The equilibrium constant Kn for the neutralization of boric acid (H3BO3) and caffeine (C8H10N4O2) is 24. What is Kb for caffeine? The Ka of boric acid is 5.8 x 10^-10.

Verified step by step guidance

1. Step 1: Understand the relationship between the equilibrium constant (Kn) for the neutralization reaction and the individual constants (Ka and Kb). The reaction involves the neutralization of boric acid (H3BO3) with caffeine (C8H10N4O2), where Kn = Ka * Kb.
2. Step 2: Write the expression for the equilibrium constant Kn in terms of Ka and Kb. Since Kn = Ka * Kb, you can rearrange this equation to solve for Kb: Kb = Kn / Ka.
3. Step 3: Substitute the given values into the equation. You have Kn = 24 and Ka = 5.8 \times 10^{-10}. Substitute these values into the equation Kb = Kn / Ka.
4. Step 4: Perform the division to find Kb. Divide the value of Kn by the value of Ka to calculate Kb.
5. Step 5: Interpret the result. The calculated Kb will give you the base dissociation constant for caffeine, indicating its strength as a base in this neutralization reaction.

Key Concepts

Equilibrium Constant (K)

The equilibrium constant (K) is a numerical value that expresses the ratio of the concentrations of products to reactants at equilibrium for a given chemical reaction. It provides insight into the extent of the reaction; a large K indicates that products are favored, while a small K suggests that reactants are favored. In this context, K is used to relate the acid-base properties of the substances involved.

Acid-Base Equilibrium

Acid-base equilibrium involves the balance between acids and bases in a solution, characterized by their dissociation constants (Ka for acids and Kb for bases). The relationship between Ka and Kb for a conjugate acid-base pair is given by the equation Kw = Ka × Kb, where Kw is the ion product of water. Understanding this relationship is crucial for calculating Kb from the given Ka.

Boric Acid and Caffeine Interaction

Boric acid (H3BO3) is a weak acid, and caffeine (C8H10N4O2) can act as a weak base. The neutralization reaction between an acid and a base leads to the formation of water and a salt, and the equilibrium constant for this reaction can be expressed in terms of the acid's dissociation constant (Ka) and the base's dissociation constant (Kb). This interaction is essential for determining the Kb of caffeine using the provided equilibrium constant for the reaction.