Approximation of X in cubic equations

[Alexandra Salata 2L]

In the example in at the beginning of Lecture 4, Dr. Lavelle said that since Kc is very small we can approximate that the concentrations of the compounds will stay roughly the same, and this is how we would calculate X to figure out the composition of the equilibrium mixture. Would Kc always be small in questions like this so we can work out the value of X in this way?

[Andrew Wang 1C]

I'm pretty sure Kc will always be small on these questions since Dr. Lavelle said we wouldn't be able to algebraically solve cubic equations, so we have to just approximate.

[Wil Chai 3D]

The rule of thumb he mentioned was that we could use the approximation whenever K<10^-4.

[Crystal Yu 1D]

Another good way to tell if Kc is small is to think of the number comparatively. If Kc is 10^-4 and all the other values are just 0.3, then Kc is relatively much smaller meaning that you can approximate and make the calculation easier. Hope this helps! :)

[alette1a]

I agree with all of the above replies! Also, be sure when approximating to only discount the x used in binomial terms (i.e. 1 - x or 1 + x). If you were to remove an x standing alone, you would get a result of 0, which would not make sense.

[Kimiya Aframian IB]

In the example in at the beginning of Lecture 4, Dr. Lavelle said that since Kc is very small we can approximate that the concentrations of the compounds will stay roughly the same, and this is how we would calculate X to figure out the composition of the equilibrium mixture. Would Kc always be small in questions like this so we can work out the value of X in this way?

Hi!! Dr. Lavelle mentioned that we shouldn't worry about solving cubic functions and that in questions where we do have a cubic function, our Kc will be small enough that we can assume x is small. Hope this helps!