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When is it appropriate to use the quadratic equation when solving for the ICE box. In lecture lavelle was completing a problem and let us know that the quadratic equation wasnt needed why is this and when is it needed.
The quadratic equation will give you the most accurate answer but the short cut is used when you are given a K value that is less than 10^-3 and this is because that number is so small that it will make no difference so you can disregard the x on the bottom of the fraction. To check this you can solve for x and make sure that it is smaller than 5% of the initial concentration if not then go back and use the quadratic equation.
If you are given a K value that is less than 10^-3 and end up with x variables that are cubed (or higher), you can use the approximation that was shown in class. Although you can use approximations for quadratic equations as well, it is safer to use the quadratic formula to obtain a more accurate answer.
If the K value is very small (less than 10^-3) then you can use the approximation method where you assume that x is so small it won't make a big difference. If the x value you get is less than 5% of the initial concentration, then using the approximation method is valid. Otherwise you need to use the quadratic equation.
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