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Divide the x value that you find by the initial concentration to check if it is less than 5% of the initial concentration (less than 5% is deprotonated). This checks if it is small enough to disregard if being subtracted from the initial concentration, making your calculations much easier.
The 5% rule is just a way of making sure that when you remove the x from the bottom of the fraction, you aren't affecting the answer. The idea is if x is less than 5% of the number its being subtracted from, it makes such a little difference that it is mathematically ok to assume x is 0 relative to the bigger number.
You can use the approximation when your K value is smaller than 10^-3 so you can save time not doing the quadratic equation. This is because a value that small in comparison to the initial values given will not affect your x value by much. After solving for x, you can do the % depronated. This is calculated by the x value over the initial value, it should be less than 5% to know that the approximation was valid.
You use the 5 percent rule to make sure that the approximation that you made where x is 0 in the denominator when k is less than 10^-3 is valid and should be used every time you solve for equilibrium concentrations using the ICE chart.
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