# Question Video: Writing an Equation for the 𝐾_𝑏 of Ammonia Chemistry

Ammonia is a weak base that ionizes in aqueous solutions according to the following reaction: NH₃ + H₂O ⇌ NH₄⁺ + OH⁻. What is the equation for 𝐾_𝑏, the ionization constant?

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### 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.