Approximately x
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Approximately x
Hello,
When is it appropriate to assume that x is so small therefore to be considered zero when calculating for the equilibrium constant? Also, would it affect sig fig condition in the end?
Thank you!
When is it appropriate to assume that x is so small therefore to be considered zero when calculating for the equilibrium constant? Also, would it affect sig fig condition in the end?
Thank you!

 Posts: 40
 Joined: Wed Nov 18, 2020 12:30 am
Re: Approximately x
We can approximate that x is small whenever the Ka < approximately 10^{3}. Professor Lavelle said that to be safe, whenever Ka < 10^{4}, you can use the approximation. You can test to see if the approximation is valid by seeing if (x/initial concentration)*100 < 5%. I don't think that approximating x is small would really affect the sigfigs at the end, as there is still usually a x somewhere else in the expression, and usually the number of sigfigs depend on the number of sigfigs in the Ka (or the Kb if that was given in the problem), the initial concentration/partial pressure, and the pH or pOH. Hope this helps!

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Re: Approximately x
Hi!
The general rule of thumb is if it is smaller than 10^4. If you think it's safe to assume that x is 0, but aren't sure, you can always calculate the percent ionization (which is (concentration/initial concentration)(100%)) after you find the concentrations. If the percent ionization is less than 5%, your approximation is correct. If it is more than 5%, you need to redo the calculation with the x. Hope this helps!
The general rule of thumb is if it is smaller than 10^4. If you think it's safe to assume that x is 0, but aren't sure, you can always calculate the percent ionization (which is (concentration/initial concentration)(100%)) after you find the concentrations. If the percent ionization is less than 5%, your approximation is correct. If it is more than 5%, you need to redo the calculation with the x. Hope this helps!

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Re: Approximately x
Whenever K is a really small value, less than 10^4, we can assume that the change in concentrations of the compounds is very small. Also, I think that if there is ever a point where you are not sure whether or not you can assume x is extremely small, Dr. Lavelle said you can use the quadratic equation regardless. That way, you will definitely calculate the correct value of x, and at the same time, it will tell you if the change in concentrations or pressure is small. Hope this helped!

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Re: Approximately x
If the K value is less than 10^4, it is safe to approximate. Just to be safe though, make sure that your xvalue is less than 5% of the initial concentration (x/initial conc. * 100% < 5%). Hope this helps!

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Re: Approximately x
Hi! If K < 10^4, then you can approximate when solving for x. If you are unsure about whether or not your approximation is valid, or if you want to check to see if your approximation is valid, you can substitute values into this expression: (x/initial concentration) x 100. If the value is less than 5%, then your approximation is valid.

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Re: Approximately x
Lavelle has said that if Ka is less than 10^4, it is ok to approximate, but I think that the safe rule is that if the initial concentration is 10^3 times bigger than the Ka, it is ok to approximate. Also, make sure that the x value that you get is less than 5% of the initial concentration. Hope this helps!

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Re: Approximately x
Lavelle has gone back and forth between saying k<10^4 and k<10^3 so honestly I would say as long as it's less than 10^3 you can assume the value of X is negligible, and if it's less than 10^4 then It's VERY reasonable to make the assumption.

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Re: Approximately x
Hello!
Typically when K is lower than 10^5, then it is a good gauge on whether or not to approximate. When the percent of ionization is less than 5%, then approximation of x can definitely be used.
x is so small that its decrease from the original reactant concentration is negligible. However, the final concentrations are significant to the K value that they cannot be neglected regardless of how small x is.
Typically when K is lower than 10^5, then it is a good gauge on whether or not to approximate. When the percent of ionization is less than 5%, then approximation of x can definitely be used.
x is so small that its decrease from the original reactant concentration is negligible. However, the final concentrations are significant to the K value that they cannot be neglected regardless of how small x is.

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Re: Approximately x
I see people saying that we can assume this when Ka is less that 10^3. Doesn't this mean that for problem 1 on the sapling, we could have assumed that x was 0? For this one I just used the quadratic formula?

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Re: Approximately x
After reading this thread I am a little confused. What does it mean to approximate x as 0? Could you do this on any of the homework problems? I solved all of them with the quadratic equation. How would you do it the other way?

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Re: Approximately x
when k is less than 10^4 if you want to be safe but check percent ionization to make sure!

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Re: Approximately x
Jaden Joodi 3J wrote:After reading this thread I am a little confused. What does it mean to approximate x as 0? Could you do this on any of the homework problems? I solved all of them with the quadratic equation. How would you do it the other way?
when you list out the ICE table, you can assume that the reactant changed very little and can approximate x=0. using the quadratic equation gives you the accurate answer, but sometimes, when K is lees than 104, the change in reactant can be very small, and thus you can neglect it.

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Re: Approximately x
It is safe to do so when the K value is 10^4 or smaller. If you think that your approximation might not be accurate you can always plug the values that you get into the equilibria equation to see if you get the same equilibrium value with your approximate concentrations. It should not affect the sig figs because the change caused by the approximation should be small enough that it has little to no effect on the value that you get.

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Re: Approximately x
According to Dr. Lavelle, we can use this approximation when the Kvalue is smaller than 10^4.

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