If equilibrium constant for the reaction, .XO^-(aq)+H2 O(1) ⇌HXO(aq)+OH^-(aq) is 0.36 ×10^-6 the

step 1 Here in this question we are given with the equilibrium constant for this reaction and we need t

If equilibrium constant for the reaction, .XO^-(aq)+H2 O(1)...

If equilibrium constant for the reaction, $\left.\mathrm{XO}^{-}(\mathrm{aq})+\mathrm{H}_2 \mathrm{O}(1) \rightleftharpoons \mathrm{HXO}_{(\mathrm{aq}}\right)+\mathrm{OH}^{-}(\mathrm{aq})$ is $0.36 \times 10^{-6}$ then find the value of dissociation constant $\left(\mathrm{K}_{\mathrm{a}}\right)$ for HXO ? (a) $0.36 \times 10^{-8}$ (b) $2.8 \times 10^{-8}$ (c) $2.8 \times 10^{-10}$ (d) $0.36 \times 10^{-6}$

If equilibrium constant for the reaction, $\left.\mathrm{XO}^{-}(\mathrm{aq})+\mathrm{H}_2 \mathrm{O}(1) \rightleftharpoons \mathrm{HXO}_{(\mathrm{aq}}\right)+\mathrm{OH}^{-}(\mathrm{aq})$ is $0.36 \times 10^{-6}$ then find the value of dissociation constant $\left(\mathrm{K}_{\mathrm{a}}\right)$ for HXO ?
(a) $0.36 \times 10^{-8}$
(b) $2.8 \times 10^{-8}$
(c) $2.8 \times 10^{-10}$
(d) $0.36 \times 10^{-6}$

Key Concepts

Acid Dissociation Constant (Ka)

The acid dissociation constant (Ka) quantifies the strength of an acid in solution by measuring the equilibrium concentration of its ions when the acid donates a proton to water. A higher Ka value indicates a stronger acid that dissociates more completely. In problems involving conjugate acid-base pairs, Ka provides insight into the tendency of the acid to lose a proton.

Base Ionization Constant (Kb)

The base ionization constant (Kb) measures the strength of a base in solution by indicating how effectively it accepts a proton from water. For the conjugate base of an acid, Kb is derived from the equilibrium between the base, water, the conjugate acid, and hydroxide ions. It is an essential parameter when working with related acid-base equilibria.

Conjugate Acid-Base Pair Relationship

Conjugate acid-base pairs involve an acid and its corresponding base that is formed after the acid donates a proton. The relationship between these pairs is governed by the expression Ka × Kb = Kw, where Kw is the ion product of water. This relationship is fundamental for converting between the acid dissociation constant and the base ionization constant in aqueous solutions.

Ion Product of Water (Kw)

The ion product of water (Kw) is the equilibrium constant for the self-ionization of water, defined as the product of the molar concentrations of the hydrogen ions and hydroxide ions. At room temperature, Kw is approximately 1 × 10?¹?. This constant links the acid and base dissociation constants in aqueous solutions through the relation Ka × Kb = Kw, and is critical for analyzing acid-base equilibria.

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