### Video Transcript

To one decimal place, what is the
degree of dissociation for a 0.25-molar solution of phenol at 25 degrees
Celsius? The dissociation constant 𝐾 𝑎 is
1.6 times 10 to the negative 10th molar.

The degree of dissociation, often
represented by the symbol 𝛼, is the proportion of a substance that is
dissociated. The degree of dissociation can be
calculated by dividing the amount of the dissociated substance by the total amount
of substance, where the amount can be given as the number of molecules or moles.

To answer this question, we need to
determine the degree of dissociation for a solution of phenol. But the question does not provide
us with the total amount of substance nor the amount of dissociated substance. So we cannot make use of this
equation. The question does provide us with
the acid dissociation constant for the solution of phenol at a given
temperature. The acid dissociation constant is
the equilibrium constant for the dissociation of an acid in water. Phenol is a weak acid that only
partially dissociates when dissolved in water. As only a very small amount of
phenol molecules will dissociate, the concentration of ions in solution at
equilibrium will be very low, while the concentration of the acid will remain
virtually unchanged.

The acid dissociation constant and
the degree of dissociation 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 times the initial concentration of
the acid. For weak acids like phenol, where
only a small percentage of the molecules dissociate, the degree of dissociation is
very small. So, one minus the degree of
dissociation is approximately equal to one. This means that for weak acids,
Ostwald’s dilution law can be simplified to 𝐾 𝑎 is approximately equal to 𝛼
squared times 𝑐 naught. As we need to solve for the degree
of dissociation, we can rearrange this equation to make 𝛼 the subject.

Now we are ready to solve the
problem. We can substitute the acid
dissociation constant and the concentration given in the question into the
equation. Dividing 1.6 times 10 to the
negative 10th molar by 0.25 molar gives us 6.4 times 10 to the negative 10th. Square rooting this value gives us
the degree of dissociation, 2.5298 times 10 to the negative fifth. The question asks us to give our
answer to one decimal place. Rounding appropriately, we have
determined that the degree of dissociation for a 0.25-molar solution of phenol at 25
degrees Celsius is 2.5 times 10 to the negative fifth.