### Video Transcript

A 0.3 molar solution of benzoic
acid was found to be 1.47 percent dissociated. What is the value of πΎ π to two
decimal places for this acid? Assume one minus πΌ is
approximately equal to one.

Benzoic acid is a weak acid. When it is dissolved in water, only
a portion of the molecules will dissociate into benzoate ions and hydrogen ions. We are told that 1.47 percent of
the acid was found to be dissociated. This means that if we dissolved 100
moles of benzoic acid in water, at equilibrium 1.47 moles will have dissociated into
ions, while the remaining 98.53 moles are undissociated. The proportion of the substance
that is dissociated is called the degree of dissociation. It is usually represented by the
symbol πΌ and is typically given as a decimal. We were given the percentage of
dissociation. We can convert the percentage of
dissociation to a decimal by dividing by 100 percent. So the degree of dissociation of
the benzoic acid given in the question is 0.0147.

We want to use the degree of
dissociation to calculate the value of πΎ π. πΎ π is the acid dissociation
constant, an equilibrium constant for the dissociation of an acid in water. The acid dissociation constant and
the degree of dissociation can be related using Oswaldβs dilution law. In this expression, π naught
represents the initial concentration of the acid. The question tells us that the
concentration is 0.3 molar. We know the degree of dissociation
and the concentration. So we could put those values into
the expression and solve for πΎ π. But the question tells us to assume
that one minus πΌ is approximately equal to one.

If the denominator of the
expression is approximately equal to one, we can rewrite the expression as πΎ π is
approximately equal to πΌ squared times π naught. We can substitute the degree of
dissociation and concentration into the expression and perform the calculation to
determine the acid dissociation constant. Rounding our answer to two decimal
places, we have determined that the value of πΎ π for benzoic acid is 6.48 times 10
to the negative fifth molar or moles per liter.