Estimate the K_eq for the following reactions based on the stability of the anions involved.
(a)

Verified step by step guidance

1. Analyze the reaction: The reaction involves the deprotonation of an alkyne to form an acetylide anion and the protonation of a ketone to form an alkoxide anion. The equilibrium constant (K_eq) depends on the relative stability of the anions formed.
2. Step 1: Evaluate the stability of the acetylide anion. Acetylide anions are stabilized by the sp hybridization of the carbon atom bearing the negative charge. The sp hybridization results in a high electronegativity, making the acetylide anion relatively stable.
3. Step 2: Evaluate the stability of the alkoxide anion. Alkoxide anions are less stable compared to acetylide anions because the oxygen atom bearing the negative charge is sp3 hybridized, which is less electronegative than sp hybridized carbon.
4. Step 3: Compare the acidity of the conjugate acids. The conjugate acid of the acetylide anion is the terminal alkyne, which has a pKa of approximately 25. The conjugate acid of the alkoxide anion is the ketone, which has a pKa of approximately 20. Since the terminal alkyne is less acidic, its conjugate base (acetylide anion) is more stable.
5. Step 4: Conclude the direction of equilibrium. Since the acetylide anion is more stable than the alkoxide anion, the equilibrium will favor the formation of the acetylide anion. Therefore, K_eq is expected to be greater than 1, favoring the products.

Key Concepts

Acid-Base Equilibrium

Acid-base equilibrium refers to the balance between acids and bases in a chemical reaction. In this context, it involves the transfer of protons (H+) between species, leading to the formation of anions. The position of equilibrium is influenced by the relative strengths of the acids and bases involved, which can be assessed through their dissociation constants (K_a and K_b).

Stability of Anions

The stability of anions is a crucial factor in determining the favorability of a reaction. More stable anions are less likely to re-accept protons, thus favoring the formation of products. Factors affecting anion stability include electronegativity, resonance, and the size of the atom bearing the negative charge. A more stable anion corresponds to a larger equilibrium constant (K_eq) for the reaction.

Equilibrium Constant (K_eq)

The equilibrium constant (K_eq) quantifies the ratio of the concentrations of products to reactants at equilibrium for a given reaction. A higher K_eq indicates that the products are favored, while a lower K_eq suggests that reactants are favored. In acid-base reactions, K_eq can be estimated based on the relative stabilities of the anions formed, with more stable anions leading to larger K_eq values.