Video Transcript
The equations below show a form of
Ostwald’s law of dilution along with its simplified form. Which of the following
approximations results in the simplified form of the equation? (A) When 𝛼 is very small, one
minus 𝛼 can be approximated to be equal to one. (B) When v is very large, one minus
𝛼 can be ignored in the equation. (C) When 𝛼 is very large, one
minus 𝛼 can be approximated to be equal to zero. (D) For strong acids, 𝛼 approaches
one, and so one minus 𝛼 can be approximated to be equal to zero.
Ostwald’s law of dilution can help
us characterize how much a chemical species, such as a weak acid, dissociates into
ions in solution. The law of dilution relates the
acid dissociation constant of the weak acid to the degree of dissociation. The degree of dissociation is equal
to the amount of dissociated substance divided by the total amount of substance.
For a weak acid, we can usually
apply an approximation that can help us simplify the law of dilution. This is because the degree of
dissociation is typically very small for a weak acid. If 𝛼 is very small, one minus 𝛼
will be approximately equal to one. If one minus 𝛼 is approximated to
be equal to one, we will arrive at the simplified form of the law of dilution. This matches answer choice (A), but
we can quickly confirm that the other approximations are incorrect.
Answer choice (B) states that when
v is very large, one minus 𝛼 can be ignored. So, for example, let’s assume v
equals 100 and one minus 𝛼 equals 0.8. Comparing the denominators of the
two expressions, there is a large difference between 100 and 80. So, this wouldn’t be a very good
approximation.
In answer choices (C) and (D), one
minus 𝛼 is approximated to be equal to zero. If one minus 𝛼 was equal to zero,
we will end up with zero in the denominator. So, the equation will be
undefined.
So, the approximation that results
in the simplified form of Ostwald’s law of dilution is statement (A). When 𝛼 is very small, one minus 𝛼
can be approximated to be equal to one.
