Video Transcript
To one decimal place, what
percentage of chloroacetic acid molecules are not dissociated in a 0.11-molar
aqueous solution at 25 degree Celsius? The dissociation constant 𝐾 𝑎 of
chloroacetic acid is 1.4 times 10 to the negative third. Assume that one minus 𝛼 is
approximately equal to one.
In this question, we want to know
what percentage of chloroacetic acid molecules in a solution are not
dissociated. The extent to which an acid
dissociates can be represented by the degree of dissociation, given the symbol
𝛼. The degree of dissociation is the
proportion of a substance that is dissociated. This value is often given as a
percentage.
The degree of dissociation can be
related to the acid dissociation constant 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 many weak acids, the degree of
dissociation is very small. So one minus the degree of the
dissociation is approximately equal to one. This means we can simplify
Ostwald’s dilution law to 𝐾 𝑎 equals 𝛼 squared times 𝑐 naught.
We are given the acid dissociation
constant and initial acid concentration in the question. We can substitute these values into
the expression to solve for the degree of dissociation. In this problem, the acid
dissociation constant is given as a dimensionless value. Degree of dissociation is also
dimensionless. So before we solve the problem, we
will need to remove the molar unit, as it won’t cancel. Dividing both sides by 0.11 gives
us 0.0127 equals 𝛼 squared. Square rooting both sides of the
equation gives us the value for the degree of dissociation, 0.1128.
Degree of dissociation is often
reported as a percentage. So we can multiply our answer by
100 percent to give us 11.28 percent. This value represents the
percentage of chloroacetic acid molecules that are dissociated. But in the question, we want to
know what percentage are not dissociated. So we simply need to subtract the
percentage of molecules that are dissociated from 100 percent to find that 88.72
percent of the molecules are not dissociated.
Lastly, we need to round our answer
to one decimal place. In conclusion, the percentage of
chloroacetic acid molecules that are not dissociated is 88.7 percent.
