2: Water and pH

Students calculate pH from pKa using the Henderson-Hasselbalch equation, predict protonation states of simple acids and bases, and analyze buffer systems.

LibreTexts reference: Unit 1, Chapter 2: Chemistry of Water

Correct Henderson-Hasselbalch Equation

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Which one of the following equations is the correct form of the Henderson-Hasselbalch equation?

• A.

  $\mathrm{pH}\hspace{0.17em}=\hspace{0.17em}{\mathrm{pK}}_a –\hspace{0.17em}{log}_{10}\left(\frac{\left[\mathrm{Acid}\right]}{\left[\mathrm{Base}\right]}\right)$

• B.

  $\mathrm{pH}\hspace{0.17em}=\hspace{0.17em}{\mathrm{pK}}_a +\hspace{0.17em}{log}_{10}\left(\frac{\left[\mathrm{Acid}\right]}{\left[\mathrm{Base}\right]}\right)$

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pH Using the Henderson-Hasselbalch Equation

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Calculate the pH of the buffer solution.
The solution contains 592.0 mM of sulfuric acid and 420.0 mM of sodium sulfate.
(pK_a of sulfuric acid = 1.99)
Henderson-Hasselbalch equation:
$\mathrm{pH}\hspace{0.17em}=\hspace{0.17em}{\mathrm{pK}}_a +\hspace{0.17em}{log}_{10}\left(\frac{\left[\mathrm{Base}\right]}{\left[\mathrm{Acid}\right]}\right)$

• A. 2.19
• B. 2.84
• C. 1.84
• D. 1.49

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pH Using the Henderson-Hasselbalch Equation

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Calculate the pH of the buffer solution.
The solution contains 20.2 mM of ammonia and 85.6 mM of ammonium chloride.
(pK_b of ammonia = 4.76)
Hint: pK_a + pK_b = 14.00 for a conjugate acid-base pair.
Henderson-Hasselbalch form:
$\mathrm{pH}\hspace{0.17em}=\hspace{0.17em}{\mathrm{pK}}_a +\hspace{0.17em}{log}_{10}\left(\frac{\left[\mathrm{Base}\right]}{\left[\mathrm{Acid}\right]}\right)$
Note: answers need to be within 1% of the correct number to be correct.

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pKa and pKb Using the Henderson-Hasselbalch Equation

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Calculate pK_b for the weak base.
The solution contains 55.0 mM of ammonia and 97.5 mM of ammonium chloride.
The measured pH of the solution is 8.99.
Hint: pK_a + pK_b = 14.00 for a conjugate acid-base pair.
Henderson-Hasselbalch form:
$\mathrm{pH}\hspace{0.17em}=\hspace{0.17em}{\mathrm{pK}}_a +\hspace{0.17em}{log}_{10}\left(\frac{\left[\mathrm{Base}\right]}{\left[\mathrm{Acid}\right]}\right)$

• A. 4.56
• B. 4.41
• C. 4.76
• D. 4.96

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pKa and pKb Using the Henderson-Hasselbalch Equation

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Calculate pK_a for the weak acid.
The solution contains 443.0 mM of butyric acid and 185.0 mM of sodium butyrate.
The measured pH of the solution is 4.44.
Henderson-Hasselbalch equation:
$\mathrm{pH}\hspace{0.17em}=\hspace{0.17em}{\mathrm{pK}}_a +\hspace{0.17em}{log}_{10}\left(\frac{\left[\mathrm{Base}\right]}{\left[\mathrm{Acid}\right]}\right)$
Note: answers need to be within 2% of the correct number to be correct.

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Acid-Base Ratios Using the Henderson-Hasselbalch Equation

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Calculate the ratio of conjugate base to weak acid.
For lactic acid / lactate, pK_a = 3.86 and the desired pH is 4.56.
What is the ratio [A^-] / [HA] ?

• A. 50.119
• B.  5.012
• C.  0.501
• D.  2.506

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Conjugate Base-Acid Ratios Using the Henderson-Hasselbalch Equation

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Calculate the ratio of conjugate base to weak acid.
For acetic acid / acetate, pK_a = 4.76 and the desired pH is 5.50.
What is the ratio [A^-] / [HA] ?
Note: answers need to be within 6% of the correct number to be correct.

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Protonation States of Functional Groups at Different pH Levels

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When the pH is more than two (2) pH units BELOW the pKa of a thiol group (e.g., -SH), what form is the chemical group in?
Select BOTH the number of hydrogens and its charge; check two boxes.

• A. no hydrogens (0 H)
• B. one hydrogen (1 H)
• C. two hydrogens (2 H)
• D. three hydrogens (3 H)
• E. positive charge (+)
• F. neutral charge (0)
• G. negative charge (-)

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Functional Groups with Single Bonds

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Which one of the following sets of three (3) functional groups all contain a double bond?

• A. phosphate, carboxyl, carbonyl
• B. carbonyl, amino, hydroxyl
• C. hydroxyl, amino, carboxyl
• D. phosphate, carbonyl, methyl
• E. methyl, amino, phosphate

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Optimal Buffering Range Using pKa

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Citric acid and its conjugate base, citrate, is an intermediate in the citric acid cycle.
Citric acid is triprotic with pK_a values of 3.13, 4.76, and 6.39.
Which one of the following pH values falls outside the optimal buffering rangeof Citric acid?

• A. pH 3.0
• B. pH 4.1
• C. pH 5.6
• D. pH 6.8
• E. pH 10.0

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Most Abundant Diprotic State at a Given pH Using pKa

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Succinic acid and its conjugate base, succinate, is an intermediate in the citric acid cycle and can act as a signaling molecule reflecting the cellular metabolic state.
Succinic acid is diprotic with pK_a values of 4.20 and 5.60.
Succinic acid has three possible protonation states in the choices below.
Which one of the following protonation states is the most abundant at pH 2.5?

• A. (CH₂)₂(COOH)₂
• B. (CH₂)₂(COOH)(COO)^-
• C. (CH₂)₂(COO)₂^2-

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Most Abundant Triprotic State at a Given pH Using pKa

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Arsenic acid and its conjugate base, arsenate, is extremely toxic, corrosive, and carcinogenic; it serves as a precursor to a variety of pesticides.
Arsenic acid is triprotic with pK_a values of 2.19, 6.94, and 11.50.
Arsenic acid has four possible protonation states in the choices below.
Which one of the following protonation states is the most abundant at pH 8.5?

• A. AsO₄^3-
• B. HAsO₄^2-
• C. H₂AsO₄^-
• D. H₃AsO₄

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Most Abundant Tetraprotic State at a Given pH Using pKa

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Ethylenediaminetetraacetic acid and its conjugate base, EDTA, is commonly used in chelation therapy and as a chelating agent in biochemical experiments..
Ethylenediaminetetraacetic acid is tetraprotic with pK_a values of 2.00, 2.67, 6.16, and 10.26.
Ethylenediaminetetraacetic acid has five possible protonation states in the choices below.
Which one of the following protonation states is the most abundant at pH 8.0?

• A. C₁₀H₁₆N₂O₈
• B. C₁₀H₁₅N₂O₈^-
• C. C₁₀H₁₄N₂O₈^2-
• D. C₁₀H₁₃N₂O₈^3-
• E. C₁₀H₁₂N₂O₈^4-

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pH Differences Between Solutions

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The pH of the pure water is 7.0, while the lemon juice is pH 2.0. This is a difference of 5 pH units.
The lemon juice has:

• A. 100,000 (10⁵) times lower [H+] than the pure water.
• B. 5 times higher [H+] than the pure water.
• C. 100,000 (10⁵) times higher [H+] than the pure water.
• D. 5 times lower [H+] than the pure water.

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