The "x-is-small" Approximation
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The "x-is-small" Approximation
How do we determine when we can use the "x is small" approximation? Is this where the 5% rule comes into play? Or are those two separate things?
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Re: The "x-is-small" Approximation
If the Ka is 10^-3 or lower we need can use the approximation, to rectify our answers we can use the 5% method.
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Re: The "x-is-small" Approximation
The rule is if k is smaller than 10^3 then x is very small so we can approximate. As for the 5% rule, I believe that's to check if the approximation was accurate.
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Re: The "x-is-small" Approximation
Hello!
If our K value in a problem is less than 10^-3 then we can approximate it. What this means is that in our ICE table calculations, when doing the change in initial concentration, we do not need to include x in the equilibrium concentration when doing our calculations. For example, if K = 1.4 x 10^-7 and our ICE table has a 0.685 - x, then when doing our calculation for x, we would only use 0.685 because the -x would be too small to have a noticeable difference. The 5% rule comes in when we get our answer. If our final concentration is less than 5% of the original concentration, then the approximation we did will work. If it is greater, we can NOT approximate and will need to go back and solve the ICE table using the quadratic equation.
If our K value in a problem is less than 10^-3 then we can approximate it. What this means is that in our ICE table calculations, when doing the change in initial concentration, we do not need to include x in the equilibrium concentration when doing our calculations. For example, if K = 1.4 x 10^-7 and our ICE table has a 0.685 - x, then when doing our calculation for x, we would only use 0.685 because the -x would be too small to have a noticeable difference. The 5% rule comes in when we get our answer. If our final concentration is less than 5% of the original concentration, then the approximation we did will work. If it is greater, we can NOT approximate and will need to go back and solve the ICE table using the quadratic equation.
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Re: The "x-is-small" Approximation
If the Ka or Kb is smaller than 10^-3 it is considered small; however, if it is larger than 10^-3 it is considered large.
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Re: The "x-is-small" Approximation
If x is smaller than 10^-3 then you can use the 5% rule. If you see that your final answer for percent ionization is bigger than %5 than that means you're not allowed to use the 5% rule and should redo it using the quadratic formula.
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Re: The "x-is-small" Approximation
If the ka or kb value we are given is smaller than 10^-3, we can approximate the change in initial concentration to be 0 and just leave the initial concentration as is. However this approximation requires us to check the percent ionization to ensure our approximation is not too large. If the percent ionization is below 5%, we can confirm the approximation is valid and that the results are accurate. If the percent ionization is greater than 5 however, we have to go back and use the quadratic equation to find the actual value of x.
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Re: The "x-is-small" Approximation
There is a 5% rule that helps identify whether we keep "x". If your K value is less than 10^-3, it is a sign to eliminate the "x" and proceed with your calculations.
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Re: The "x-is-small" Approximation
In order to calculate and disregard the value that follows x, it must pass the test where the percent ionization is lower than 5%. You must then follow the rule that if the k value is less than 10^-4 or greater than 10^4, it can be disregarded.
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Re: The "x-is-small" Approximation
If the K value is less than 10^-3, then you can use the 5% rule and get rid of the x. If it is larger, you cannot apply it and you have to solve for x using the quadratic formula.
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Re: The "x-is-small" Approximation
Hi,
You can use the "x-is-small" approximation when the equilibrium constant has a value of less than 10^-3. With this condition, you can assume that the concentration of the reactants stays the same throughout the reaction to equilibrium because a very small amount is being consumed to make products.
The 5% rule can be used to "check" if the "x-is-small" approximation is true. For the approximation to be applicable, the percent ionization must be less than 5%.
Hope this helps!
You can use the "x-is-small" approximation when the equilibrium constant has a value of less than 10^-3. With this condition, you can assume that the concentration of the reactants stays the same throughout the reaction to equilibrium because a very small amount is being consumed to make products.
The 5% rule can be used to "check" if the "x-is-small" approximation is true. For the approximation to be applicable, the percent ionization must be less than 5%.
Hope this helps!
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Re: The "x-is-small" Approximation
The 5% rule is applicable to the "x-is-small" approximation, indicating the absence of the minus X for the concentration of the reactants in the K equilibrium expression. In my opinion, an easier way to determine whether the (-x) is needed in the denominator of the equilibrium expression is to use the given K value and if it is less than 10^-3, then the (-x) in the denominator isn't needed.
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Re: The "x-is-small" Approximation
Hi! if the k is smaller than 10^3 we approximate; where as, for the 5% rule you use it to check your answer.
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Re: The "x-is-small" Approximation
Yes, this is where the 5% rule comes into play, which determines if the error would be less than 5%.
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