# Problems in pH

We know pH is measured by the negative logarithm of concentration of Hydrogen ion. But what if the concentration in HCl is 10-9M then the pH will be 9. But how can it be possible since a pH of 9 is basic while HCl is an acid???

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TeethWhitener
Gold Member
You have to remember the autoionization of water. In neutral water, the pH = 7, meaning the concentration of H+ is 10-7M, even without adding any HCl. So the concentration of H+ for 10-9M HCl is (10-7+10-9M), the negative log of which will be slightly less than 7.

Borek
Mentor
So the concentration of H+ for 10-9M HCl is (10-7+10-9M)

Not exactly, addition of the acid shifts the water dissociation equilibrium slightly to the left, so the concentration of H+ is not 10-7 + 10-9 = 1.01×10-7 M, but a little bit lower - 1.005×10-7 M.

Compare http://www.chembuddy.com/?left=pH-calculation&right=pH-strong-acid-base

ZetaOfThree and fireflies
But what if the concentration is 102M? The pH will be negative then, not within the range of 0 to 14

Borek
Mentor
Whoever told you pH must lie within 0-14 range was wrong. Negative pH (or a pH higher than 14) is rare, but perfectly correct.

Please note that the concentration of H+ equal to 100 M is impossible to reach. Pure water has a concentration of 55.55 M, and this is - more or less - the highest molar concentration we can expect of water solutions (unless you are willing to use extreme pressures to squeeze the volume down).

fireflies
DrDu
So be the concentration of your acid ##c_0##, then the total concentration of H+ is ##c_0+x## and that of OH- ##x##, as the dissociation of x moles of H2O yields x moles of H+ and x moles of OH-. The autodissociation constant is then
##K_w=x(x+c_0)##, which is a quadratic equation in x with the solution ##x=(-c_0+\sqrt{c_0^2+4K_w})/2##. If ##c_0<< \sqrt{K_w}## then we can approximate
##\sqrt{c_0^2+4K_w}/2\approx \sqrt{K_w}## and get ##c_{H^+}\approx \sqrt{K_w}+c_0/2## which is consistent with the calculation of Borek.
In the opposite limit ##c_0>>\sqrt{K_w}##, we can approximate ##\sqrt{c_0^2+4K_w}/2\approx c_0## and
##c_{H^+}\approx c_0##.

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fireflies
Thanks, I really got the point.

But another question popped out:

Why pure water should hold concentration near about 55.55M only when we know strong acids can dissociate to any level?

Borek
Mentor
Why pure water should hold concentration near about 55.55M only when we know strong acids can dissociate to any level?

This is only an approximation of the upper limit, but quite a good one. Density of the pure water is almost exactly 1 g/mL, so 1000 g per 1L, or 1000/18=55.55 moles per 1 L. Water has quite a low molar mass. Most substances you can dissolve will have much higher molar masses, so even taking into account fact that their solutions have a little bit higher density (in extreme cases up to 2 g/mL) number of moles present will be lower (and the concentration will be lower).

Take for example sulfuric acid. When pure, its density is about 1.831 g/mL, so 1831 g per 1 L. However, molar mass of the sulfuric acid is 98 g/mL, so 1 L is around 18.7 moles. Even if dissociated completely, both steps (which is not going to happen), concentration of H+ would be much lower than 55.

This is only an approximation of the upper limit, but quite a good one. Density of the pure water is almost exactly 1 g/mL, so 1000 g per 1L, or 1000/18=55.55 moles per 1 L. Water has quite a low molar mass. Most substances you can dissolve will have much higher molar masses, so even taking into account fact that their solutions have a little bit higher density (in extreme cases up to 2 g/mL) number of moles present will be lower (and the concentration will be lower).

Take for example sulfuric acid. When pure, its density is about 1.831 g/mL, so 1831 g per 1 L. However, molar mass of the sulfuric acid is 98 g/mL, so 1 L is around 18.7 moles. Even if dissociated completely, both steps (which is not going to happen), concentration of H+ would be much lower than 55.

I must say that's an amazing derivation. I never thought it that way. It really helped to solve out my problems I was stucking at regarding pH. Thanks :)

I must say question always is popping up my head. I was watching other threads relating pH, and another question-

pOH=14-pH
This is as much I used to know thinking the range of pH within 0 to 14.But now I know pH can be negative and, maybe, more than 14. Than how is equation is changing to determine pOH?

Borek
Mentor
It doesn't change at all, it still holds.

Silicon Waffle and fireflies
I think, I understand

Silicon Waffle
Borek
Mentor
The pH-calculation for the superacids and bases don't work with negativ decadic logarithm of H3O+ concentration.

As written this is not true. Hammet function is useful for highly concentrated solutions, but not needed otherwise. Mentioning it in the context of pH below 0 (over 14) is definitely a good idea, but the way you worded your post it sounds like these acids can't be described by the normal pH when diluted. They can.

Part o the problem here is the fact that pH is defined for water solutions. When the concentration of the acid goes up, at some point we no longer deal with a water solution. At this moment we have to stop using pH, as it no longer applies.

No you can't because you can't assume that the activity coefficient is 1 in every case. If you can say that activity coefficient is 1 then use pH scale. But you don't know the activity. So it's better to use the acidity function to avoid unwanted mistakes.

Borek
Mentor
No you can't because you can't assume that the activity coefficient is 1 in every case. If you can say that activity coefficient is 1 then use pH scale. But you don't know the activity. So it's better to use the acidity function to avoid unwanted mistakes.

Activity coefficient is almost never equal to 1, which doesn't create a problem for most solutions, regardless of whether we deal with strong acids/bases or weak acids/bases. For diluted solutions you use D-H theory, for more concentrated solutions there are several other models producing reasonable results (Bromley, Pitzer, SIT from those best known).

But this is all moot, I will reiterate what I wrote earlier: contrary to what your post suggests pH is a perfectly correct tool for describing the acidity of water solutions of superacids or superbases, as long as their solutions are not too concentrated. Yes, when they are concentrated Hammet function is much better.

Ok then please make an example calculation for the pks values from the pH values of an hydrochloric acid solution and a perchloric acid solution. Due to the leveling effect of water this is not possible and therefore you have to use the acidity function for every acid stronger than sulfuric acid no matter how diluted they are. For every acid weaker than sulfuric acid it works and i never told something else.

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Borek
Mentor
The pH-calculation for the superacids and bases don't work with negativ decadic logarithm of H3O+ concentration.

Ok then please make an example calculation for the pks values

You have switched from calculation of pH to calculation of pKs to cover your mistake. This is moving goalposts, and counts as trolling.

According to basic water chemistry literature we can only use the pH scale for ionic strenghts not higher than 0.1 mole/l. The ionic strenght of a 10 percent by weight solution of nitric acid is 1.7 mole/l. So for diluted nitric acid solutions the theory of pH is not working and nitric acid is not stronger than sulfuric acid.

Here's your literature: http://samples.sainsburysebooks.co.uk/9780470421543_sample_381012.pdf [Broken] G. A. Olah et al. (2009), Superacid Chemistry, John Wiley & Sons, 2nd Edition, page 3.

And my switch i can explain. The only thing i want to mention was that there are superacids which we are not able to describe with the basic theory of water chemistry but then you came and told for diluted acids it's possible without mentioning how diluted the whole thing is and now i show you that only for extremely diluted strong acids the pH scale is working without mistakes. And i was wrong with the statement that we can't calculate the pH from the concentration of H3O+, but you can't measure this concentration and a normal pH electrode is not working with it so you can't calculate the concentration of H3O+ from the measured pH values except the ionic strenght is under 0.1 mole/l. I was a bit confused but want to point that out. So for the most solutions of strong acids also these ones which are not extremely diluted the pH scale is not working.

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