When x is negligible in Equilibrium constant

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Marcus Lagman 2A
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When x is negligible in Equilibrium constant

Postby Marcus Lagman 2A » Fri Jan 15, 2021 1:01 pm

Hello!

This was discussed on Wednesday's lecture about cubic equations in solving equilibrium constants. How small does the K have to be in order to remove the x to make an approximation?

Thank you!

Selena Quispe 2I
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Re: When x is negligible in Equilibrium constant

Postby Selena Quispe 2I » Fri Jan 15, 2021 1:04 pm

The equilibrium constant has to be smaller than 10^-3 in order for the x to be negligible. But try to double check by using the 5 percent rule!! Which is when your x has to be less than 5 percent of your initial concentration!!

Stephen Min 1I
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Re: When x is negligible in Equilibrium constant

Postby Stephen Min 1I » Fri Jan 15, 2021 1:04 pm

I believe K has to be less than 10^-4, but there are certain numbers where 10^-3 is also small enough. To verify, you can check that the x is less than 5% of the initial molarity.

Lucy Wang 2J
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Re: When x is negligible in Equilibrium constant

Postby Lucy Wang 2J » Fri Jan 15, 2021 1:07 pm

Hi!

I think Professor Lavelle said that in order for x to negligible, the value must be smaller that 10^-3 but to be safe under 10^-4.

SavannahScriven_1F
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Re: When x is negligible in Equilibrium constant

Postby SavannahScriven_1F » Fri Jan 15, 2021 5:08 pm

For this class, because we are considering small K values to be those that are x 10^-3, we can safely use the x approximation when K is x 10^-4.

Andersen Chu 2H
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Re: When x is negligible in Equilibrium constant

Postby Andersen Chu 2H » Fri Jan 15, 2021 5:15 pm

It needs to be smaller than 10^-3, but be careful because 9.9 x 10^-3 is really close to 10^-2, so you probably shouldn't approximate there. To be safe, you could also just consider 10^-4

Samudrala_Vaishnavi 3A
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Re: When x is negligible in Equilibrium constant

Postby Samudrala_Vaishnavi 3A » Fri Jan 15, 2021 5:15 pm

According to the latest lecture, an easy way to determine this is if the K value is less than 10^-4 or if the x value is less than 5% of the initial value. I think just using the guideline of when K<10^-4 is better considering you won't have to find the x value from the approximation method first and then compare it to the initial value to see if it works as an answer. Basically, you would need to find the x through the approximation method no matter what and see if it's less than 5% of the initial value if you don't use the 10^-4 guideline.

Gwirnowski 3B
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Re: When x is negligible in Equilibrium constant

Postby Gwirnowski 3B » Fri Jan 15, 2021 5:46 pm

X is negligible when K is less than 1x10^-4. This is due to the minute effect it will have on the concentration of whatever is undergoing change, and can be omitted to make solving the problem much easier. It was taught to us that when K is less than 1x10^-3, X is negligible, however always check to make sure the % product produced is under 5%, as then the approximation is fine and will have no effect on your calculations.

Sophia Spungin 2E
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Re: When x is negligible in Equilibrium constant

Postby Sophia Spungin 2E » Fri Jan 15, 2021 5:50 pm

As mentioned, K should be less than 10-3 and ideally less than 10-4. If you want to check whether this approximation is valid, at the very end you can calculate percent ionization using the concentrations you calculated using the approximation. If the value for percent ionization is less than 5%, then your approximation is adequate. Remember that it is not x that is negligible, but the change in concentration of the reactant is so small that it can be assumed to stay the same. X is not zero, it is just adequately small that it has little effect on change in concentration of the reactant. For example, if the initial concentration was 0.340000000000045 M and the final concentration was 0.340000000, these numbers are essentially the same in terms of using them in a calculation.

Mackenzie Van Val 3E
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Re: When x is negligible in Equilibrium constant

Postby Mackenzie Van Val 3E » Fri Jan 15, 2021 7:27 pm

Dr. Lavelle said that x must be smaller than 10^-3, but, to be safe, you should make sure that x is significantly smaller than the molar concentrations- as other commenters have said, 5% is a really good benchmark to use (because 10^-3, in some situations, could be large enough to not be negligible).

Akemi Karamitsos 1E
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Re: When x is negligible in Equilibrium constant

Postby Akemi Karamitsos 1E » Fri Jan 15, 2021 8:17 pm

If we determine that K is less than 10^-3 or, to be safe, less than 10^-4, but get an x greater than 5%, does that mean that we had a mathematical error when calculating our K? Or are we simply unable to use approximation for that particular problem?

Earl Garrovillo 2L
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Re: When x is negligible in Equilibrium constant

Postby Earl Garrovillo 2L » Fri Jan 15, 2021 9:53 pm

As others have said K should be less than 10^-3 but to using 10^-4 is safer. If that's hard to remember, Sapling says that if the molarity of the initial concentration is 1000 times greater than the K, you can assume x is negligent.

austin-3b
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Re: When x is negligible in Equilibrium constant

Postby austin-3b » Fri Jan 15, 2021 10:58 pm

It has to be 10^-4 or smaller, but you can always check using the 5% rule. If x is less than 5% of initial, the approximation is valid.

Talia Dini - 3I
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Re: When x is negligible in Equilibrium constant

Postby Talia Dini - 3I » Fri Jan 15, 2021 11:42 pm

Hi! In order for x to be negligible, K needs to be smaller than 10^-4. One way you can verify your approximation is through the 5% rule which states that if x is less than 5% of the initial value, then x is a valid value.

LeanneBagood_2F
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Re: When x is negligible in Equilibrium constant

Postby LeanneBagood_2F » Fri Jan 15, 2021 11:44 pm

since there's sort of two values being given, just to check my understanding, K should be less than 10^-3 but to be safe (as values can be close to one another) we should just use 10^-4 as our sort of baseline to determine when x is negligible?

Catherine Bubser 2C
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Re: When x is negligible in Equilibrium constant

Postby Catherine Bubser 2C » Sat Jan 16, 2021 7:59 am

If K is greater than 10^-3 would we just use the quadratic formula and not assume x is negligible?

Katie Lam 2J
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Re: When x is negligible in Equilibrium constant

Postby Katie Lam 2J » Sat Jan 16, 2021 10:28 am

Catherine Bubser 2C wrote:If K is greater than 10^-3 would we just use the quadratic formula and not assume x is negligible?

Yes! We cannot assume x is negligible in this case, so we would have to use all of the x values in the quadratic formula.

BKoh_2E
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Re: When x is negligible in Equilibrium constant

Postby BKoh_2E » Sat Jan 16, 2021 10:38 am

It is safest to assume this only when K is less than 10^-4. Remember this is not the same as assuming x is zero in all cases, because we still need to solve x for the problem.

Devin Patel 2D
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Re: When x is negligible in Equilibrium constant

Postby Devin Patel 2D » Sat Jan 16, 2021 10:39 am

In the lecture, I believe we were informed that if the K value is less than 10^-3, we can assume that x is negligible. However, as many others have stated, just to be safe you can use the 5% rule.

Justin Lin 1B
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Re: When x is negligible in Equilibrium constant

Postby Justin Lin 1B » Sat Jan 16, 2021 11:02 am

For x to be negligible, our equilibrium concentration needs to be a value smaller than 10^-4. Professor Lavelle also mentioned in his lecture that we can verify the approximation if x is less than 5% of the initial concentration given to you.

apurva-3E
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Re: When x is negligible in Equilibrium constant

Postby apurva-3E » Sat Jan 16, 2021 11:54 am

The equilibrium constant has to be smaller than 10^-3

George Hernandez 3I
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Re: When x is negligible in Equilibrium constant

Postby George Hernandez 3I » Sat Jan 16, 2021 12:08 pm

Smaller than 10^-3 to be safe. A value that incredibly small will have pretty much zero effect on yoyr approximations

ShinwooKim_3E
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Re: When x is negligible in Equilibrium constant

Postby ShinwooKim_3E » Sat Jan 16, 2021 1:31 pm

Less than 10^-3, I believe!

keely_bales_1f
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Re: When x is negligible in Equilibrium constant

Postby keely_bales_1f » Sat Jan 16, 2021 5:58 pm

Smaller than 10^-3 he said!

DavidTabib 3H
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Re: When x is negligible in Equilibrium constant

Postby DavidTabib 3H » Sat Jan 16, 2021 6:40 pm

The safest bet is when K is less than 10^-4

Austin Aldujaili 2D
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Re: When x is negligible in Equilibrium constant

Postby Austin Aldujaili 2D » Sat Jan 16, 2021 7:59 pm

It is probably best to assume x is negligible when K is < 10^-4 although. sometimes I hear Professor Lavelle say 10^-3.

Kyle Dizon 3A
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Re: When x is negligible in Equilibrium constant

Postby Kyle Dizon 3A » Sat Jan 16, 2021 8:18 pm

Based on some of the UA's, an equilibrium constant smaller than 10^-4 would allow you to disregard the x for an approximation.

Annie Liang 3D
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Re: When x is negligible in Equilibrium constant

Postby Annie Liang 3D » Sat Jan 16, 2021 8:50 pm

The K must be smaller than K^-3!

Bryan Le 2K
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Re: When x is negligible in Equilibrium constant

Postby Bryan Le 2K » Sat Jan 16, 2021 8:51 pm

X is negligible when the value is smaller than 10^ -4.

Ashley Wagner 2A
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Re: When x is negligible in Equilibrium constant

Postby Ashley Wagner 2A » Sat Jan 16, 2021 8:57 pm

It is negligible when K is smaller than 10^-3, the safer option is 10^-4.

Javier Perez M 1H
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Re: When x is negligible in Equilibrium constant

Postby Javier Perez M 1H » Sat Jan 16, 2021 9:36 pm

Yeah this is a bit confusing given that he had mentioned that the concentration had to be smaller than 10^-3 but most recently 10^-4. Lavelle please clarify this.

Jason_John_2F
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Re: When x is negligible in Equilibrium constant

Postby Jason_John_2F » Sat Jan 16, 2021 10:10 pm

i think k needs to be under 10^-4

Taylor Newville 1C
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Re: When x is negligible in Equilibrium constant

Postby Taylor Newville 1C » Sat Jan 16, 2021 10:15 pm

Even in K is less than 10^-4 and we are able to approximate, will we get the correct answer if we use the quadratic formula instead?

Halle Villalobos 3E
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Re: When x is negligible in Equilibrium constant

Postby Halle Villalobos 3E » Sat Jan 16, 2021 11:11 pm

Hi! Lavelle noted in a lecture that if the K value is less than 10^-4, the x can be negligible. Another way of checking is to see if the x value is less than 5% of the initial concentration given. I hope this helps!

Gian Boco 2G
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Re: When x is negligible in Equilibrium constant

Postby Gian Boco 2G » Sun Jan 17, 2021 3:37 am

According to Lavelle, the safest would be below 10^-4


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