both present in significant amounts, creating a buffer system that resists pH changes. This is why adding a relatively large volume of base produces only a small pH change. The second observation—pH jumping 3.6 units (8.2 to 11.8) with just 0.5 mL of base—signals you've passed the equivalence point. At the equivalence point, all the weak acid has been neutralized, and the buffer capacity is exhausted. Any additional strong base dramatically increases the pH because there's nothing left to neutralize it. Answer A correctly identifies both regions. Answer B is wrong because strong buffering would mean small pH changes, not the large 3.6-unit jump observed in the second addition. Answer C is incorrect because the second addition occurs past the equivalence point, not at it—the equivalence point for a weak acid-strong base titration typically has a pH around 8-9, and we've clearly moved beyond that. Answer D is wrong because dramatic pH changes near the equivalence point are completely normal and expected in titrations. Study tip: Memorize the titration curve shape—gentle slopes indicate buffering regions, while steep slopes indicate equivalence point areas where small additions cause large pH changes.
In the titration of 40.0 mL of 0.100 M acetic acid with 0.100 M NaOH, what volume of NaOH is required to reach the equivalence point?
Answer: 40.0 mL When you encounter titration problems, you're looking for the point where moles of acid equal moles of base - this is the equivalence point for a monoprotic acid like acetic acid. To find the equivalence point, start by calculating moles of acetic acid: $\text{moles} = M \times V = 0.100 \text{ M} \times 0.0400 \text{ L} = 0.00400 \text{ mol}$ Since acetic acid (CH₃COOH) is monoprotic, it donates one proton per molecule, and NaOH accepts one proton per molecule. This creates a 1:1 molar ratio, meaning you need exactly 0.00400 mol of NaOH to neutralize the acid. Now calculate the volume of NaOH needed: $V = \frac{\text{moles}}{M} = \frac{0.00400 \text{ mol}}{0.100 \text{ M}} = 0.0400 \text{ L} = 40.0 \text{ mL}$ This confirms answer C is correct. Answer A (20.0 mL) represents a common error where students might divide the acid volume by 2, perhaps confusing this with a diprotic acid scenario. Answer B (30.0 mL) doesn't correspond to any logical calculation for this problem. Answer D (50.0 mL) might result from incorrectly adding the volumes or miscalculating the molar relationship. Remember this key pattern: for monoprotic acid-monobasic base titrations with equal concentrations, the volumes at the equivalence point will be equal. When concentrations differ, use the relationship $M_1V_1 = M_2V_2$ where the moles of acid equal moles of base.
In the titration of a polyprotic acid, the first equivalence point occurs at 15.8 mL and the second at 31.6 mL of added base. If the volume ratio is exactly 2:1, this suggests:
Answer: The acid has two protons with significantly different $K_a$ values allowing separate detection. When you encounter polyprotic acid titrations, focus on what the volume pattern tells you about the acid's structure and ionization behavior. The 2:1 volume ratio (31.6 mL : 15.8 mL) is the key insight here. This exact doubling occurs because the acid releases its protons sequentially in two distinct, separate steps. The first equivalence point represents complete removal of the first proton from all acid molecules, while the second equivalence point represents removal of the second proton. Since equal volumes of base are needed for each step, the acid must be diprotic with each proton requiring the same amount of base to neutralize. This pattern only emerges when the two $K_a$ values are sufficiently different—typically differing by at least a factor of 10⁴. This large difference allows you to see two distinct equivalence points rather than one broad, poorly-defined endpoint. Answer B correctly identifies this scenario. Answer A is wrong because identical $K_a$ values would produce a single, broad equivalence point, not two distinct ones. Answer C incorrectly suggests a mixture of monoprotic acids, but this would require additional information about their relative concentrations to predict the volume ratio. Answer D misinterprets the clear 2:1 pattern as experimental error, when this precise ratio actually indicates excellent experimental technique revealing the acid's true diprotic nature. Study tip: In polyprotic titrations, a clean 2:1 volume ratio always signals a diprotic acid with well-separated $K_a$ values. Look for this pattern to distinguish true diprotic acids from mixtures or experimental problems.
During the titration of formic acid (HCHO₂, $K_a = 1.8 \times 10^{-4}$ ) with NaOH, the pH at the half-equivalence point is:
Answer: 3.74 When you encounter a titration question asking for pH at the half-equivalence point, you're dealing with a buffer system where the weak acid and its conjugate base are present in equal concentrations. At the half-equivalence point of any weak acid titration, exactly half of the original acid has been converted to its conjugate base. For formic acid (HCHO₂) being titrated with NaOH, half has been converted to formate ion (CHO₂⁻). This creates a buffer where [HCHO₂] = [CHO₂⁻]. Using the Henderson-Hasselbalch equation: $pH = pK_a + \log\frac{[A^-]}{[HA]}$ Since the concentrations are equal, $\frac{[CHO₂^-]}{[HCHO₂]} = 1$ , and $\log(1) = 0$ . Therefore: $pH = pK_a$ First, calculate $pK_a$ : $pK_a = -\log(1.8 \times 10^{-4}) = 3.74$ So the pH at the half-equivalence point is 3.74, confirming answer B. Looking at the wrong answers: A) 2.87 might result from incorrectly calculating $pK_a$ or confusing it with the initial pH of the acid solution. C) 7.00 represents the pH of pure water, which would only occur at the equivalence point of a strong acid-strong base titration, not here. D) 10.26 could result from mistakenly calculating $pK_b$ of the conjugate base instead of using $pK_a$ . Key takeaway: At the half-equivalence point of any weak acid titration, $pH = pK_a$ . This is a direct relationship that eliminates the need for complex equilibrium calculations.
A titration curve shows a sharp pH change from 4.0 to 10.0 when only 0.1 mL of titrant is added near the equivalence point. This observation is most consistent with which type of titration?
Answer: Strong acid titrated with strong base, showing complete neutralization behavior. When analyzing titration curves, the sharpness of the pH change at the equivalence point reveals crucial information about the acid-base strength combination. A dramatic pH jump from 4.0 to 10.0 with just 0.1 mL of titrant indicates an extremely sharp transition, which is the hallmark of strong acid-strong base titrations. In strong acid-strong base titrations, both species completely ionize, creating a situation where you rapidly transition from excess $H^+$ ions to excess $OH^-$ ions with minimal buffering near the equivalence point. This produces the characteristic steep, nearly vertical section of the titration curve. The correct answer is A because this sharp 6-unit pH change with such a small volume addition is exactly what you'd expect from complete neutralization between strong electrolytes. Option B is incorrect because weak acid-strong base titrations show more gradual transitions due to the buffer region created by the weak acid and its conjugate base. While there is a pH jump at equivalence, it's less dramatic than what's described. Option C is wrong because weak acid-weak base combinations produce very gradual pH changes throughout the entire titration, lacking any sharp transitions. Option D misses the mark because polyprotic acids would show multiple, separate equivalence points spread across different pH ranges, not a single sharp jump. Remember this pattern: the sharper and more dramatic the pH change at equivalence, the stronger both the acid and base involved. Strong-strong combinations always produce the steepest curves, while any weak component creates buffering that softens the transition.
A titration curve shows that the equivalence point occurs at pH 7.8 when 28.4 mL of 0.125 M NaOH neutralizes 35.0 mL of an unknown acid. The fact that the equivalence point pH is above 7.0 indicates:
Answer: The unknown acid is a weak acid whose conjugate base hydrolyzes to produce OH⁻ ions. When you encounter titration problems where the equivalence point pH differs from 7.0, think about the nature of the acid and base involved. The key insight is that only strong acid-strong base titrations have equivalence points at exactly pH 7.0. Let's analyze what's happening here. At the equivalence point, all the acid has been neutralized, but the pH is 7.8 (basic). This occurs because we have a weak acid being titrated with a strong base (NaOH). When a weak acid is completely neutralized, its conjugate base remains in solution. This conjugate base is itself a weak base that hydrolyzes water: $A^- + H_2O \rightleftharpoons HA + OH^-$ . The production of hydroxide ions makes the solution basic at the equivalence point. Answer A is incorrect because over-titration would push the pH much higher than 7.8, and we're told this is the equivalence point, not a point beyond it. Answer C misses the fundamental chemistry - even if the NaOH concentration were different, it would change the volume needed to reach equivalence, not the pH at equivalence. Answer D reflects a common misconception; only strong acid-strong base titrations have equivalence points at pH 7.0. The correct answer is B because the weak acid's conjugate base hydrolyzes to produce OH⁻ ions, creating the basic equivalence point. Study tip: Remember the equivalence point pH pattern: strong acid + strong base = pH 7.0; weak acid + strong base = pH > 7.0; strong acid + weak base = pH < 7.0. The "leftover" ion (conjugate base or acid) determines the pH.
A student performs a titration and observes that 22.4 mL of 0.150 M NaOH is required to neutralize 25.0 mL of an unknown monoprotic acid solution. What is the molarity of the unknown acid?
Answer: 0.134 M Acid-base titration problems test your understanding of stoichiometry and the principle that at the equivalence point, moles of acid equal moles of base (for monoprotic acids). When you see a titration question, identify what's given and use the relationship $M_1V_1 = M_2V_2$ where the moles of acid equal the moles of base. Here's the step-by-step solution: First, calculate the moles of NaOH used: $\text{moles NaOH} = 0.150 \text{ M} \times 0.0224 \text{ L} = 0.00336 \text{ mol}$ Since the acid is monoprotic, it donates one proton per molecule, so at neutralization, moles of acid = moles of base = 0.00336 mol. Now find the molarity of the acid: $\text{Molarity of acid} = \frac{0.00336 \text{ mol}}{0.0250 \text{ L}} = 0.134 \text{ M}$ This confirms answer A) 0.134 M is correct. Looking at the wrong answers: B) 0.150 M incorrectly assumes the acid and base have the same molarity, ignoring the different volumes used. C) 0.168 M results from incorrectly calculating $\frac{0.150 \times 25.0}{22.4}$ , which reverses the volume relationship. D) 0.179 M comes from calculation errors or incorrect unit conversions. Study tip: Always convert mL to L, calculate moles of the known solution first, then use stoichiometry to find moles of the unknown. For monoprotic acids with strong bases, the mole ratio is always 1:1 at the equivalence point.
Which statement best explains why the equivalence point of a weak base-strong acid titration occurs at a pH below 7?
Answer: The conjugate acid of the weak base undergoes hydrolysis, producing H₃O⁺ ions in solution. When you encounter titration questions involving weak bases and strong acids, focus on what happens to the salt formed at the equivalence point and how it affects solution pH. At the equivalence point of a weak base-strong acid titration, all the weak base has been neutralized, forming a salt containing the conjugate acid of the weak base. This conjugate acid is what determines the final pH. Since the original base was weak, its conjugate acid retains significant acidity and undergoes hydrolysis with water: $\text{BH}^+ + \text{H}_2\text{O} \rightleftharpoons \text{B} + \text{H}_3\text{O}^+$ . This reaction produces hydronium ions, making the solution acidic (pH < 7). Answer B correctly identifies this hydrolysis mechanism. Answer A incorrectly suggests the strong acid "overwhelms" the weak base. At the equivalence point, stoichiometrically equivalent amounts have reacted completely—there's no excess strong acid present. Answer C misunderstands the neutralization process. While weak bases don't dissociate completely, they still react completely with strong acids given sufficient time and proper stoichiometry. Answer D incorrectly implies the strong acid continues donating protons after equivalence. At this point, the strong acid has been consumed; any additional acidity comes from the conjugate acid hydrolysis, not the original strong acid. Remember this key principle: in weak base-strong acid titrations, the equivalence point pH is always determined by the hydrolysis of the conjugate acid formed. Strong acid-weak base combinations always yield acidic equivalence points, while strong base-weak acid combinations yield basic equivalence points.
A student uses bromocresol green indicator (transition range pH 3.8-5.4) for the titration of ammonia with hydrochloric acid. The equivalence point pH for this titration is approximately 5.3. What problem might occur with this choice of indicator?
Answer: The indicator choice is appropriate and will accurately detect the equivalence point. When analyzing indicator choice for acid-base titrations, you need to match the indicator's transition range with the pH at the equivalence point. The key is understanding what happens when the indicator range doesn't align properly with the endpoint. In this ammonia-HCl titration, you're dealing with a weak base being titrated by a strong acid. The equivalence point occurs at pH 5.3, which falls right at the upper edge of bromocresol green's transition range (pH 3.8-5.4). This creates a timing problem. The indicator will begin changing color at pH 5.4 and complete its transition by pH 3.8. Since the equivalence point is at pH 5.3, the indicator starts changing color before you actually reach equivalence. As you continue adding HCl past the true equivalence point, the pH drops rapidly through the indicator's range, but you've already begun seeing the color change. This makes it difficult to pinpoint exactly when equivalence was reached, leading you to think it occurred earlier than it actually did. Choice A correctly identifies this issue - the indicator changes color too early. Choice B is wrong because the color change begins before, not after, the equivalence point. Choice C misses the mark since the transition range width isn't the problem - it's the positioning relative to the equivalence point. Choice D is incorrect because ammonia doesn't interfere with the indicator's chemical behavior. Study tip: Always check that your indicator's transition range brackets the expected equivalence point pH, with the equivalence point falling near the middle of that range for maximum accuracy.
In the titration of 50.0 mL of 0.200 M $NH_3$ ( $K_b = 1.8 \times 10^{-5}$ ) with 0.200 M HCl, what is the pH when 25.0 mL of HCl has been added?
Answer: 9.26 When you encounter a weak base-strong acid titration problem, you need to identify what chemical species are present at each stage and determine which controls the pH. At the start, you have 50.0 mL × 0.200 M = 10.0 mmol of $NH_3$ . Adding 25.0 mL × 0.200 M = 5.0 mmol of HCl means you're at the halfway point to the equivalence point. The HCl converts some $NH_3$ to $NH_4^+$ : $NH_3 + HCl \rightarrow NH_4^+ + Cl^-$ After reaction: 5.0 mmol $NH_3$ remains and 5.0 mmol $NH_4^+$ forms. This creates a buffer solution with equal concentrations of the weak base and its conjugate acid. For any buffer at the halfway point of a titration, $pH = pK_a$ (or $pOH = pK_b$ ). Since $K_b = 1.8 \times 10^{-5}$ , then $pK_b = 4.74$ , so $pOH = 4.74$ . Therefore: $pH = 14.00 - 4.74 = 9.26$ Answer choice A (4.74) represents the $pK_b$ value, not the pH. This is a common error when students confuse acid and base equilibrium expressions. Answer choice C (9.95) would be closer to the pH of pure $NH_3$ solution before any acid is added. Answer choice D (10.34) is too high and doesn't correspond to any meaningful calculation for this system. Remember: at the halfway point of any weak base titration, $pH = 14 - pK_b$ . This shortcut saves time and reduces calculation errors on exams.
Based on the titration data provided above, what is the approximate concentration of the original HF solution?
Answer: 0.120 M When you encounter a weak acid-strong base titration problem, focus on identifying the equivalence point to determine the original acid concentration. The equivalence point occurs when moles of acid equal moles of added base. Looking at the pH data, the dramatic jump from pH 3.2 to 8.9 (after adding 10.0 to 20.0 mL NaOH) indicates the equivalence point lies in this range. For a weak acid-strong base titration, the equivalence point pH should be above 7 due to the formation of the conjugate base. The pH of 8.9 at 20.0 mL strongly suggests this is near the equivalence point. Using 20.0 mL as the equivalence point volume: - Moles of NaOH added = $0.150 \text{ M} \times 0.0200 \text{ L} = 0.00300 \text{ mol}$ - Since HF and NaOH react 1:1, moles of HF = 0.00300 mol - Concentration of HF = $\frac{0.00300 \text{ mol}}{0.0250 \text{ L}} = 0.120 \text{ M}$ This confirms answer (B) 0.120 M. (A) 0.075 M would require only 12.5 mL of NaOH to reach equivalence, which doesn't match the pH jump location. (C) 0.150 M would need 25.0 mL, but the pH at 25.0 mL (12.1) is too high for an equivalence point—this represents excess base. (D) 0.180 M would require 30.0 mL, which exceeds our data range entirely. Study tip: In titration problems, locate the steepest pH change to find the equivalence point, then use stoichiometry to calculate the unknown concentration. The equivalence point pH also helps confirm your answer—above 7 for weak acid-strong base titrations.
A student titrates 25.0 mL of 0.100 M acetic acid ( $CH_3COOH$ , $K_a = 1.8 \times 10^{-5}$ ) with 0.100 M sodium hydroxide. What is the pH at the equivalence point?
Answer: 8.72 When you encounter a weak acid-strong base titration, the key insight is that the equivalence point pH depends on the salt formed, not the original acid strength. At equivalence, all the acetic acid has been converted to acetate ion ( $CH_3COO^-$ ), which acts as a weak base. First, calculate the concentration of acetate at equivalence. Since you're mixing equal volumes of equal concentrations, the acetate concentration becomes $\frac{0.100 \text{ M} \times 25.0 \text{ mL}}{50.0 \text{ mL}} = 0.0500 \text{ M}$ . Next, find $K_b$ for acetate using $K_w = K_a \times K_b$ : $K_b = \frac{1.0 \times 10^{-14}}{1.8 \times 10^{-5}} = 5.6 \times 10^{-10}$ Set up the equilibrium expression for acetate hydrolysis: $CH_3COO^- + H_2O \rightleftharpoons CH_3COOH + OH^-$ Using $K_b = \frac{[OH^-]^2}{0.0500} = 5.6 \times 10^{-10}$ , solve for $[OH^-] = 5.3 \times 10^{-6} \text{ M}$ Calculate pOH: $pOH = -\log(5.3 \times 10^{-6}) = 5.28$ , so $pH = 14.00 - 5.28 = 8.72$ Answer A (7.00) would be correct for a strong acid-strong base titration, but ignores the basic nature of acetate. Answer C (9.26) likely comes from using the original acid concentration instead of the diluted concentration. Answer D (10.87) represents an error in the $K_b$ calculation or equilibrium setup. Remember: weak acid-strong base equivalence points are always basic due to the conjugate base's hydrolysis. Calculate the diluted salt concentration carefully after mixing volumes.
The use of a pH meter versus visual indicators in acid-base titrations offers which primary advantage?
Answer: pH meters work better in colored solutions where visual indicator changes might be obscured. When evaluating analytical methods in chemistry, you need to consider both capabilities and limitations of different detection techniques. pH meters and visual indicators each have distinct advantages depending on the titration system. The key advantage of pH meters is their ability to detect equivalence points in weak acid-weak base titrations, where visual indicators typically fail. In weak acid-weak base systems, the pH change at the equivalence point is very gradual - often less than 2 pH units over a large volume range. This shallow pH transition makes it nearly impossible for indicators to provide a sharp, observable color change. pH meters, however, can precisely track these subtle pH changes and identify the inflection point through mathematical analysis of the titration curve. Let's examine why the other options are incorrect. Option A is false because pH meters don't eliminate all error sources - they have their own limitations like electrode drift, calibration errors, and temperature effects. Option C misrepresents cost considerations; pH meters are actually more expensive initially and require more maintenance than simple indicators. Option D confuses the detection methods entirely - pH meters provide digital readouts, not color changes, while indicators are the ones that produce visual color transitions. Remember that analytical method selection depends on the specific chemical system you're studying. For strong acid-strong base titrations, simple indicators work perfectly well, but for challenging systems like weak-weak combinations, instrumental methods like pH meters become essential tools for accurate endpoint detection.
Which factor most significantly affects the sharpness of the equivalence point in an acid-base titration?
Answer: The strength of the acid and base involved, with strong acid-strong base showing the sharpest change. When analyzing acid-base titrations, the sharpness of the equivalence point depends on how dramatically the pH changes as you add titrant near the endpoint. This sharpness is fundamentally determined by the ionization behavior of the acids and bases involved. Strong acids and strong bases ionize completely in solution, meaning they release or accept protons readily. When you titrate a strong acid with a strong base (or vice versa), the neutralization reaction goes to completion quickly and decisively. This creates a steep, dramatic pH change over a very small volume of added titrant - typically jumping several pH units with just a drop or two. Weak acids or bases, by contrast, only partially ionize and resist pH changes due to their buffering capacity, creating a more gradual, less distinct equivalence point. Option A is incorrect because while higher concentrations do affect the overall pH values, they don't fundamentally change the steepness of the pH transition at the equivalence point. Option C misses the mark - temperature affects reaction rates and equilibrium constants slightly, but doesn't significantly impact equivalence point sharpness. Option D is wrong because larger volumes simply mean you're working with more moles of reactants; the shape and sharpness of the titration curve remain essentially the same when plotted against volume. Remember this key principle: strong acid-strong base titrations always give the sharpest equivalence points, while any combination involving weak acids or bases will show more gradual transitions. This is why phenolphthalein works well for strong acid-strong base titrations but methyl orange might be better for weak base-strong acid combinations.

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