Solving for Cubic Equations
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Solving for Cubic Equations
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?
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Re: Solving for Cubic Equations
I believe you can make x negligible any time K is less than 10^-4, whether it is a cubic, quadratic equation, etc. !
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Re: Solving for Cubic Equations
X can also be made negligible in quadratic equations, for example if you were solving for the [H] concentration of a solution and the Ka or Kb value is very small (less than 10-3). Your equation would be x2/(concinitial-x) = Ka, and you could simplify this to x2/(concinitial) = Ka.
Last edited by Leo Naylor 2F on Sun Jan 31, 2021 10:29 pm, edited 2 times in total.
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Re: Solving for Cubic Equations
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%).
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Re: Solving for Cubic Equations
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.
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Re: Solving for Cubic Equations
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.
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Re: Solving for Cubic Equations
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.
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Re: Solving for Cubic Equations
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!
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Re: Solving for Cubic Equations
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.
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Re: Solving for Cubic Equations
You can make x negligible for any equation where the k value is very small. It is not limited to just cubic equations.
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Re: Solving for Cubic Equations
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.
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Re: Solving for Cubic Equations
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.
Re: Solving for Cubic Equations
depends whenever I solve for pH I always make X negligible since it's not always necessary.
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Re: Solving for Cubic Equations
The value of K must be 1.0x10^-4 or less in order for x to be negligible.
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