Approximations

[KyLee 1H]

Hi!
So, I know that when the K is small enough, we can make an approximation to make the calculation slightly easier. And, we confirm the appx by making sure the amount is less than 5% the initial. However, if it isn't less than 5%, what do we do from there? Do we just re-do the problem without making the approximation?
Thanks

[Anna Dai-Liu 3B]

Yes, I think so - since your calculation is telling you that the approximation doesn't work, you'd need to then make the exact calculation.

[Warren Jolicoeur 1B]

So if its not less that 5% you do the quadratic formula or whatever specific calculation you need to do. Pray that it is not a cubic equation. (Don't think we're doing those in this class)

[Ben Zhang 2H]

Yeah the rule is that if Ka is less than 10^-3 you can approximate. I think Lavelle mentioned you could do 10^-4 to be safe because some instances of 10^-3 it might not be <5%. If it's greater than 5% than you need to redo the problem without the approximation and hope it doesn't get too ugly.

[Macy_Anderson_2F]

Yes, if you approximate and the percent ionization is less than 5% you need to redo the problem using the quadratic formula. Achieve confirmed this.

[Darren Apostol 2L]

Yep, you gotta redo it or use the calculator's Solver function from the start. Don't think problems will be too harsh in that regard, since the focus is on chemistry and not the math, at this stage anyway.

[Sophie Cresitello 1B]

If K is not small or big enough and we cannot use an approximation, we just solve the equation normally with algebra. Most likely you will end up with a quadratic equation and have to plug your numbers into the quadratic formula. It'll just take some more time and make the equation a little more advanced, but its not that bad most of the time.

[Anna Furton]

Yes, you should make sure that the x (calculated) that you're subtracting off of the initial concentration is less than 5% of the initial concentration to verify your approximation. If it isn't, you should go back and calculate the x again without the approximation, which is more difficult math-wise -- you need to use the quadratic formula (or the solve function on your calculator if you want).