a. Which is a stronger acid: one with a pK_a of 5.2 or one with a pK_a of 5.8?
b. Which is a stronger acid: one with an acid dissociation constant of 3.4 × 10⁻³ or one with an acid dissociation constant of 2.1 × 10⁻⁴?

Verified step by step guidance

1. Step 1: Understand the relationship between pKa and acid strength. The lower the pKa value, the stronger the acid. This is because pKa is inversely related to the acid dissociation constant (Ka), which measures the extent of ionization of the acid in solution.
2. Step 2: Compare the pKa values given in part (a). The acid with a pKa of 5.2 is lower than the acid with a pKa of 5.8, indicating that the acid with a pKa of 5.2 is stronger.
3. Step 3: Understand the relationship between Ka and acid strength for part (b). The higher the Ka value, the stronger the acid. This is because a larger Ka indicates greater ionization of the acid in solution.
4. Step 4: Compare the Ka values given in part (b). The acid with a Ka of 3.4×10⁻³ is larger than the acid with a Ka of 2.1×10⁻⁴, indicating that the acid with a Ka of 3.4×10⁻³ is stronger.
5. Step 5: Summarize the findings: For part (a), the acid with a pKa of 5.2 is stronger. For part (b), the acid with a Ka of 3.4×10⁻³ is stronger. This demonstrates the inverse relationship between pKa and Ka when determining acid strength.

Key Concepts

pKa and Acid Strength

The pKa value is a logarithmic measure of the acidity of a substance, where a lower pKa indicates a stronger acid. This is because pKa is derived from the acid dissociation constant (Ka), which quantifies the extent to which an acid donates protons in solution. Therefore, comparing pKa values allows us to determine which acid is stronger based on their numerical values.

Acid Dissociation Constant (Ka)

The acid dissociation constant (Ka) is a quantitative measure of the strength of an acid in solution. It represents the equilibrium constant for the dissociation of an acid into its conjugate base and a proton. A larger Ka value indicates a stronger acid, as it signifies a greater tendency to lose protons, making it essential for comparing acid strengths directly.

Relationship Between pKa and Ka

The relationship between pKa and Ka is expressed by the equation pKa = -log(Ka). This means that as the Ka increases, the pKa decreases, reinforcing the idea that stronger acids have lower pKa values. Understanding this relationship is crucial for interpreting acid strength comparisons, as it allows for the conversion between the two measures and aids in determining which acid is stronger.