Calculate K_eq for the following acid–base reaction.

Verified step by step guidance

1. Step 1: Identify the acid and base on both sides of the reaction. In this reaction, the methyl anion (CH₃⁻) acts as the base, and isopropanol (CH₃CHOHCH₃) acts as the acid on the left side. On the right side, methane (CH₄) is the conjugate acid, and the isopropoxide ion (CH₃CH⁻OCH₃) is the conjugate base.
2. Step 2: Recall the relationship between pKa values and equilibrium constants (Keq). The equilibrium constant for an acid-base reaction can be calculated using the formula: Keq = 10^(pKa(acid on left) - pKa(acid on right)).
3. Step 3: Look up the pKa values for the acids involved. The pKa of isopropanol (CH₃CHOHCH₃) is approximately 16. The pKa of methane (CH₄) is approximately 50.
4. Step 4: Substitute the pKa values into the formula for Keq. Using the formula Keq = 10^(pKa(acid on left) - pKa(acid on right)), substitute pKa(acid on left) = 16 and pKa(acid on right) = 50.
5. Step 5: Simplify the expression to determine the magnitude of Keq. The calculation will show that Keq is a very small number, indicating that the equilibrium strongly favors the reactants (left side of the reaction).

Key Concepts

Acid-Base Reactions

Acid-base reactions involve the transfer of protons (H+) between reactants. In organic chemistry, these reactions are fundamental for understanding the behavior of various compounds, particularly in determining their reactivity and stability. The strength of acids and bases is often quantified using the pKa scale, which helps predict the direction of the reaction.

Equilibrium Constant (K_eq)

The equilibrium constant (K_eq) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given reaction. It provides insight into the favorability of a reaction; a K_eq greater than 1 indicates that products are favored, while a K_eq less than 1 suggests that reactants are favored. Calculating K_eq is essential for understanding the extent of acid-base reactions.

Relationship Between pKa and K_eq

The relationship between pKa and K_eq is crucial in acid-base chemistry. The pKa of an acid is the negative logarithm of its acid dissociation constant (Ka), and it can be used to derive K_eq for acid-base reactions. Specifically, K_eq can be calculated using the difference in pKa values of the acids and bases involved, allowing for a quantitative assessment of the reaction's equilibrium position.