jk1245, what is [H[sub]3[/sub]O+]? I know it’s the “concentration”, but what precisely is it? An illustrative example would help, (maybe the case I posted two of my messages ago).
Great link! Thanks, jk1245. It’s the answer I was hoping someone would post way back in this thread when I said…
So, I guess the answer to the OP is: “not normally, but follow this link!” Activity can be >1.0. jk1245’s point that 0-14 pH is only valid for dilute solutions is the important distinction (note that the Debye-Huckel theory equations only work for I <0.5).
ZenBeam, sometimes pH is defined as -log [H[sub]3[/sub]O[sup]+[/sup]]:
H[sub]2[/sub]O = H[sup]+[/sup] + OH[sup]-[/sup]
can also be expressed as:
2 H[sub]2[/sub]O = H[sub]3[/sub]O[sup]+[/sup] + OH[sup]-[/sup]
I don’t think that there is any real difference between the “hydrogen ion” and the “hydronium ion”–just that it’s a matter of convention.
I’m not asking what is H[sub]3[/sub]O[sup]+[/sup], I’m asking what exactly is [H[sub]3[/sub]O[sup]+[/sup]], i.e. the concentration, i.e. the number, including an example.
ZenBeam,
is just a short hand way to write “the concentration of X”
For example,
[NaCl] = 0.1M
[alcohol] = 20%
This is just a habit I picked up in undergrad school and never really let go of. It’s not that useful since “100mM NaCl” also implies the same thing.
you could also (in informal communication at least) use it without a number.
“… in order to increase the reaction rate, we need to lower [PO4]…”
Again, I wouldn’t submit a paper to Nature like that, but for notebooks and such it’s fine.
thanks jk1245, but I know it’s the concentration. My question is, how exactly is that defined.
My reason for trying to pin this down precisely is that Pantellerite tells me the concentration can’t be larger than 1. My chemistry book, on the other hand, tells me concentration is given by the molarity, M, which is “the number of moles of solute per exactly one liter of solution.” This could easily be greater than 1. The first example even finds the molarity of 18.23 grams of HCl in 0.250 liters of solution to be 2.00 M.
Is my chemistry book’s definition correct? Since there are 55.6 moles of water in a liter, why is it so hard to imagine a concentration of HCl or H[sub]2[/sub]SO[sub]4[/sub] substantially greater than 1? Consequently, why should anyone even expect a hard boundary at 0 pH?
So is this the answer (finally. You still here, mongrel_8?) to the OP?: Concentration is measured in moles of H[sup]+[/sup] (or H[sub]3[/sub]O[sup]+[/sup]) per liter of solution, and there is no reason you can’t have more than 1 mole of H[sup]+[/sup], or fewer than 10[sup]-14[/sup] moles of H[sup]+[/sup], in a solution.
By the way, my book talks a little about Debye-Huckel theory, but in the context of salt. It sounds like this would complicate matters for high concentration acids or bases, but there’s no reason this would cause a hard boundary at 0 and 14.
When we’re dealing with activity (which is what’s really important here), and trying to determine it from concentration, we recast concentration in terms of 100%, or 1.0. That’s what I’m talking about here. Yes, you could have a solution with a concentration of 2 mol/L of something. So, there’s 2 mol/L of that something and 2 mol/L TOTAL in the system, which means that X = 1.0, or 100% of the total stuff in the system is that something. So, whether the total amount of substance in a system is 0.0000001 moles or 1000 moles, it’s always just 100% of what it is.
We do that to make concentration an intensive parameter (ie., a parameter independent of the size of the system) instead of an extensive parameter.
Way back on the 22nd, you wrote:
My chemistry book also has pH = -log [H+]. But my book uses the notation [H+] to mean moles per liter of H+ ions. Now, if you are using [H+] to mean X, i.e. proportion of H+ to solution, then your equation disagrees with my book, both notationally and numerically. Neglecting the difference in densities between water and the solution, you essentially have
pH = -log(X) = -log([H+] / 55.6)
where now [H+] is in moles/liter, since there are 55.6 moles of solution in 1 liter. You should be able to easily verify this, since if you 1 mole/liter of H+ in 55.6 moles (= 1 liter) of solution, X = 1/55.6.
If, in your quoted lines above, you are using the notation [H+] to mean moles per liter of H+, then 1) you are switching definitions without telling us and 2) your conclusion is wrong because [H+] = 1 is not the largest that [H+] can get.
I just wanted to say that yes I am still here and following closely what is being said, even though I am having a bit of trouble comprehending it all. I still have yet to see an answer other than that you can get pH values above 14 or below 1 at temperatures other than 25 C. Correct me if I am wrong.
Alright… once more…
The sum of the proportion of all of the elements (in this case, ions) in any system is 100%, which is to say 1.0. A system may consist of H, OH, and SO4 (as an example). No matter what the actual amount of these components are in terms of grams, moles, or whatever, their proportions sum to 1.0 (100%): if the system is half H, then (H) = 0.5, if the system is one-eighth OH, then (OH) = 0.125, and since everything else (not including the solvent) is everything else, (SO4) must equal 0.375.
When we want to know pH, we need to know activity. Once again, activity is related to concentration by:
a = yX,
where the units for X are molecular proportion, not moles per liter, not milligrams per kilogram, not drams per ounce–these units and many like them can be >1, but molecular proportion can NOT.
In ideal conditions, y = 1.0 and therefore a = X. Therefore, in ideal conditions, the maximum value for a = 1.0. And, thus, the minimum possible pH is 0.
In real conditions, y <> 0.0. In dilute systems (like natural waters), Henry’s Law is obeyed and y is a constant (which can be calculated using Debye-Huckel), activity and concentration are linearly related, and the lower constraint for pH is still 0, but is more realistically (like you calculated way back when) more like 0.3.
In some real conditions, like the extreme cases that jk1245 linked us to, a > 1.0 and “negative pH” happens… but X is still in units of molecular proportion. But pH, like most concepts in physical chemistry, are rooted in ideal conditions, under which pH always has a range of 0 to 14. Which is why, like the link taught us, they cease using the pH scale in those situations.
Well, you’re half wrong. My previous answer was that, even at 25 C, and for ideal conditions (y = 1.0 in pantellerite’s post),
pH = -log[H[sup]+[/sup]]
where [H[sup]+[/sup]] is the concentration given in moles / liter. Since 55.6 moles = 1 liter of water, you might expect a maximum for [H[sup]+[/sup]] of about 55.6, for a minimum pH of about -1.75, neglecting differences in density. For the cases in your OP, this agrees with what you quoted. For H[sub]2[/sub]SO[sub]4[/sub], pH = -log(6) = -0.78. For 3 M KOH, pOH = -log(3) = -0.48, so pH = 14 - pOH = 14.48, also in agreement.
Now, this is all according to my college chemistry book (surprisingly enough, titled College Chemistry. I don’t have it here, so I can’t give you the authors), and it all hinges on how the concentration [H[sup]+[/sup]] is defined. pantellerite is using seemingly the same equation for his ideal case
pH = -log[H[sup]+[/sup]]
but he has the concentration [H[sup]+[/sup]] given as “molecular proportion, not moles per liter”. This leads to roughly a factor of 55.6 difference in what those two numbers are, which leads to a log(55.6) = 1.75 difference in the pH quoted using his formula and mine. Under pantellerite’s formula, pH is limited to between 0 and 14, except in exceptional cases. Under my formula, the minimum would be more like -1.75.
I don’t believe this is a difference in semantics, or that two different definitions are actually in use. I believe one of these two definitions for concentration is incorrect in the context of pH. And maybe I’m the one who’s wrong, but I’ll have to see a link somewhere stating that concentration used is supposed to be proportion, not molarity. It seems clear from reading my book that they mean molarity, so I’m not just going to take someone’s word for it.
And just for laughs, jk1245 is no help. He writes
The first definition agrees with me, the second with pantellerite. :rolleyes:
Anyway, it’s late. I’m gone.
OK, I did some more searching. A site called Acids, Bases and pH is a site which says
Since pure water has a pH of 7, this site agrees with me, and contradicts Pantellerite. The concentration of hydronium ions in terms of molecular proportion would be 1.8 x 10[sup]-9[/sup]. so -log(molecular proportion) for pure water gives about 8.75.
Another site, called Understanding pH, says it more clearly (bolding mine).
There’s a neat little applet which lets you select pH or [H[sup]+[/sup]], and see how the other changes.
**
Hey! Last time I try to help. Lousy ingrates 
I think both definitions are “correct” for most cases. That is, the differance is insignificant. From what I recall, the “true” definition is moles/L though.
Ultimately though, you may want to take my suggestions with a grain of NaCl; I’m a biochemist so I only work at physiological pH (6-8). Makes it a LOT easier. 
I’d just like to say: “You guys have WAY too much time on your hands!”
Yeah, we could be dabating which “Star trek” episode is better.
But we don’t, because everyone in this thread agrees it’s the one with the space hippies, where when they finally get to their paradise planet, all the plants are full of acid! :eek:
Hear, hear!
Okay, ZenBeam you linked me your cite. Here’s mine… unfortunately, being net-un-savy and bookish, mine comes from my handy desk reference Concepts in Physical Chemistry by Peter Atkins (1995, WH Freeman and company). If you grab a copy (or hell, I’ll FAX you a copy of the page!), it’s on page 6.
Bearing in mind that pH = -log a[sub]H[/sub],
Emphasis, obviously, mine. Why mole fractions (0.0 to 1.0, another way of saying mole proportion)? Because…
pH units are dimensionless; activity is dimensionless; concentration is not dimensionless. If you wanna see the proof that activity is dimensionless, just say so.
But there’s my cite. While I was researching this (instead of working, I might add), I found yet another definition of pH. I’ll hold back… for now.
New sig line idea: “Honk if you passed P-chem!”
Before I start, I want to say that my copy of Atkins’ Physical Chemistry is five years older than Pantellerite’s (he has the fifth edition; I have the fourth edition sitting here).
On page 227, pH is defined as:
pH = -log a(H[sub]3[/sub]O[sup]+[/sup])
a in this case is defined as the activity of hydronium (or protons) in the solution of interest.
This activity is defined as:
a = ym/m[sup]0[/sup]
where m[sup]0[/sup] is a hypothetical standard state of molality 1 mol/kg. (In these equations, molality rather than molarity is used. Molality measures moles of solute per kilogram of solvent; Molarity measures moles of solute per liter of solution.)
So, while Pantellerite is correct that, basically, mole fractions are to be used in this equation (because m/m[sup]0[/sup] will be a dimensionless “fraction”), he is incorrect in that this mole fraction will have a size essentially equal to the concentration of the solution.
Thus, for a 2.0 molal solution of HCl, m/m[sup]0[/sup] = 2.0 (dimensionless)
Now, onto the question of negative pH.
Before we move on, don’t forget that y (really a gamma) in these equations. That’s the activity coefficient. For very dilute solutions, it can be calculated from the Debye-Hückel Limiting Law:
y = 10^(-|z[sub]-[/sub]z[sub]+[/sub]|AI[sup]0.5[/sup])
where
I = 0.5(m[sub]+[/sub]z[sub]+[/sub]+m[sub]-[/sub]z[sub]-[/sub])
If this law continued to hold true for solutions to 1 molal (it doesn’t), the activity coefficient would be seen to drop tremendously, to about 0.3 for 1 molal HCl (or similar solutes with two singly-charged ions).
However, this law only holds up to, at best, about 0.1 molal. It’s shaky even there. There’s a refinement of it that holds around 0.1 molal and gets shaky as you approach 1 molal. According to my text, no current theory is reliable at or above 1 mol/kg.
That leaves us is a bit of a bind, theoretically speaking. At 1 molal, we can be pretty sure the pH will not be 0 yet, because y will be (extrapolating from experimental results in Atkins) between 0.4 and 0.7 for HCl (lower for solutions with more ions or higher charges). For this, then,
pH = -log ym(H[sup]+[/sup]) = -log (~-0.5)(1) = ~0.3
(to approximate)
As the molality increases, the activity coefficient will decrease, causing ym/m to move ever more slowly toward 1 as m increases above 1. (For the pH to be less than zero, the term ym/m must be greater than 1.)
In other words, I can’t give you a theoretical answer. The only answer to be had lies in experimental evidence, or newer theory that I don’t have here–and I think that the latter is unlikely, given that the Debye-Hückel law is something around 100 years old. But I can give you some answers:
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The pH of a 1 molar solution of any strong acid is alomst guaranteed to be higher than 0. In fact, from my experience with actually putting the pH meter in 1 M acids, generally you’re looking at 1-1.5 for a pH;
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Accurate determination of pH does require use of dimensionless numbers, but not in the way Pantellerite was indicating;
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There’s no such thing as an ideal case, but because most students of general chemistry haven’t had all that much math, they just teach the ideal, simplified case and leave it at that. (It’s even worse in Chemical Engineering, where you’re told "just assume it’s the ideal case. That’s close enough.);
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Doing any science on the boards requires the use of way too many vB tags.
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I really should haul my ass to work.
Thanks for listening
LL <–B.S. Chemistry, B.S. Chemical Engineering, M.S. Neuroscience
My bad. There’s a capital A in my third equation down; it’s 0.509 kg/mol at 25 °C. Sorry.
LL
So, where the fuck have you been???
Thanks for the clarification!
(And thank you everybody else in this thread for offering me the rare opportunity to “pad” my meager post count!)
Watching from a distance as this nearly turned into a Great Debate. I felt I needed to actually look at my old P-Chem book because, well, I was curious as to the answer myself
No problem!
LL