Solving for Cubic Equations

[Bronson Mathos 1H]

Hello, I was wondering if making X negligible when solving equilibrium questions is possible with other scenarios than a cubic equation? I do understand that the K value must be extremely small, but is a cubic set up the only time we can make X negligible?

[Giselle Granda 3F]

I believe you can make x negligible any time K is less than 10^-4, whether it is a cubic, quadratic equation, etc. !

[Leo Naylor 2F]

X can also be made negligible in quadratic equations, for example if you were solving for the [H] concentration of a solution and the K_a or K_b value is very small (less than 10^-3). Your equation would be x²/(conc_initial-x) = K_a, and you could simplify this to x²/(conc_initial) = K_a.

[Kelly Ha 1K]

The change in X can be considered negligible whenever K is less than 10^-4. This approximation isn't just limited to solving cubic equations since we can do this with quadratics too. (Keep in mind this approximation is only valid if percent dissociation is less than 5%).

[lauren_tran_1L]

I believe Dr. Lavelle said we are only sticking to quadratic equations right now. But make sure to double check the K value! This would give away when you can make the assumption.

[Sarah Salam 1J]

I believe we were given an example where the X was negligible in a quadratic equation. It just depends on whether X is small enough, under 10^-4.

[Kaihan_Danesh_2J]

Making x negligible is alright anytime K is 10^-4 or less. It does not matter the situation, if the K value is that small, you can make x negligible. But, it can only be negligible for the denominator because you must still solve for the x in the numerator of the K equation.

[Jack_Pearce_2H]

You can approximate the solution (make X negligible) if the K value for the acid/base is at least 1.0x10^-4 or less than that. This method can be used for any setup (quadratic, cubic) but you should always test the approximation by taking the value, subtracting the x you achieved using approximation and dividing it by the initial concentration of the acid/base. If it is less than or equal to 5% then you are in the clear!

[Andy Hon 3E]

I was reviewing some of the lectures and the example that was used for the weak acid problem was to calculate the percent ionization, which is the final product over its initial (not at equilibrium) value. If the percentage was less than 5 percent then approximating was valid.

[Shruti Kulkarni 2I]

You can make x negligible for any equation where the k value is very small. It is not limited to just cubic equations.

[Michelle Nguyen 3F]

You can make x negligible anytime that the equilibrium constant, K, is less than 10^-4, regardless of whether it is a quadratic, cube, etc.

[Alexandra Ahlschlager 1L]

Cubic equations are not the only instance where you can make X negligible. You can use this process anytime the equilibrium constant is less than 10^-4. You can also use the 5% rule by making sure that your final concentration is less than 5% than the initial concentration. If it is, then you can consider X negligible.

[Anvy 1G]

depends whenever I solve for pH I always make X negligible since it's not always necessary.

[Katelynn Shaheen 2C]

The value of K must be 1.0x10^-4 or less in order for x to be negligible.