Ch. 2 - Acids and Bases: Central to Understanding Organic Chemistry

Bruice8th EditionOrganic ChemistryISBN: 9780135213711Not the one you use?Change textbook

Bruice 8th Edition

Ch. 2 - Acids and Bases: Central to Understanding Organic Chemistry

Problem 45a

Chapter 3, Problem 45a

At what pH is the concentration of a compound, with a pK_a = 8.4, 100 times greater in its acidic form than in its basic form? At what pH is 50% of a compound, with a pK_a = 7.3, in its basic form?

Verified step by step guidance

Step 1: Understand the relationship between pH, pKa, and the ratio of acidic to basic forms of a compound using the Henderson-Hasselbalch equation: \( \text{pH} = \text{pKa} + \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) \). Here, \([\text{A}^-]\) represents the concentration of the basic form, and \([\text{HA}]\) represents the concentration of the acidic form.

Step 2: For the first part of the problem, where the concentration of the acidic form is 100 times greater than the basic form, set up the ratio \( \frac{[\text{A}^-]}{[\text{HA}]} = \frac{1}{100} \). Substitute this ratio into the Henderson-Hasselbalch equation: \( \text{pH} = \text{pKa} + \log \left( \frac{1}{100} \right) \). Simplify \( \log \left( \frac{1}{100} \right) \) to \( -2 \).

Step 3: Substitute the given \( \text{pKa} = 8.4 \) into the equation: \( \text{pH} = 8.4 - 2 \). This will give the pH at which the acidic form is 100 times greater than the basic form.

Step 4: For the second part of the problem, where 50% of the compound is in its basic form, recognize that \( \frac{[\text{A}^-]}{[\text{HA}]} = 1 \). When the concentrations of the acidic and basic forms are equal, \( \log \left( \frac{[\text{A}^-]}{[\text{HA}]} \right) = \log(1) = 0 \).

Step 5: Substitute \( \text{pKa} = 7.3 \) into the Henderson-Hasselbalch equation: \( \text{pH} = \text{pKa} + 0 \). This means the pH at which 50% of the compound is in its basic form is equal to its \( \text{pKa} \).

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Key Concepts

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

Henderson-Hasselbalch Equation

The Henderson-Hasselbalch equation relates the pH of a solution to the pKa of an acid and the ratio of the concentrations of its deprotonated (basic) and protonated (acidic) forms. It is expressed as pH = pKa + log([A-]/[HA]). This equation is essential for determining the pH at which a specific ratio of acidic to basic forms exists, making it crucial for solving the given question.

pKa and pH Relationship

The pKa value of an acid indicates the pH at which half of the acid is dissociated into its conjugate base. A lower pKa means a stronger acid, while a higher pKa indicates a weaker acid. Understanding this relationship is vital for determining the pH at which a compound exists predominantly in its acidic or basic form, as required in the question.

Concentration Ratios

In the context of acid-base chemistry, concentration ratios refer to the relative amounts of the acidic and basic forms of a compound. For example, if the acidic form is 100 times greater than the basic form, this translates to a ratio of 100:1. Recognizing how to manipulate these ratios using the Henderson-Hasselbalch equation is key to finding the specific pH values requested in the question.

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Related Practice

Textbook Question

For each of the following compounds, indicate the pH at which

a. 50% of the compound is in a form that possesses a charge.

1. CH₃CH₂COOH (pK_a= 4.9)

2. CH₃N⁺H₃ (pK_a= 10.7)

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Textbook Question

A naturally occurring amino acid such as alanine has a group that is a carboxylic acid and a group that is a protonated amine. The pK_a values of the two groups are shown.

d. Draw the structure of alanine in a solution at pH = 12.

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Textbook Question

A naturally occurring amino acid such as alanine has a group that is a carboxylic acid and a group that is a protonated amine. The pK_a values of the two groups are shown.

e. Is there a pH at which alanine is uncharged (that is, neither group has a charge)?

f. At what pH does alanine have no net charge (that is, the amount of negative charge is the same as the amount of positive charge)?

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Textbook Question

A naturally occurring amino acid such as alanine has a group that is a carboxylic acid and a group that is a protonated amine. The pK_a values of the two groups are shown.

c. Draw the structure of alanine in a solution at physiological pH (pH 7.4).

Textbook Question

For each of the following compounds, indicate the pH at which

b. more than 99% of the compound is in a form that possesses a charge.

1. CH₃CH₂COOH (pK_a= 4.9)

2. CH₃N⁺H₃ (pK_a= 10.7)

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Textbook Question

At what pH is the concentration of a compound, with a pK_a = 4.6, 10 times greater in its basic form than in its acidic form?

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