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Chris Harding — Chemical Engineer and Biological Scientist
a year ago
Update! At 12:50 am I solved the problem mentioned in paragraph 5 of this text.
Well, I finally gave up on a couple problems in chapter 1 on solubility and acids and bases review. I earned a 'B'.[1]
The author, a Harvard Professor, mentioned that the book will be tough. I spent 2 days on one problem. It wasn't all a loss. I now have many, if not most, of the chapter's equations memorized. I will forget them over time, but second and third readings will just make me stronger over time.
I want to become knowledgeable so that I can accurately write about CO2 Mineralization in ex-situ and in-situ processes. This is just chapter 1 of Part 1. The first 4 chapters are foundational material, but, as an example, activity coefficients were introduced in chapter 1[1]. That is for non-ideal solutions. That is important for, for example, seawater. We will go into more details later. Part two is applications.
The author expects one to derive equations. It take me time to do that. Note, I was an A student in algebra in college and online ASU course in 2016. Still, there was an algebra problem that I did NOT get. There was a pesky variable that I just couldn't combine with other variables without getting C^2 and C^3 in other variables. I came real close, but didn't get it. I was missing fundamental knowledge somewhere. C = HA + A- for a weak acid. For a strong Base, at the equivalence point, OH- = HA. This means OH = C*H/(H+Ka') while A- = C*Ka'/(H+Ka'). The equation of interest is H+ = A- + OH- + Ca - Cb. At the equivalence point C = Cb. Ca = 0. At the half-titration point Cb = 1/2 C, and pH=pKa. Ka' is multiplied by its activity coefficient, and Ca = H. I believe. At a really strong base, like when OH- = A-, H is negligible and Cb-Ca = OH- = A- AT strong acid Ca-Cb = H
So, as you can see, there are many possibilities. The answer to the problem is 1/2 *C(H - Kw' - Ka'(Kw'/H - H)). I could NOT get C associated with Kw' without and quadratic terms of C in all other variables. Of course, the whole chapter is needed and I have given a brief overview. I know the equations and typed them all from memory. I think That was the authors intention. Of course, it would have been nice to get the problem.
References:
[1] Butler, J. N. (2019). Carbon Dioxide Equilibria and Their Applications. United States: CRC Press.
[2] PDF of MATLAB solution and explanation of assumptions:
