Quadratic Equation vs Approximating

[CaitlinDu_2A]

I'm having trouble deciphering when I would approximate vs when I would use the quadratic equation. For example, I thought in the Achieve hw for week 2 (image below) I could approximate because the Ka is smaller than 10^-3 but the problem tells me to use the quadratic equation instead. Is there something else I need to base it off of?

[Megan Mitchell 2B]

I believe that you can only make the approximation when x is less than 5% of the initial concentration. In this case, the percent ionization was 8.4%, which is above the 5% threshold so you would have to use the full quadratic equation rather than using the approximation.

[Kathleen Vo 1G]

Hey there!

Like mentioned earlier, you can only omit the (-x) from the denominator and approximate if the percent ionization or protonization is less than 5%. But personally, I would recommend taking the extra minute to do the quadratic formula if you are unsure if you can approximate or not. Once you get more comfortable identifying the % ionizations, then should you approximate. It may take a bit more time, but your answers will always be accurate!

[Dolores B]

You also have to be more specific on achieve, sometimes my rounding could be off by .1 and it won't take the answer so it's always best to calculate it all the way through on achieve and just get the extra practice.

[SohelaBedi1E]

You can only remove x from the denominator if the percent ionization or protonation comes out to be less than 5%. I usually opt to use the quadratic equation to solve anyway just to stay on the safe side!

[Kaitlin Lemke 2K]

I would recommend being as specific as possible and only rounding your answer at the end when it comes to Achieve!

[Lauren Hsieh 2I]

If you are unable to determine beforehand whether to approximate or not, I would suggest just approximating for all cases and calculating percent protonation; if it is greater than 5%, then this means the approximation is not valid, meaning you would need to go back and recalculate using the quadratic.