Nicotine 1C10H14N22 can accept two protons because it hastwo basic N atoms 1Kb1 = 1.0 * 10-6; Kb2 = 1.3 * 10-112.Calculate the values of Ka for the conjugate acidsC10H14N2H+ and C10H14N2H22 + .

Verified step by step guidance

1. Identify the relationship between the base dissociation constant \( K_b \) and the acid dissociation constant \( K_a \) for conjugate acid-base pairs: \( K_w = K_a \times K_b \), where \( K_w \) is the ion-product constant of water (\( 1.0 \times 10^{-14} \) at 25°C).
2. For the first conjugate acid \( C_{10}H_{14}N_2H^+ \), use the given \( K_{b1} = 1.0 \times 10^{-6} \) to find \( K_{a1} \) using the formula: \( K_{a1} = \frac{K_w}{K_{b1}} \).
3. For the second conjugate acid \( C_{10}H_{14}N_2H_2^{2+} \), use the given \( K_{b2} = 1.3 \times 10^{-11} \) to find \( K_{a2} \) using the formula: \( K_{a2} = \frac{K_w}{K_{b2}} \).
4. Substitute \( K_w = 1.0 \times 10^{-14} \) and the respective \( K_b \) values into the formulas to calculate \( K_{a1} \) and \( K_{a2} \).
5. Interpret the calculated \( K_a \) values to understand the strength of the conjugate acids: smaller \( K_a \) values indicate weaker acids.

Key Concepts

Acid-Base Equilibrium

Acid-base equilibrium refers to the balance between acids and their conjugate bases in a solution. In this context, nicotine can accept protons, acting as a base, and its conjugate acids are formed when it gains protons. Understanding this equilibrium is essential for calculating the acid dissociation constants (Ka) for the conjugate acids.

Base Dissociation Constant (Kb)

The base dissociation constant (Kb) quantifies the strength of a base in solution, indicating how well it can accept protons. In the given question, Kb1 and Kb2 represent the dissociation constants for nicotine's two basic nitrogen atoms. These values are crucial for determining the corresponding Ka values for the conjugate acids using the relationship between Kb and Ka.

Relationship Between Ka and Kb

The relationship between the acid dissociation constant (Ka) and the base dissociation constant (Kb) is given by the equation Ka × Kb = Kw, where Kw is the ion product of water (1.0 × 10^-14 at 25°C). This relationship allows us to calculate the Ka values for the conjugate acids of nicotine from the provided Kb values, facilitating the understanding of their acidity in solution.