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The 5% rule generally applies to approximation when trying to find x, after performing an ICE table. Instead of using the quadratic formula, you can disregard x relative to the initial if what you get from the approximation is less than 5% of the initial value. The procedure to finding that value is through the percent Ionization.
The 5% rule can be applied after making an approximation for x. You calculate x/[initial concentration given] and if the value is less than 5% (0.05) then the approximation is valid. However, if the value is greater than 5% then you must reject the approximation and recalculate x
it means you can only approximate a value for x on an ice table. you can sidestep the quadratic equation when you apply the approximation threshold. you do this because the value is so insignificant that it doesn't necessarily affect the solution
The 5% rule is used normally in indicating if when setting up the Kc expression if x should be factored into the concentration of the initial reactant. You normally approximate without using that x and if the resulting value x/(initial conc) is less than 5% it is valid to not factor that x in the concentration of the initial reactant.
The 5% Rule essentially means you can approximate the value for x on an ice table because the value is so small it doesn't make a significant change in the concentration. For example, Professor Lavelle talked about how a millionaire giving away $1,000 would barely notice the difference.
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