pH Scale
pH Scale
** The
concentration of H+ or OH− in aqueous solution
can vary over extremely wide ranges, from 1 M or greater to 10−14 M
or less.
** To construct
a plot of H+ concentration against some variable would be very
difficult if the concentration changed from, say, 10−1 M to 10−13 M.
This range is common in a titration. It is more convenient to compress the
acidity scale by placing it on a logarithm basis.
** The pH of a solution
was defined by Sørenson as:
** The minus
sign is used because most of the concentrations encountered are less than 1 M,
and so this designation gives a positive number. (More strictly, pH is now
defined as −log aH+ , but we will use the simpler definition of
Equation above)
** In
general, pAnything = −log Anything, and this method of notation will be
used later for other numbers that can vary by large amounts, or are very large
or small (e.g., equilibrium constants).
** Carlsberg
Laboratory archives In 1909, Søren Sørenson, head of the chemistry department
at Carlsberg Laboratory (Carlsberg Brewery) invented the term pH to describe
this effect and defined it as −log[H+].
** The term pH
refers simply to (the power of hydrogen).
** In 1924, Søren
Sørenson realized that the pH of a solution is a function of the “activity” of
the H+ ion, and published a second paper on the subject,
defining it as pH = −log aH+.
** A similar
definition is made for the hydroxide ion concentration:
So
Solved problems
Example (1): Calculate the pH of a 2.0 × 10−3 M
solution of HCl.
Solution:
HCl is
completely ionized, so
Example(2): Calculate the pOH and the pH of a 5.0 × 10−2 M
solution of NaOH at 25◦C.
Solution:
Example (3): Calculate the pH of a solution prepared by mixing 2.0mL of a strong acid solution of pH 3.00 and 3.0mL of a strong base of pH 10.00.
Solution:
Example (4): The pH of a solution is 9.67. Calculate the
hydrogen ion concentration in the solution
Solution:
Important Notes for pH
pH =
- log [H+] , [H+] = 10−pH
[H+]
= [OH−], the solution is neutral , pH = pOH = 7
[H+]
> [OH−], the solution is acidic. , pH <7
[H+]
< [OH−], the solution is alkaline. pH >7
** The hydrogen
ion and hydroxide ion concentrations in pure water at 25◦C are each 10−7 M,
and the pH of water is 7. A pH of 7 is therefore neutral.
** Values of pH
that are greater than this are alkaline, and pH values less than this are
acidic. The reverse is true of pOH values. A pOH of 7 is also neutral.
** Note that the
product of [H+] and [OH−] is always 10−14 at
25◦C, and the sum of pH and pOH is always 14. If the temperature is
other than 25◦C, then Kw is different from 1.0 × 10−14,
and a neutral solution will have other than 10−7 M H+ and
OH− (see below).
** If the
concentration of an acid or base is much less than 10−7 M, then
its contribution to the acidity or basicity will be negligible compared with
the contribution from water. The pH of a 10−8 M sodium
hydroxide solution would therefore not differ significantly from 7. If the
concentration of the acid or base is around 10−7 M, then its
contribution is not negligible and neither is that from water; hence the sum of
the two contributions must be taken. So,
The pH of 10-9 M
HCl is not 9!
Negative pH
** Some
mistakenly believe that it is impossible to have a negative pH. There is no
theoretical basis for this.
** A negative pH
only means that the hydrogen ion concentration is greater than 1 M.
** In actual
practice, a negative pH is uncommon for two reasons:
(1) The First
reason: even strong acids may become partially undissociated at high
concentrations. For example, 100% H2SO4 is so weakly
dissociated that it can be stored in iron containers; more dilute H2SO4 solutions
would contain sufficient protons from dissociation to attack and dissolve the
iron.
(2) The second
reason: has to do with the activity, which we have chosen to neglect for dilute
solutions. Since pH is really −log aH+ (this is what a pH meter
reading is a measure of), a solution that is 1.1 M in H+ may
actually have a positive pH because the activity of the H+ is
less than 1.0 M. This is because at these high concentrations, the activity
coefficient is less than unity (although at still higher concentrations the
activity coefficient may become greater than unity).
** Nevertheless,
there is mathematically no basis for not having a negative pH (or a negative
pOH), although it may be rarely encountered in situations relevant to
analytical chemistry.
Example: 10 M
HCl solution should have a pH of −1 and pOH of 15
Example (5): Calculate the pH and pOH of a 1.0 × 10−7 M
solution of HCl.
Solution:
Since the
hydrogen ions contributed from the ionization of water are not negligible
compared to the HCl added
** Note that,
owing to the presence of the added H+, the ionization of water is
suppressed by 38% by the common ion effect (Le Chˆatelier’s principle). At
higher acid (or base) concentrations, the suppression is even greater and the
contribution from the water becomes negligible. The contribution from the
autoionization of water can be considered negligible if the concentration of
protons or hydroxyl ions from an acid or base is 10−6M or greater.
** The
calculation in this example is more academic than practical because carbon
dioxide from the air dissolved in water substantially exceeds these concentrations,
being about 1.2 × 10−5 M carbonic acid. Since carbon dioxide in
water forms an acid, extreme care would have to be taken to remove and keep
this from the water, to have a solution of 10−7 M acid.
Reference: Analytical chemistry/ Seventh edition / Gary D.
Christian, University of Washington, Purnendu K. (Sandy) Dasgupta, University
of Texas at Arlington, Kevin A. Schug, University of Texas at Arlington.
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