Approximation and Quadratic Formula

[405513470]

I thought that we ca assume x is negligible if the K is 10^-4 or less. However I read on achieve that if the percent ionization is >5% we must we the quadratic formula. How would that be possible since we need to calculate for x concentrations in order to calculate the ionization percentage?

[Mari Masunaga 1G]

Hi. I think I also remember learning that as long as Ka<10^-4 we can assume that x is negligible.The 5% rule may be a little bit more accurate however. I think the reason the professor told us we can neglect x if Ka is less than 10^-4 is because in most cases the percent ionization will also be less than 5%. I think in this problem you will notice that the percent ionization is pretty close to 5% anyways and your answers only vary by a little. hope this helps!

[Sharlene Duong 3E]

I think you calculate the x using the approximation first. Once you find x, if the concentration you get is less than 5% of the initial concentration then you can use this approximation of x. However, if x is more than 5% of the initial concentration then you would have to use the quadratic formula to find x. Hope this is a little clearer!

[Andrew Yim 1K]

Hi,
You always have to check the percent ionization after you use the approximation shortcut. If the percent ionization if over 5%, you have to go back and use the quadratic formula.

[Ethan Cheng 2k]

On achieve the solution says that another way to tell if you can approximate is to see if the initial concentration is more than 1000 times greater than Ka. If it is, then you can approximate. This might be a more accurate way of seeing if you can approximate than just looking at Ka to see if it is <10_3, but I'm not sure.

[Wren Xu 3A]

I think it is because the approximation is not as accurate when percent ionization is >5%

[Macy_Anderson_2F]

If the Ka is <10^-4 then you are able to approximate x in your calculations. If you find that the percent ionization is greater than 5% using the approximated x value then you should redo the problem using the quadratic formula to get a more precise answer

[Albert Chen 1G]

Hello, I think for a problem like this, it is always safe to check it over again if ionization percentage is greater than 5 percent. So, first, calculate assuming x is negligible and if percent ionization is greater than 5 percent, you must use the quadratic formula.

[Natasha]

When percent ionization is over 5 percent then approximation cannot be used because the value would be too big. This is when the quadratic formula should be used instead.

[Jessica Sun 2I]

if the ionization % is below 5%, then it is okay to approximate the x value to be negligible. This is a good check because sometimes a Ka value is below 10^-4 but the ionization % is above 5% so the quadratic formula is needed to solve the problem.

[Michelle Jeong 1B]

Hi since it is pretty quick to get x if you approximate, if I think the Ka value is small enough I will approximate then find the % ionization and it is <5% then I will use that but if it is >5% you have to use the quadratic formula.

[Savannah Licciardello 2C]

In this situation, even though 10^-4 is less than 10^-3, that does not guarantee you can approximate. For this scenario, 10^-4 is too big, hence why it failed the 5% test, so you have to use the unsimplified form.

[Srikar_Chintala_1E]

You actually use both for an accurate answer! First you can approximate, but then you have to see if the percent ionization is less than 5% to make sure you approximation is correct.

[Naomi Christian 1E]

Even if you approximate, once you find X you should always check to make sure the percent ionization is less than 5%. If it isn't you have to redo it with the quadratic formula.