Making X Negligible

[Bronson Mathos 1H]

Hello, I just have a question as to why we cannot make X negligible in quadratic and cubic equations in equilibrium concentration problems when K is greater than 10^-4?

[Lilyana Villa 3L]

I'm not sure about quadratics, but from a previous lecture, I remember Dr. Lavelle saying you can make X negligible when solving for cubic equations since it is really difficult to solve for it and we aren't expected to do that. I hoped this helped!

[Earl Garrovillo 2L]

We can't make X negligible because X has a significant effect on K when it's greater than 10^-4. We say X is negligible when K is less than 10^-4 because it essentially has no effect on the denominator of the fraction. For instance (X^2)/(3-X). As K becomes smaller, ignoring K on the bottom matters less since it'd be like subtracting 0 from 3. But as K increases, lets say K=1, if we assume X is negligible, we will get X=1.7. But if we don't assume X is neglible, we get that X=1.3. This is actually a pretty big difference.

[alette1a]

In an ICE table, x usually represents the amount of reactant that is converted into product. So, when K is very small (we use K < 10^-4 as a threshold in this course), this means that the reaction's equilibrium sits towards the reactants side, and so not a lot of product is made. Therefore, we can exclude the x in the binomial term of the equilibrium expression because its amount is negligible; like a single raindrop in an ocean.

[Caelin Brenninkmeijer 1G]

It's safe to make X negligible when K is less than or equal to 10^-4 because it's difficult to solve and the change is so small it's easier to just approximate. You can always divide X by the initial concentration and if the value is less than 5%, you know that you can use approximation. However, when K is greater than 10^-4, the difference is large enough to have a significant effect on the answer, making it necessary and not negligible.

[Jose Miguel Conste 3H]

the reason for x being negligible is because it is such a small value that it wont really have an effect to a larger number, thats why it is negligble, so any number larger than 10^-4, would mean the change is large enough to consider it

[Kiyoka Kim 3C]

X represents the change in concentration therefore you can ignore X when the equilibrium constant is very small as it means the equilibrium is to the reactants side and not a lot of product is made (a very small change in concentration).