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).
