Question

Phosphoric acid ionizes in three steps with their ionization constant values $K_{a_1}$, $K_{a_2}$ and $K_{a_3}$, respectively, while K is the overall ionization constant. Which of the following statements are true?

• A. log K = log $K_{a_1}$ + log $K_{a_2}$ + log $K_{a_3}$
• B. $H_3PO_4$ is a stronger acid than $H_2PO_4^-$ and $HPO_4^{2-}$.
• C. $K_{a_1} > K_{a_2} > K_{a_3}$
• D. $K_{a_1} = \frac{K_{a_3} + K_{a_2}}{2}$

Answer 1

Answer: (A), (B), (C)

A, B and C

Answer 2

Phosphoric acid ($H_3PO_4$) is a triprotic acid, meaning it can donate three protons in successive steps.

1. Ionization Steps and Equilibrium Constants:

The ionization of phosphoric acid occurs in three steps:

• Step 1: $H_3PO_4(aq) \rightleftharpoons H^+(aq) + H_2PO_4^-(aq)$ $K_{a_1} = \frac{[H^+][H_2PO_4^-]}{[H_3PO_4]}$

• Step 2: $H_2PO_4^-(aq) \rightleftharpoons H^+(aq) + HPO_4^{2-}(aq)$ $K_{a_2} = \frac{[H^+][HPO_4^{2-}]}{[H_2PO_4^-]}$

• Step 3: $HPO_4^{2-}(aq) \rightleftharpoons H^+(aq) + PO_4^{3-}(aq)$ $K_{a_3} = \frac{[H^+][PO_4^{3-}]}{[HPO_4^{2-}]}$

The overall ionization reaction is: $H_3PO_4(aq) \rightleftharpoons 3H^+(aq) + PO_4^{3-}(aq)$

The overall ionization constant, K, is given by: $K = \frac{[H^+]^3[PO_4^{3-}]}{[H_3PO_4]}$

Relationship between K and $K_{a_1}$, $K_{a_2}$, $K_{a_3}$:

$K = K_{a_1} \times K_{a_2} \times K_{a_3}$.

Taking the logarithm:

$\log K = \log (K_{a_1} \times K_{a_2} \times K_{a_3}) = \log K_{a_1} + \log K_{a_2} + \log K_{a_3}$

Acid Strength:

Acid strength decreases with each successive proton removal due to increased electrostatic attraction. Thus, $H_3PO_4$ is stronger than $H_2PO_4^-$, and $H_2PO_4^-$ is stronger than $HPO_4^{2-}$.

Magnitude of Ionization Constants:

Since acid strength decreases with each step, $K_{a_1} > K_{a_2} > K_{a_3}$.

Statement D is false because it proposes an arithmetic relationship that doesn't hold true for ionization constants.