Ask A Scientist Chemistry Archive

name         Eric L. M.
status       educator
age          40s

Question -   Question #26 in the Chemistry archive asks why the bounds
on pH are 0-14.  Though this mistake is commonly repeated in text books,
I believe that there are no such bounds on pH.  For example, direct
application of the definition of pH (-log10(conc[H+])) shows that the pH
of standard 10M nitric acid is -1.  This is true of any 10M strong acid,
because strong acids are fully ionized in water.  Similar reasoning with
strong bases reveals that pH can be above 14 (and thus pOH is less thanzero).
Perhaps this misunderstanding about pH results from the fact that no
common pH indicators can read below 0 or beyond 14.  What do you think?
------------------------------------------------
Two factors make your suggestion more complicated than it appears at first
glance:
1.    The pH, as it is customarily defined, only applies to aqueous
solutions. Advanced texts generalize the definition to other solvents, but
the treatment is too long to give in detail here.

2.    The pH, as it is correctly defined, is not (-log10(conc.[H+])) but is
(-log10(activity[H+])). The activity and the concentration are only equal
for ideal solutions. This will NOT be the case for concentrated solutions --
not even close. In the case of H2SO4 for example the activity coefficient
(the activity / conc.(in molality units)) is 0.130 for 1 molal solution. It
increases to a value of 6.91 for 70 molal acid and then decreases to a value
of 0.92 for 1000 molal H2SO4.

You can find the details in the definitive paper on the thermodynamic
properties of H2SO4 by W. F. Giauque et. al. in J. Amer.Chem.Soc., vol. 82,
p. 62ff.,(1960).

Vince Calder
=========================================================
Hi, Eric !!!

I agree with you.
Just to recall, the water dissociates like this :
H2O <=>  H+   +    OH-
And the ionic product is a constant ( variable with
temperature ), like this :
Kw = [H+].[OH-] = 10^-14
At a neutral condition :
[H+] = [OH-] .:   10^-7 .   10^-7  = 10^-14
and pH = -log [H+] = -log 10^-7 = 7
At a chosen value, you could have :
[H+] = 10 , as you propose.
And pH = - log [H+]  =  - log 10 = -1
The same would happen with OH-

Best Regards
Alcir Grohmann
=========================================================
Of course, there is no theoretical limit to pH in either direction.  The
practical limits are imposed by the possibility of producing a given
concentration of H+ in solution.  Since the concentration of pure water is
about 55 moles per liter, and water is about as small as molecules get, it is
not practically possible to make [H+] any higher than that.  That would
correspond to a pH of -1.74.  So although the bounds on pH are not 0 to 14,
as you note, pH is not a boundless quantity.

Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois
=========================================================
Two factors make your suggestion more complicated than it appears at
first glance:
1.    The pH, as it is customarily defined, only applies to aqueous
solutions. Advanced texts generalize the definition to other solvents, but
the treatment is too long to give in detail here.
2.    The pH, as it is correctly defined, is not (-log10(conc.[H+])) but
is (-log10(activity[H+])). The activity and the concentration are only equal
for ideal solutions. This will NOT be the case for concentrated
solutions --
not even close. In the case of H2SO4 for example the activity coefficient
(the activity / conc.(in molality units)) is 0.130 for 1 molal solution.
It increases to a value of 6.91 for 70 molal acid and then decreases to a
value of 0.92 for 1000 molal H2SO4.
You can find the details in the definitive paper on the thermodynamic
properties of H2SO4 by W. F. Giauque et. al. in J. Amer.Chem.Soc., vol.
82, p. 62ff.,(1960).

Vince Calder
=========================================================