### Video Transcript

Ammonia is a weak base that ionizes
in aqueous solutions according to the following reaction: NH3 plus H2O are in
equilibrium with NH4+ plus OH‒. What is the equation for 𝐾 𝑏, the
ionization constant?

Ammonia is a weak base that
partially ionizes to produce ammonium and hydroxide ions in solution. To answer the question, we need to
determine an equation for the 𝐾 𝑏 of ammonia.

𝐾 𝑏 is the ionization constant or
base dissociation constant. The base dissociation constant is
the equilibrium constant for the reaction of a base with water. An equilibrium constant is a value
that expresses the relationship of the reactants and products at equilibrium under
certain conditions even when the initial concentrations are different.

For the general equation A plus B
is in equilibrium with C plus D, we can write this equilibrium constant
expression. In the reaction equation and
expression, the capital letters represent the chemical formulas of the reactants and
products, the lowercase letters represent the molar coefficients, and the brackets
indicate that we must use the concentration in moles per liter. We can apply the same principle to
the reaction given in the question to write the base dissociation constant
expression.

Following the generic equation for
an equilibrium constant, we get 𝐾 𝑏 equals the concentration of ammonium times the
concentration of hydroxide divided by the concentration of ammonia times the
concentration of water. 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 equation. This gives us our final equation
for the base dissociation constant.

The equation for 𝐾 𝑏 is 𝐾 𝑏
equals the concentration of NH4+ times the concentration of OH‒ divided by the
concentration of NH3.