pH and pK - AP Chemistry

1. A $0.10\,\text{M}$ solution of the weak acid HA has $K_a = 1.0\times 10^{-5}$ (so $pK_a = 5.00$). Which statement best relates the value of $pK_a$ to the acidity of the solution?
   Answer: A smaller $pK_a$ would indicate a stronger acid and thus a more acidic solution (lower pH), assuming the same initial concentration. This question tests understanding of pH and pK relationships. The pKa value represents the negative logarithm of the acid dissociation constant (Ka), where pKa = -log(Ka). A smaller pKa value corresponds to a larger Ka value, which indicates a stronger acid that dissociates more completely in water. Since stronger acids produce more H+ ions at the same concentration, they result in lower pH values (more acidic solutions). The incorrect option C reverses this relationship by claiming larger pKa means stronger acid, when actually larger pKa means smaller Ka and therefore weaker acid. Remember: lower pKa means stronger acid and lower pH at the same concentration.
2. A weak acid HA has $K_a=1.0\times10^{-5}$ at $25^\circ\text{C}$. Which value is closest to $pK_a$ for HA?
   Answer: 5 This question assesses the skill of pH and pK. The pKa is calculated as -log(Ka), transforming the exponential Ka into a linear scale for easier comparison of acid strengths. Lower pKa values indicate stronger acids due to the inverse logarithmic relationship. For Ka=1.0×$10^{-5}$, pKa=5, as -log($10^{-5}$)=5. A tempting distractor is choice D, which is the Ka value itself, confusing pKa with the dissociation constant rather than its logarithmic form. Remember as a transferable strategy that lower pKa means stronger acid because it corresponds to a larger Ka.
3. A weak base B is dissolved in water. Its base-dissociation constant is $K_b = 1.0\times 10^{-3}$ (so $pK_b = 3.00$). Which statement is correct?
   Answer: A smaller $pK_b$ would indicate a stronger base and thus a higher pH, assuming the same initial concentration. This problem involves pH and pK relationships for bases. The pKb value is the negative logarithm of the base dissociation constant (Kb), where pKb = -log(Kb). A smaller pKb corresponds to a larger Kb, indicating a stronger base that accepts protons more readily and produces more OH- ions. Since stronger bases create more hydroxide ions at the same concentration, they result in higher pH values (more basic solutions). Option B incorrectly claims that larger pKb means stronger base, when actually larger pKb means smaller Kb and therefore weaker base. Remember the pattern: smaller pKb means stronger base and higher pH at the same concentration.
4. A student states: "Because a solution has p$K_a=5.0$, its pH must be 5.0." The student is referring to a $0.10\,\text{M}$ aqueous solution of a weak monoprotic acid HA with p$K_a=5.0$ at $25^\circ\text{C}$. Which statement best evaluates the student's claim?​
   Answer: The claim is incorrect because p$K_a$ is a measure of acid strength, not the actual pH of a particular solution. This question addresses a common misconception about pH and pK values. The pKa is a property of the acid itself, representing its strength through the relationship pKa = -log(Ka). The pH of a solution depends on both the acid's strength (Ka or pKa) and its concentration, requiring equilibrium calculations. For a 0.10 M solution of an acid with pKa = 5.0, the actual pH will be less than 5.0 (typically around 3.0) because the acid only partially dissociates. Choice A incorrectly defines pKa as the pH of the solution, confusing an intrinsic acid property with a solution property. Remember: pKa is a constant for a given acid at a specific temperature, while pH varies with concentration.
5. A student prepares separate $0.10\,\text{M}$ aqueous solutions of two weak acids, HA and HB, at the same temperature. The acids have the following $K_a$ values: $K_a(\text{HA})=1.0\times10^{-4}$ and $K_a(\text{HB})=1.0\times10^{-6}$. Which statement correctly compares the pH values of the two solutions?
   Answer: The HA solution has a lower pH than the HB solution. This question assesses the skill of pH and pK. The pH of a solution measures the concentration of H+ ions on a logarithmic scale, where lower pH indicates higher acidity. For weak acids, pKa is defined as -log(Ka), so a lower pKa corresponds to a larger Ka and thus a stronger acid that dissociates more, producing more H+ and lowering the pH. Comparing two acids of the same concentration, the one with the larger Ka (or lower pKa) will have a lower pH because it generates more H+ ions relative to the weaker acid. A tempting distractor is choice E, which incorrectly states that the HB solution has a lower pH because HB has the smaller Ka, confusing acid strength with the magnitude of Ka. Remember as a transferable strategy that a lower pKa means a stronger acid because it corresponds to a larger Ka, leading to lower pH in solutions of equal concentration.
6. A weak acid HA is dissolved in water to make an aqueous solution of fixed concentration. The $K_a$ of HA is then changed from $1.0\times10^{-6}$ to $1.0\times10^{-4}$ (all other conditions unchanged). Which statement best describes how the pH of the solution changes?
   Answer: The pH decreases because the acid is stronger. This question assesses the skill of pH and pK. Increasing Ka means decreasing pKa, indicating a stronger acid that dissociates more, producing higher [H+] and lower pH. The pH is -log[H+], so changes in strength directly affect pH logarithmically. At fixed concentration, larger Ka lowers pH. A tempting distractor is choice A, which incorrectly states pH increases with stronger acid, misunderstanding that stronger acids decrease pH. Remember as a transferable strategy that lower pKa means stronger acid because it corresponds to a larger Ka, leading to lower pH.
7. Two separate $0.10\,\text{M}$ aqueous solutions are prepared at the same temperature: Solution 1 contains weak acid HX with $K_a = 1.0\times 10^{-4}$, and Solution 2 contains weak acid HY with $K_a = 1.0\times 10^{-6}$. Which comparison is correct?
   Answer: Solution 1 has a lower pH because HX is the stronger acid (larger $K_a$) at the same concentration. This question requires comparing pH and pK values for two weak acids. Since Ka represents the acid dissociation constant, a larger Ka value indicates a stronger acid that produces more H+ ions in solution. HX has Ka = 1.0 × $10^{-4}$ while HY has Ka = 1.0 × $10^{-6}$, making HX the stronger acid (its Ka is 100 times larger). At the same initial concentration, the stronger acid HX will produce more H+ ions and therefore have a lower pH than the weaker acid HY. Option A incorrectly states that larger Ka leads to higher pH, when the opposite is true. The key principle: larger Ka means stronger acid and lower pH when comparing acids at the same concentration.
8. A weak acid HA in water has $K_a = 1.0\times 10^{-5}$. Without doing an equilibrium calculation, which change would most likely result in a solution with a lower pH, assuming the same initial concentration and temperature?
   Answer: Replacing HA with an acid that has $K_a = 1.0\times 10^{-3}$. This problem tests understanding of how pH and pK values relate to acid strength. The original acid HA has Ka = 1.0 × $10^{-5}$ (pKa = 5.00). To achieve a lower pH at the same concentration, we need a stronger acid with a larger Ka value. Option B suggests an acid with Ka = 1.0 × $10^{-3}$, which is 100 times larger than the original Ka, making it a much stronger acid that will produce more H+ ions and lower the pH. Options A and C suggest weaker acids (smaller Ka or larger pKa), which would actually increase the pH. The key strategy: to lower pH, choose an acid with larger Ka (or smaller pKa) than the original acid.
9. Two weak bases, $\text{NH}_3$ and B, are each dissolved separately in water to make solutions of the same initial concentration at $25^\circ\text{C}$. The bases have $K_b$ values $K_b(\text{NH}_3)=1.0\times10^{-5}$ and $K_b(\text{B})=1.0\times10^{-3}$. Which statement correctly compares the $pK_b$ values?
   Answer: $pK_b(\text{NH}_3) > pK_b(\text{B})$ because $\text{NH}_3$ has the smaller $K_b$. This question assesses the skill of pH and pK. The pKb measures base strength logarithmically as -log(Kb), where a smaller pKb indicates a larger Kb and stronger base. For bases of the same concentration, relative pKb values allow comparison without calculating exact pOH or pH. Here, NH3 with smaller Kb has higher pKb than B, indicating it's weaker. A tempting distractor is choice A, which incorrectly states pKb(NH3) < pKb(B) despite NH3's smaller Kb, misunderstanding the inverse logarithmic relationship. Remember as a transferable strategy that lower pKb means stronger base because it corresponds to a larger Kb.
10. A weak base $\text{B}$ has $K_b=1.0\times10^{-6}$ at $25^\circ\text{C}$. Which value is closest to $pK_b$ for $\text{B}$?
    Answer: $pK_b=6$ This question tests understanding of pH and pK. The relationship between Kb and pKb is defined as pKb = -log(Kb), analogous to the acid relationship. For a weak base with Kb = 1.0×10⁻⁶, we calculate pKb = -log(1.0×10⁻⁶) = -(-6) = 6. This logarithmic transformation converts the very small Kb value into a more convenient pKb value. The incorrect choice C confuses pKb with Kb itself, failing to apply the logarithmic relationship. Always remember: pKb = -log(Kb), and for Kb = 1.0×10⁻ⁿ, pKb = n.
11. A student is given two weak acids of equal initial concentration in water at $25^\circ\text{C}$. Acid X has $pK_a=3.0$ and acid Y has $pK_a=5.0$. Which statement is correct?
    Answer: Acid X is stronger than acid Y, so the solution of X has the lower pH. This question assesses the skill of pH and pK. The pKa relates to acid strength as -log(Ka), with lower pKa signifying stronger acids that lower the pH more effectively. For equal concentrations, comparing pKa values directly indicates relative strengths and thus relative pH values. Acid X with pKa=3 is stronger than Y with pKa=5, leading to lower pH for X. A tempting distractor is choice C, which incorrectly suggests stronger acids have higher pH, confusing the inverse relationship between strength and pH. Remember as a transferable strategy that lower pKa means stronger acid because it corresponds to a larger Ka, resulting in lower pH for the solution.
12. At $25^\circ\text{C}$, two weak bases are compared: Base 1 has $pK_b = 4.00$ and Base 2 has $pK_b = 6.00$. Equal concentrations of each base are dissolved separately in water. Which statement is correct?
    Answer: Base 1 produces the more basic solution because its $pK_b$ is smaller. This question tests understanding of pH and pK for comparing base strengths. Base 1 has pKb = 4.00 while Base 2 has pKb = 6.00, meaning Base 1 has the smaller pKb value. Since pKb = -log(Kb), a smaller pKb corresponds to a larger Kb value, indicating Base 1 is the stronger base. At equal concentrations, the stronger base (Base 1) will produce more OH- ions and create a more basic solution with higher pH. Option A incorrectly states that larger pKb produces a more basic solution, reversing the actual relationship. The key insight: smaller pKb means larger Kb, stronger base, and higher pH when comparing bases at the same concentration.
13. For the weak acid HF in water, $K_a=1.0\times10^{-4}$ at $25^\circ\text{C}$. Which relationship between $K_a$ and $pK_a$ for HF is correct?
    Answer: $pK_a=-\log(K_a)$ This question assesses the skill of pH and pK. The pKa is the negative logarithm of the acid dissociation constant Ka, reflecting the strength of the acid where lower pKa indicates stronger acids due to greater dissociation. Similarly, pH is -log[H+], so both are logarithmic measures that allow relative comparisons without full calculations. For HF with Ka=1.0×$10^{-4}$, pKa=4, illustrating how pKa inversely relates to Ka's magnitude. A tempting distractor is choice A, which incorrectly uses pKa=log(Ka) without the negative sign, leading to positive values that don't align with typical pKa ranges for weak acids. Remember as a transferable strategy that lower pKa means stronger acid because it corresponds to a larger Ka.
14. A weak base, B, has $K_b=1.0\times10^{-5}$ at $25^\circ\text{C}$. Which value is closest to the p$K_b$ of B?​
    Answer: p$K_b=5$ This question tests the calculation of pKb from Kb, applying pH and pK relationships to bases. The pKb is defined as -log(Kb), analogous to how pKa relates to Ka. For base B with Kb = 1.0×$10^{-5}$, we calculate pKb = -log(1.0×$10^{-5}$) = -(-5) = 5. This logarithmic transformation converts the exponential Kb value to a linear pKb scale. Choice D incorrectly attempts to use the relationship pKa + pKb = 14, which only applies to conjugate acid-base pairs, not to finding pKb from Kb alone. Remember: pKb = -log(Kb), so when Kb = $10^{-n}$, then pKb = n.
15. A weak base B is dissolved in water to form an aqueous solution. The base has $K_b=1.0\times10^{-5}$ at $25^\circ\text{C}$. Which statement best describes the effect of increasing $K_b$ (with concentration held constant) on the pH of the solution?
    Answer: The pH increases because the base produces more $\text{OH}^-$. This question assesses the skill of pH and pK. For weak bases, pKb is -log(Kb), so a lower pKb indicates a stronger base that produces more OH- ions, raising the pH. The pH relates to pOH via pH + pOH = 14, where pOH = -log[OH-], so increasing Kb decreases pOH and increases pH. Thus, larger Kb leads to higher pH by enhancing base strength and OH- production at constant concentration. A tempting distractor is choice E, which incorrectly claims a larger Kb means a weaker base, reversing the relationship between Kb and base strength. Remember as a transferable strategy that lower pKb means stronger base because it corresponds to a larger Kb, leading to higher pH in solutions.
16. A weak base B has $K_b = 1.0\times 10^{-6}$, while weak base C has $K_b = 1.0\times 10^{-4}$. Equal concentrations are dissolved separately in water. Which statement is correct?
    Answer: Base C produces the higher pH because its $K_b$ is larger. This problem tests understanding of pH and pK for bases with different Kb values. Base B has Kb = 1.0 × $10^{-6}$ while Base C has Kb = 1.0 × $10^{-4}$, making Base C the stronger base (its Kb is 100 times larger). The base dissociation constant Kb measures how readily a base accepts protons - larger Kb means more OH- ions are produced at equilibrium. At equal concentrations, Base C will produce more hydroxide ions than Base B, resulting in a higher pH (more basic solution). Option A incorrectly states that smaller Kb produces higher pH, when actually larger Kb means stronger base and higher pH. The key principle: larger Kb means stronger base and higher pH when comparing bases at the same concentration.
17. A weak acid, HX, has $K_a=1.0\times10^{-6}$ at $25^\circ\text{C}$. Which value is closest to the p$K_a$ of HX?​
    Answer: p$K_a=6$ This question requires calculating pKa from Ka using the relationship involving pH and pK. The pKa is defined as -log(Ka), which represents the negative logarithm of the acid dissociation constant. For HX with Ka = 1.0×$10^{-6}$, we calculate pKa = -log(1.0×$10^{-6}$) = -(-6) = 6. This logarithmic relationship transforms the exponential Ka value into a more manageable pKa scale. Choice B incorrectly treats pKa as if it equals $10^{-6}$, confusing the definition with the Ka value itself. The key strategy is to remember that pKa = -log(Ka), so when Ka has the form $10^{-n}$, then pKa = n.
18. Two solutions are prepared at the same temperature with the same initial concentration: Solution A contains weak acid HA with $pK_a = 3.00$, and Solution B contains weak acid HB with $pK_a = 5.00$. Which statement is correct?
    Answer: Solution A is more acidic because HA has the smaller $pK_a$ (larger $K_a$). This problem requires comparing pH and pK values for two weak acids at the same concentration. Solution A contains HA with pKa = 3.00, while Solution B contains HB with pKa = 5.00. Since pKa = -log(Ka), a smaller pKa means a larger Ka value and therefore a stronger acid. HA (pKa = 3.00) is stronger than HB (pKa = 5.00) because its Ka is 100 times larger. At the same initial concentration, the stronger acid HA will dissociate more, producing more H+ ions and resulting in a lower pH (more acidic solution). Option D incorrectly assumes pH equals pKa, which is only true at the half-equivalence point of a titration. The principle: smaller pKa means stronger acid and lower pH at the same concentration.
19. Two weak acids, HJ and HK, are each prepared as $0.20\,\text{M}$ solutions in water at $25^\circ\text{C}$. HJ has $K_a=1.0\times10^{-2}$ and HK has $K_a=1.0\times10^{-6}$. Which statement correctly compares the $pK_a$ values?
    Answer: $pK_a(\text{HJ}) < pK_a(\text{HK})$ because HJ has the larger $K_a$. This question assesses the skill of pH and pK. The pKa is -log(Ka), so acids with larger Ka have smaller pKa, indicating greater strength. Relative pKa comparisons highlight strength differences without needing concentrations for the comparison itself. HJ with larger Ka has lower pKa than HK. A tempting distractor is choice E, which incorrectly links smaller pKa to smaller Ka, reversing the inverse relationship. Remember as a transferable strategy that lower pKa means stronger acid because it corresponds to a larger Ka.
20. Two $0.10\,\text{M}$ weak bases are compared at $25^\circ\text{C}$. Base $\text{B}_1$ has $pK_b=2.00$ and base $\text{B}_2$ has $pK_b=5.00$. Which statement is correct?
    Answer: $\text{B}_1$ is the stronger base because it has the smaller $pK_b$ This question tests understanding of pH and pK. For bases, the relationship between strength and pKb is inverse: smaller pKb indicates a stronger base because pKb = -log(Kb). Since B₁ has pKb = 2.00 and B₂ has pKb = 5.00, B₁ has the smaller pKb and is therefore the stronger base. This means B₁ has a larger Kb value (Kb = 10⁻² for B₁ versus Kb = 10⁻⁵ for B₂), resulting in greater hydroxide ion production. The misconception in choice A incorrectly assumes that larger pKb means stronger base, reversing the actual relationship. Remember: for bases, lower pKb = larger Kb = stronger base.

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