when is the approximation justified?

[Nithya Narapa Reddy]

Textbook problem 6E.3 says to ignore the second deprotonation if the approximation is justified. What conditions must be met in order for the approximation to be justified and when can we ignore the second deprotonation?

[Ethan Cheng 2k]

I think we can always ignore the second deprotonation for weak polyprotic acids because Ka2 is much smaller than Ka1. For H2SO4, which is a strong polyprotic acid, you can't ignore the second deprotonation.

[jessicahedayi1H]

Hi,

To calculate the pH of a polyprotic acid, we only take the first deprotonation into account because we are treating it as a monoprotic weak acid. This is because Ka2 is typically less than Ka1/1000, so the following deprotonations don't impact pH significantly and can be ignored. One exception would be sulfuric acid, which acts as a strong acid in its first deprotonation.

[Madison Dawson 1A]

Approximation tends to be justified in problems such as this when the Ka/Kb value is so small (under 1.0x10^3) that it is essentially negligible.

[jadyndavidson]

Hi! I have a follow up question for this. On the second Achieve homework assignment for number 3, I was attempting to find the answers utilizing approximation. I am getting the answer, but feel as though approximation should be utilized considering the given Ka = 8.4 x 10^-4. Any suggestions?

[Audrey Hanna]

Hi Jaydn, I'm not sure I totally understand your question. Was using approximation not giving you the correct answer? Sometimes on achieve, the values it requires might be hyper-sensitive or not super sensitive. So sometimes if you round to one decimal it accepts it, but other times it seems like you need a more specific answer. I think it might just be an inconsistency, but if you think the approximation should be working and it isn't, I would recommend double checking that you're not rounding anything until your final answer.

[jadyndavidson]

Hi! Thank you for your response! I was referring to question number 3 on the achieve assignment. When speaking of approximation I was not referring to rounding but rather when solving for x.The questions reads:
Muscles produce lactic acid, CH3CH(OH)COOH(aq), during exercise. Calculate the percent ionization (deprotonation), pH, and pOH
of a 0.1080 M solution of lactic acid. The acid‑dissociation (or ionization) constant, Ka, of this acid is 8.40×10−4. Because Ka is a very small value, smaller than 10^-3, I assumed that you could assume that x is really small and make an approximation/ assume x=0 for initial conditions. When I do the math I get a percent ionization of about 8.2% meaning that approximation does not work and I was wondering why.

[Lilian Doan 1c]

Hi Jadyn, to answer your question:

For number 3 on the achieve, the reason why your approximation doesn't work is because the percent ionization is 9.13% when you say x is negligible. Because 9.13% > 5%, it doesn't pass the rule so we can not the approximation. We have to use a quadratic formula to solve instead.