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.

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

• B.

  $\mathrm{pH}\hspace{0.17em}=\hspace{0.17em}{\mathrm{pK}}_a +\hspace{0.17em}{log}_{10}\left(\frac{\left[{\mathrm{A}}^{–}\right]}{\left[\mathrm{HA}\right]}\right)$

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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 390.0 mM of acetic acid and 534.0 mM of sodium acetate.
(pK_a of acetic acid = 4.76)
Henderson-Hasselbalch equation:
$\mathrm{pH}\hspace{0.17em}=\hspace{0.17em}{\mathrm{pK}}_a +\hspace{0.17em}{log}_{10}\left(\frac{\left[\mathrm{Base}\right]}{\left[\mathrm{Acid}\right]}\right)$

• A. 4.90
• B. 5.90
• C. 4.30
• D. 4.70

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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 668.0 mM of butyric acid and 693.0 mM of sodium butyrate.
(pK_a of butyric acid = 4.82)
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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pKa and pKb Using the Henderson-Hasselbalch Equation (Multiple Choice)

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Calculate pK_a for the weak acid.
The solution contains 335.0 mM of glycolic acid and 158.0 mM of sodium glycolate.
The measured pH of the solution is 3.50.
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. 4.03
• C. 4.83
• 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 357.0 mM of glycolic acid and 279.0 mM of sodium glycolate.
The measured pH of the solution is 3.72.
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 10.18.
What is the ratio [base] / [conjugate acid] ?
Hint: pK_a + pK_b = 14.00 for a conjugate acid-base pair.

• A.  2.958
• B.  0.676
• C. 14.791
• D.  1.479

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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 ethylamine / ethylammonium, pK_b = 3.99 and the desired pH is 10.66.
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 BELOW the pKa of a amine group (e.g., -NH₂), 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, amino, phosphate
• B. carboxyl, carbonyl, phosphate
• C. carboxyl, phosphate, hydroxyl
• D. amino, hydroxyl, carboxyl
• E. carbonyl, amino, hydroxyl

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Optimal Buffering Range Using pKa

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Pyrophosphoric acid and its conjugate base, pyrophosphate, is abbreviated PP_i and is formed by cells from the hydrolysis of ATP into AMP.
Pyrophosphoric acid is tetraprotic with pK_a values of 0.91, 2.10, 6.70, and 9.32.
Which one of the following pH values falls outside the optimal buffering rangeof Pyrophosphoric acid?

• A. pH 1.1
• B. pH 1.6
• C. pH 7.5
• D. pH 9.6
• E. pH 11.6

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Most Abundant Diprotic State at a Given pH Using pKa

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Oxalic acid and its conjugate base, oxalate, is found in many plants and vegetables and is a product of metabolic processes.
Oxalic acid is diprotic with pK_a values of 1.27 and 4.28.
Oxalic acid has three possible protonation states in the choices below.
Which one of the following protonation states is the most abundant at pH 5.5?

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

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Most Abundant Triprotic State at a Given pH 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.
Citric 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. HOC₃H₄(COO)₃^3-
• B. HOC₃H₄(COOH)(COO)₂^2-
• C. HOC₃H₄(COOH)₂(COO)^-
• D. HOC₃H₄(COOH)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 0.5?

• 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 milk of magnesia is 10.4, while the gastric juice is pH 1.4. This is a difference of 9 pH units.
The gastric juice has:

• A. 1 billion (10⁹) times lower [H+] than the milk of magnesia.
• B. 1 billion (10⁹) times higher [H+] than the milk of magnesia.
• C. 9 times higher [H+] than the milk of magnesia.
• D. 9 times lower [H+] than the milk of magnesia.

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