Question Video: Identifying the Correct Equation for the Base Dissociation Constant of a Generic Weak Base | Nagwa Question Video: Identifying the Correct Equation for the Base Dissociation Constant of a Generic Weak Base | Nagwa

Question Video: Identifying the Correct Equation for the Base Dissociation Constant of a Generic Weak Base Chemistry • Third Year of Secondary School

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The equation for the dissociation of B, a weak base, is B(aq) + H₂O(l) ⇌ BH⁺(aq) + OH⁻(aq). What is the corresponding expression for the base dissociation constant (𝐾 𝑏)?

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Video Transcript

The equation for the dissociation of B, a weak base, is B aqueous plus H2O liquid are in equilibrium with BH+ aqueous plus OH− aqueous. What is the corresponding expression for the base dissociation constant, 𝐾 𝑏? (A) 𝐾 𝑏 equals the concentration of B aqueous. (B) 𝐾 𝑏 equals the concentration of BH+ aqueous times the concentration of OH− aqueous. (C) 𝐾 𝑏 equals the concentration of BH+ aqueous times the concentration of OH− aqueous times the concentration of B aqueous. (D) 𝐾 𝑏 equals the concentration of BH+ aqueous times the concentration of OH− aqueous divided by the concentration of B aqueous. (E) 𝐾 𝑏 equals the concentration of B aqueous divided by the concentration of BH+ aqueous times the concentration of OH− aqueous.

A base dissociation constant, represented by 𝐾 𝑏, is an equilibrium constant for the reaction of a base with water. An equilibrium constant is a value that expresses the relationship between the reactants and products at equilibrium.

Let’s consider a generic equilibrium reaction equation. In this equation, the lowercase letters represent stoichiometric coefficients and the uppercase letters represent chemical formulas. We can write an expression for the equilibrium constant for this reaction. In this expression, the concentrations of the products are divided by the concentrations of the reactants, where each concentration is raised to the power of the respective stoichiometric coefficient.

We can use this generic equilibrium constant expression to write an expression for the base dissociation constant for the given reaction. We start by writing each of the products inside of brackets in the numerator. Then, we write each of the reactants inside of brackets in the denominator. All of the stoichiometric coefficients in the chemical equation are one. So it seems we have arrived at the correct expression for the base dissociation constant. However, for dilute aqueous solutions, the concentration of water will remain virtually unchanged over the course of the reaction. So, we can assume that the concentration of water is constant and remove it from the expression. This gives us the correct expression for the base dissociation constant. 𝐾 𝑏 equals the concentration of BH+ aqueous times the concentration of OH− aqueous divided by the concentration of B aqueous, answer choice (D).

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