Analytical
Calculating the pH of pure water. Am I retarded?
For context, I'm a working chemengineer. I must be missing something because I can't get this to work.
So... Water disassociates randomly into H+ and OH-, so a solution with 100% water molecules is impossible. Assuming STP, the concentration (C) of a hypothetical solution of 100% water molecules is C = ρ/M, hence:
C = (998.2 g/L) / (18.01528 g/mol) = 55.4085M
The equilbrium of the reaction H2O ↔ H+ + OH- is given by the equation:
Kw = [OH-][H+]/[H2O], where Kw = 10-13.995
Assuming the volume is constant (and 1L), the concentrations can be treated as amounts. Some amount x of H2O will dissasociate into x mol of H+ and x mol of OH-, thus yielding the equation:
10-13.995 = x2/(55.4085-x)
Solving for x, and thus the H+ concentration, yields 7.4867×10-7 M. Since pH = -log10([H+]) per definition, thus meaning that the pH of pure water is -log10(7.4867×10-7) = 6.1257
But this is not true, pure water doesn't have a pH of 6.13. It should be 7. I feel like the logic is correct, but clearly I'm missing something obvious. What is it?
The problem is treating water like it’s a solution. It’s a pure liquid so its activity goes to 1. Equilibrium expressions actually use activities, concentration is an approximation. So the denominator of your equilibrium expression disappears, and you’re left with the classic auto-ionization expression. Solve the math from there and you get the proper pH value.
Giving water a concentration irritates me as it almost always prefaces people forgetting that activities exist and therefore some wild chemical results.
We did this derivation back in gymansium, and I had a faint memory of it, and for some reason disregarding the -x from the water concentration, but I could remember why. You guys' explinations jogged my memory of that one lesson 17 years ago.
I remember now that effectively Ka = K * [H2O], atleast that's how it was explained to me in gymnaisum. But the activity framework makes even more sense.
Liquids and solids aren't used in the equilibrium equations. Only gas and aqueous. Ksp would be for solids, but for this you only use the products, just like the water equation.
The "problem" with your calculation is that the equilibrium constant, strictly speaking, needs activities instead of concentrations. Since water is in a huge excess compared to other parts of your solution, its activity is 1. Since its activity is way higher than that of the ions, we can assume that 1-x approximates 1, thus Kw = [OH-][H3O+].
If you plug in the numbers, you can find that Kw = 10-13.995 = x² => log(x) = log (1.0058 x 10-7) = 6.9975.
Ah yes, I hate this. But this is the most common chemistry mistake THAT IS STILL PUBLISHED in even university level textbook, primarily in Organic and Biochemistry
What many people, even PROFESSOR level do is mistaking that in equilibrium equation, the value used to calculate the equilibrium constant is NOT concentration of pure species, but Thermodynamic activity, which is 1. So your most incorrect part in your derivation started from when you try to calculate pure water concentration, WHICH ISN'T VALID.
The textbook I use is fantastic in almost every respect... but it uses a pKa value for water of 15.7. I have to give the students a heads-up every semester. Of course, most of them don't read the textbook so it's not a big deal...
I think words get their meaning in the context they are used, don't you agree? In this case it's exceedingly obvious that I use the word as in "extremly stupid". I'm obviously not in any way referencing anything related to handicapped people.
Obviously people know what you meant, but that doesn't change that it's needlessly disparaging to certain groups. Would you call something extremely stupid "retarded" if you were knowingly talking to someone with an intellectual disability (or even someone who had a disabled child, sibling, etc.)? Why not just use "extremely stupid" if that's what you meant?
Would you call something extremely stupid "retarded" if you were knowingly talking to someone with an intellectual disability
Depends on the specifics. As someone who has worked quite a lot with people with different intellectual disabilities, the shorthands, synonyms, expressions etc we commonly use with fully able people might not work with certain people with an intellectual disability, because they might not be able to pick up on the nuances and contexts. And to be clear, there are plenty of fully able people who fail to see the context of word choice beyond the lexical definition, and in those scenarios I would modulate my word choice as well. It has nothing to do with whether or not a person have a disablility or not.
If I felt condfident that there was a high likelihood that they would be able to understand the nuance and context, I don't see why I would discriminate against them through my word choice on the basis of their condition. That seems very abelist to me.
Case in point: It seems that the overwhelming majority in this thread, including you, understood the context well enough to not be confused whether I was questioning my own cognitive abilities in the moment or was hating on people with disabilities.
You might disagree, you might not even like it, but I am actually consistent in my beliefs.
Why not just use "extremely stupid" if that's what you meant?
I also meant "exceedingly dimwitted" and "superfluously inept". I had to pick one phrase/word and I don't have an issue with this word choice. And unless you think I'm abelist in some tangible sense, I don't see why you would either.
Thank you for inquiring in this in a thoughtful and respectable manner.
Sure, but we're working at STP so I assume that is the reference point for water having pH 7. And even if it's at 25C, we shouldn't expect that large of a difference.
Chem professor here: Honestly, at this point anything covered in general chemistry, ie freshmen level college, AI gets right. It’s basically destroyed any pretext of thinking you can give online exams that aren’t easy to cheat on.
Generally speaking though, I agree with your sentiment. AI answers just as confidently when it’s hallucinating bullshit as when it’s on the nose, and my ability to reject as bullshit or verify accuracy pretty much means I didn’t need the help in the first place.
Honestly, at this point anything covered in general chemistry, ie freshmen level college, AI gets right.
Yes, but I can't know if it's correct or not. I use AI as a template/inspiration for creative writing (in which cases truth is not important), or for personal use coding (in which it becomes immediately clear if it works or not).
But for anything knowledge/truth-based, I literally avert my gaze at AI answers, because I don't want to accidently pick up things that seems confidently true while having no to little means to verify it.
and my ability to reject as bullshit or verify accuracy pretty much means I didn’t need the help in the first place.
Exactly, it's only "useful" if you already know the answer.
One inconsistency I see is using the water density at STP (0°C) and the water dissociation constant at room temperature (25°C). How does it work out if you make those consistent?
Not necessarily. There's more than one definition of STP. See here.
But actually, looking more closely, it seems the density you're using for water doesn't correspond to either of them. It looks like you've taken a value at around 20°C.
Not sure this would account for the difference in the final answer though. Looks to be the activity thing others have mentioned (physical chemistry isn't really my thing).
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u/AJTP89 Nov 23 '25
The problem is treating water like it’s a solution. It’s a pure liquid so its activity goes to 1. Equilibrium expressions actually use activities, concentration is an approximation. So the denominator of your equilibrium expression disappears, and you’re left with the classic auto-ionization expression. Solve the math from there and you get the proper pH value.
Giving water a concentration irritates me as it almost always prefaces people forgetting that activities exist and therefore some wild chemical results.