For the bases shown, draw the conjugate acid and identify a pK_a value from Table 4.5 that would help you accurately estimate its stability.
(d)

Verified step by step guidance

1. Step 1: Identify the base shown in the image. The structure represents an isopropyl anion (CH₃)₂CH⁻, which is a negatively charged carbon atom bonded to two methyl groups and one hydrogen atom.
2. Step 2: To draw the conjugate acid, add a proton (H⁺) to the base. This will neutralize the negative charge on the carbon atom, resulting in isopropane (CH₃)₂CH₂.
3. Step 3: Recall that the conjugate acid of a base has a pKₐ value that reflects its acidity. The pKₐ value can be found in Table 4.5, which lists the pKₐ values of common acids. For isopropane, the pKₐ of its conjugate acid is approximately 50, indicating it is a very weak acid.
4. Step 4: Use the pKₐ value to estimate the stability of the base. A high pKₐ value (like 50) suggests that the conjugate acid is very stable, and the base (isopropyl anion) is relatively unstable.
5. Step 5: Summarize the findings: The conjugate acid of the isopropyl anion is isopropane, and its pKₐ value of approximately 50 indicates that the base is unstable and the conjugate acid is highly stable.

Key Concepts

Conjugate Acids and Bases

In acid-base chemistry, a conjugate acid is formed when a base accepts a proton (H⁺). Understanding this concept is crucial for predicting the behavior of substances in reactions. For example, when ammonia (NH₃) acts as a base, it can accept a proton to form its conjugate acid, ammonium (NH₄⁺). This relationship helps in determining the strength of acids and bases.

pKₐ and Acid Strength

pKₐ is a quantitative measure of the strength of an acid in solution, with lower values indicating stronger acids. It is derived from the acid dissociation constant (Kₐ), which reflects the extent to which an acid donates protons. Understanding pKₐ values is essential for comparing the stability of conjugate acids and bases, as they provide insight into the equilibrium position of acid-base reactions.

Stability of Conjugate Acids

The stability of a conjugate acid is influenced by factors such as electronegativity, resonance, and inductive effects. A more stable conjugate acid corresponds to a weaker base, as it is less likely to donate a proton. Evaluating the stability of conjugate acids helps in predicting the direction of acid-base reactions and understanding the relative strengths of the corresponding bases.