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 Form of the Henderson-Hasselbalch Equation

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

• A.

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

• 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 (Multiple Choice)

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Calculate the pH of the buffer solution.
The solution contains 113.1 mM of ethylamine and 75.9 mM of ethylammonium chloride.
(pK_b of ethylamine = 3.99)
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. 9.98
• B. 10.18
• C. 10.78
• D. 9.18

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pH Using the Henderson-Hasselbalch Equation (Numeric)

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Calculate the pH of the buffer solution.
The solution contains 52.1 mM of ethylamine and 42.5 mM of ethylammonium chloride.
(pK_b of ethylamine = 3.99)
Hint: pK_a + pK_b = 14.00 for a conjugate acid-base pair.
Henderson-Hasselbalch form:
$\mathrm{pH}\hspace{0.17em}=\hspace{0.17em}{\mathrm{pK}}_a +\hspace{0.17em}{log}_{10}\left(\frac{\left[\mathrm{Base}\right]}{\left[\mathrm{Acid}\right]}\right)$
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 (Multiple Choice)

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Calculate pK_a for the weak acid.
The solution contains 635.0 mM of glycolic acid and 160.0 mM of sodium glycolate.
The measured pH of the solution is 3.23.
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. 3.83
• B. 3.63
• C. 4.18
• D. 4.43

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pKa and pKb Using the Henderson-Hasselbalch Equation (Numeric)

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Calculate pK_a for the weak acid.
The solution contains 672.0 mM of glycolic acid and 571.0 mM of sodium glycolate.
The measured pH of the solution is 3.76.
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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Conjugate Base-to-Acid Ratios Using the Henderson-Hasselbalch Equation (Multiple Choice)

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Calculate the ratio of weak base to conjugate acid.
For ethylamine / ethylammonium, pK_b = 3.99 and the desired pH is 10.70.
What is the ratio [base] / [conjugate acid] ?
Hint: pK_a + pK_b = 14.00 for a conjugate acid-base pair.

• A.  4.898
• B.  0.490
• C.  2.449
• D.  0.204

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Conjugate Base-to-Acid Ratios Using the Henderson-Hasselbalch Equation (Numeric)

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Calculate the ratio of weak base to conjugate acid.
For ammonia / ammonium, pK_b = 4.76 and the desired pH is 9.05.
What is the ratio [base] / [conjugate acid] ?
Hint: pK_a + pK_b = 14.00 for a conjugate acid-base pair.
Note: answers need to be within 5% of the correct number to be correct.

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Protonation States of Chemical Groups

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When the pH is more than two (2) pH units ABOVE the pKa of a carboxyl group (e.g., -COOH), 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. carbonyl, phosphate, carboxyl
• B. phosphate, carbonyl, sulfhydryl
• C. sulfhydryl, carbonyl, hydroxyl
• D. amino, hydroxyl, carboxyl
• E. phosphate, amino, sulfhydryl

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Optimal Buffering Range 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.
Which one of the following pH values falls outside the optimal buffering rangeof Arsenic acid?

• A. pH 2.1
• B. pH 2.8
• C. pH 4.6
• D. pH 6.8
• E. pH 7.3

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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 3.0?

• A. (CH₂)₂(COO)₂^2-
• B. (CH₂)₂(COOH)(COO)^-
• C. (CH₂)₂(COOH)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 4.0?

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

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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 11.5?

• 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 black coffee is 5.1, while the lemon juice is pH 2.1. This is a difference of 3 pH units.
The lemon juice has:

• A. 1,000 (10³) times higher [H+] than the black coffee.
• B. 1,000 (10³) times lower [H+] than the black coffee.
• C. 3 times higher [H+] than the black coffee.
• D. 3 times lower [H+] than the black coffee.

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