### Video Transcript

A weak acid with a dissociation
constant of 1.54 times 10 to the negative fifth moles per liter is found to be 1.26
percent dissociated. What is the concentration of H plus
ions? Give your answer to two decimal
places.

A weak acid, represented in this
generic equation as HA, is an acid that only partially dissociates in aqueous
solution to produce H+ and A− ions. The strength of the acid can be
quantified by its acid dissociation constant. An acid dissociation constant is
the equilibrium constant for the dissociation of an acid in water. It can be calculated by dividing
the equilibrium concentrations of H+ and A− by the equilibrium concentration of the
acid. As acid strength increases, more of
the acid molecules will dissociate into H+ and A− ions and the equilibrium constant
will be larger.

In this question, we’ve been given
the acid dissociation constant of the weak acid. We’ve also been told what
percentage of the acid dissociates. This value is the degree of
dissociation. The degree of dissociation and acid
dissociation constant can be related using Ostwald’s dilution law. Ostwald’s dilution law states that
the acid dissociation constant is equal to the degree of dissociation squared
divided by one minus the degree of dissociation all times the initial concentration
of the acid.

For weak acids, where only a very
small percentage of the acid molecules dissociate, one minus the degree of
dissociation can be approximated to one. So, Ostwald’s dilution law can be
approximated to 𝐾 𝑎 equals 𝛼 squared times 𝑐 naught. Since we’ve been given the acid
dissociation constant and degree of dissociation, we can use Ostwald’s dilution law
to calculate the initial concentration of the weak acid. We’ve been given the degree of
dissociation as a percentage, but before we can substitute it into the equation, we
need to convert the percentage into decimal form by dividing by 100 percent.

Now, we can substitute the 𝐾 𝑎
and 𝛼 into Ostwald’s dilution law. The degree of dissociation squared
is 1.5876 times 10 to the negative fourth. Rearranging to solve for 𝑐 naught,
we find that the initial concentration of the acid is 0.0970 moles per liter. To answer the question, we need to
solve for the concentration of H+ ions at equilibrium. One mole of acid produces one mole
of H+ ions and one mole of A minus ions. This means that the concentrations
of H+ and A− in the solution will be equal. So, we can rewrite the 𝐾 𝑎
expression as 𝐾 𝑎 equals the concentration of H+ times the concentration of H+
divided by the concentration of HA. This can further be simplified to
𝐾 𝑎 equals the concentration of H+ squared divided by the concentration of HA.

Earlier, we calculated the initial
concentration of the acid, but what about the equilibrium concentration? For a weak acid like this one,
where only a small percentage of the molecules dissociate, we can say that the
initial concentration of the acid is approximately equal to the equilibrium
concentration of the acid.

With this in mind, we can
substitute the acid dissociation constant and acid concentration into the
equation. Multiplying both sides of the
equation by the acid concentration gives us 1.4938 times 10 to the negative six
moles squared per liters squared equals the concentration of H+ ions squared. Square rooting both sides of the
equation gives us the concentration of H+ ions, 1.2222 times 10 to the negative
third moles per liter. Rounding our answer to two decimal
places, we have determined that the concentration of H+ is 1.22 times 10 to the
negative third moles per liter.