X was ignored
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X was ignored
In my discussion, when solving for x after doing the ice table we got x^2/(.10-x). Then when we plugged in the Ka= 1.8 x 10^-5 so the equation was 1.80 x 10^-5 = x^2/.10. Why is it that the -x was ignored?
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Re: X was ignored
The -x was ignored because the value would have been so small that 0.1-x would be rounded to 0.1. If K is less than 10^-3, you generally ignore the -x and use the initial concentration without explicitly factoring in the change.
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Re: X was ignored
If you are unsure about the cutoff for ignoring X, you can generally ignore if K is less than 10^-3 but you can always ignore if less than 10^-5.
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Re: X was ignored
X was ignored since K was so small (less than 10^-3) and X would make such a small change to .10
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Re: X was ignored
x was ignored in this case because K is less than 10^-3 so you know that x is going to be too small for it to make a difference in that case. You can test to see if this approximation is accurate as long as your final answer is less than 5% of the initial
Re: X was ignored
This is called the X is small approximation. Relative to the initial concentration, the change is so small, less than 10^-3 smaller, so we can treat it as the same number before and after without significant change. This makes our math much, much easier.
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Re: X was ignored
If the given K is less than 10^-3, then you can use approximation, meaning that you can disregard the X because it is small enough that it would not profoundly impact your equilibrium expression.
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Re: X was ignored
when the K is less than 10^-3, the x subtracted. is going to make such a small difference it's acceptable and easier to just ignore it. Only ignore when it is addition or subtraction though, you should include it in multiplication or division I believe. If concentration. found is less than 5% of the initial concentration that also confirms it was ok to do the. approximation
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Re: X was ignored
Since X had such a small value, removing it wouldn't change anything. The x wouldn't have had a big enough change on the 0.10.
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Re: X was ignored
The removal of the -x occurs because it is extremely small relative to the chemical equilibrium. We don’t say it is 0 because the numerator would be affected. We say it is small relative to the rest of the equilibrium allowing it to be ignored.
Re: X was ignored
The x value is so small that when you subtract it from .10 it doesn't make a big chante to it, so you can ignore it. When you ignore it, it becomes easier to solve for x because you would now have Ka = x^2/.10
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Re: X was ignored
X value was ignored because the K value was so small, meaning the amount of product formed compared to the reactants was very small. This means that the amount of products (x) can technically be ignored as a change factor which is why you can eliminate it.
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Re: X was ignored
Because K is such a small value, < 10^-3, we can assume x will be so small that it is inconsequential. As a result, we ignore the -x in the denominator and solve as if it were not there.
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Re: X was ignored
Why do we see if our approximation is correct by checking if the final answer is less than 5% of the initial? Is there a particular reason we use 5% as the cutoff?
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Re: X was ignored
the -x was ignored because the value is so small that it makes no difference to include it or not. This is called a small approximation.
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Re: X was ignored
1.8x10^-5 expanded is the same thing as .000018. .1-.000018 = .09999 something, which is very very close to .1. So when x is very small, it will not affect the constant in any significant way
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Re: X was ignored
X was ignored because 0.10 is less than 10^-3, which means it is so small that it would not make a difference to decrease by X; therefore, you only use the 0.10 (think of Dr.Lavelle's example of the million dollars minus $10).
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Re: X was ignored
x is very small so it is basically zero for the denominator (0.0000000000000000001), but we leave x alone in the numerator cause having 0 up top would make the whole thing=0.
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Re: X was ignored
The x is ignored because it is such a small value, thus will not affect the answer extremely. When doing calculations with small x, make sure you do not just plug in 0, but rather emphasize that it is negligible not 0.
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Re: X was ignored
Since Ka is smaller than 103 you can ignore the x in the denominator. Since K is so small, x is negligible in this case and can be ignored for the sake of convenience of calculating.
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Re: X was ignored
Because your Ka is less than 10^-3. Since Ka then is so small, you can ignore it for the denominator
Re: X was ignored
you usually ignore the -x when the Ka or Kb is less than 10^-3 because it has little effect to the concentrations
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Re: X was ignored
If the Ka or Kb is less than 10^-3, then the x on the bottom can be ignored because the x value will be so small that it won't make a big difference to the original concentration.
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Re: X was ignored
If you were unsure as to if x is a small enough value to ignore you could also just solve the problem as you usually would and get a correct answer it would just be more work.
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Re: X was ignored
you can ignore x when making an approximation. this can be done when Kb or Ka is less than 10^-3
Re: X was ignored
The X can be ignored because it is so small and wouldn't cause a change in concentration
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