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Ch.16 - Acid-Base Equilibria
Brown - Chemistry: The Central Science 15th Edition
Brown15th EditionChemistry: The Central ScienceISBN: 9780137542970Not the one you use?Change textbook
All textbooksBrown 15th EditionCh.16 - Acid-Base EquilibriaProblem 107
Chapter 16, Problem 107

Succinic acid (H2C4H6O4), which we will denote H2Suc, is a biologically relevant diprotic acid with the structure shown below. At 25 °C, the acid-dissociation constants for succinic acid are Ka1 = 6.9 * 10^-5 and Ka2 = 2.5 * 10^-6. (a) Determine the pH of a 0.32 M solution of H2Suc at 25 °C, assuming that only the first dissociation is relevant. (b) Determine the molar concentration of Suc2- in the solution in part (a). (c) Is the assumption you made in part (a) justified by the result from part (b)?

Verified step by step guidance
1
Step 1: Write the chemical equation for the first dissociation of succinic acid: \( \text{H}_2\text{Suc} \rightleftharpoons \text{H}^+ + \text{HSuc}^- \).
Step 2: Set up the expression for the acid dissociation constant \( K_{a1} \) for the first dissociation: \( K_{a1} = \frac{[\text{H}^+][\text{HSuc}^-]}{[\text{H}_2\text{Suc}]} \).
Step 3: Assume that the initial concentration of \( \text{H}_2\text{Suc} \) is 0.32 M and that the change in concentration due to dissociation is \( x \). Therefore, \([\text{H}^+] = x\), \([\text{HSuc}^-] = x\), and \([\text{H}_2\text{Suc}] = 0.32 - x\).
Step 4: Substitute these expressions into the \( K_{a1} \) expression and solve for \( x \), which represents \([\text{H}^+]\). Use the approximation that \( 0.32 - x \approx 0.32 \) if \( x \) is small compared to 0.32.
Step 5: Calculate the pH from \([\text{H}^+]\) using the formula \( \text{pH} = -\log([\text{H}^+]) \).

Key Concepts

Here are the essential concepts you must grasp in order to answer the question correctly.

Diprotic Acids

Diprotic acids, like succinic acid, can donate two protons (H+) per molecule in solution. The dissociation occurs in two steps, each characterized by its own acid dissociation constant (Ka). Understanding the behavior of diprotic acids is crucial for calculating pH and concentrations of species in solution, as the first dissociation is typically stronger than the second.

Acid Dissociation Constant (Ka)

The acid dissociation constant (Ka) quantifies the strength of an acid in solution, indicating the extent to which it donates protons. A higher Ka value signifies a stronger acid that dissociates more completely. For diprotic acids, the first dissociation constant (Ka1) is usually larger than the second (Ka2), which influences the pH and the concentrations of the resulting species in solution.
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Characteristics of Ka and Kb

pH Calculation

pH is a measure of the hydrogen ion concentration in a solution, calculated using the formula pH = -log[H+]. For weak acids, the pH can be determined using the acid dissociation constant and the initial concentration of the acid. In the case of diprotic acids, if the first dissociation is significantly stronger than the second, it is often sufficient to consider only the first dissociation for pH calculations, simplifying the analysis.
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pH Calculation Example
Related Practice
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Calculate the pH of a solution made by adding 2.50 g of lithium oxide 1Li2O2 to enough water to make 1.500 L of solution.

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Butyric acid is responsible for the foul smell of rancid butter. The pKa of butyric acid is 4.84. (c) Calculate the pH of a 0.050 M solution of sodium butyrate.

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Butyric acid is responsible for the foul smell of rancid butter. The pKa of butyric acid is 4.84. (a) Calculate the pKb for the butyrate ion.

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Textbook Question

The following observations are made about a diprotic acid H2A: (i) A 0.10 M solution of H2A has pH = 3.30. (ii) A 0.10 M solution of the salt NaHA is acidic. Which of the following could be the value of pKa2 for H2A: (i) 3.22, (ii) 5.30, (iii) 7.47, or (iv) 9.82?

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