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Solving Cubics

Posted: Wed Jan 16, 2019 1:26 am
by Michelle Fu 1H
I know in the module Dr. Lavelle solved ICE tables involving cubics using the fact the change in X is small because the K value is small. However, what if the K value was large? How would we go about solving the cubic then? Are we expected to know how to for the exam?

Re: Solving Cubics  [ENDORSED]

Posted: Wed Jan 16, 2019 6:39 am
by Chem_Mod
For Chem 14B simplifying the cubic equation when K is small is part of the syllabus.

Solving cubic equations is not part of the syllabus. Therefore examples with large K and solving cubic equations will not occur in Chem 14B.

See my detailed Outlines.

Below is an example simplifying a cubic equation (which can be done whenever K < 10-3).
When K is smaller than 10-3 then X is much smaller than the initial concentration, [I], and therefore: [I] - X is approximately equal to [I].

Note: X is not zero.

But X is much smaller than [I] and therefore the difference is approximately the initial value.

For example, someone with $1 million gives $1,000 to someone with no money. The $1,000 is meaningful (not zero) to the person receiving it.
But initial - change is essentially the initial ($1 million - $1,000 is approximately $1 million).

Cubic Equation.png

In the above example the equilibrium constant is really small.