### Video Transcript

Write the balanced chemical
equation for the reaction represented by the equation below.

The K in this equation is an
equilibrium constant. The subscript b indicates that the
equilibrium constant is a base dissociation constant. Base dissociation constants are
measured where water is the solvent and the reactant. Let’s have a quick review of what
an equilibrium constant is. The equilibrium constant for
equilibrium is equal to the concentration of the products multiplied by their
stoichiometric coefficients all multiplied together, divided by the equivalent for
the reactants. So we know that the ammonium ion
and the hydroxide ion are products in the equation and that ammonia is one of the
reactants. Now we can start constructing the
chemical equation.

The reactants are ammonia and
water. We know that water is there because
base dissociation constants express the equilibrium between a base and water. As this is an equilibrium, we use
the equilibrium arrow. And the products are ammonium and
hydroxide. The question asks for the balanced
chemical equation. So we should check that this
equation is balanced. There’s one equivalent of nitrogen
on both sides of the equation, five equivalents of hydrogen, and one equivalent of
oxygen. The equation therefore is
balanced.

One more thing we can do to make
sure this is the right answer is work backwards and see whether the base
dissociation constant makes sense. The top half of the base
dissociation constant looks right. But what about the bottom half? The concentration of water does not
appear in the original base dissociation constant expression. If we look back at the equation, we
can tell why. Ammonia, ammonium, and hydroxide
are all dissolved in the water whereas water, the liquid, is a solvent. Therefore, its concentration is
assumed to be constant and is eliminated from the dissociation constant
expression. So we’re back to our original base
dissociation constant expression.

And our balanced chemical equation
for the reaction represented by the base dissociation constant expression is NH₃
plus H₂O in equilibrium with NH₄+ plus OH-.