Approximation in Calculations
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Approximation in Calculations
When going through the ICE box calculations for weak acids and bases, how do you know when it is ok to assume that x is really small and just approximate? Thanks!
Re: Approximation in Calculations
I believe that to start you can always assume that x is small enough to approximate, but at the end, once you have X you have to go back and make sure that it's less than 5% of the initial molarity. (You do this by doing X/Initial) If it is, then the approximation is okay. If it isn't then the approximation isn't valid and you'd have to re-do the problem with the quadratic equation.
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Re: Approximation in Calculations
Good question! :) Generally, in a K expression, make the assumption that x is very small compared to a number so that you can avoid using the quadratic formula to solve for x. Once you solve for x, use this formula: x/(the number you said it was very small compared to) times 100. If this formula gives you 5 or lower, your assumption is good and you don't have to use the quadratic formula. If the formula gives you more than 5, your assumption isn't very good and you do have to use the quadratic formula to solve for x. (this is called the 5% rule)
Re: Approximation in Calculations
If one can approximate would it be recommended to approximate then solve through the quadratic equation?
Re: Approximation in Calculations
no, you only need to solve the quadratic equation if the approximation doesn't meet the 5% rule! :) If it does meet the rule then it means that x is small enough that the approximation gives an answer that's essentially the same as if you had done the quadratic equation
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