pH PRIMER
pH is defined in International Standard ISO 31-8: operationally
as follows. For a solution X, first measure the electromotive force EX of
the galvanic cell where
F is the Faraday constant;
R is the molar gas constant;
T is the thermodynamic temperature.
Defined this way, pH is a dimensionless quantity. Values pH(S) for a range
of standard solutions S, along with further details, are given in the relevant
IUPAC recommendation.
pH has no fundamental meaning as a unit; its official definition is a practical
one. However in the restricted range of dilute aqueous solutions having an
amount-of-dissolved-substance concentrations less than 0.1 mol/L, and being
neither strongly alkaline nor strongly acidic (2 < pH < 12), the definition
is such that
where [H+] denotes the amount-of-substance concentration of hydrogen ion H+
and γ1 denotes the activity coefficient of a typical univalent electrolyte
in the solution.
Another visual representation of the pH scale.In simpler terms, the number
arises from a measure of the activity of hydrogen ions (or their equivalent)
in the solution. The pH scale is an inverse logarithmic representation of
hydrogen proton (H+) concentration. Unlike linear scales, which have a constant
relationship between the item being measured (H+ concentration in this case)
and the value reported, each individual pH unit is a factor of 10 different
than the next higher or lower unit. For example, a change in pH from 2 to
3 represents a 10-fold decrease in H+ concentration, and a shift from 2 to
4 represents a one-hundred (10 × 10)-fold decrease in H+ concentration. The
formula for calculating pH is:
Where αH+ denotes the activity of H+ ions, and is dimensionless. In solutions
containing other ions, activity and concentration will not generally be the
same. Activity is a measure of the effective concentration of hydrogen ions,
rather than the actual concentration; it includes the fact that other ions
surrounding hydrogen ions will shield them and affect their ability to participate
in chemical reactions. These other ions change the effective amount of hydrogen
ion concentration in any process that involves H+.
In dilute solutions (such as tap water), activity is approximately equal
to the numeric value of the concentration of the H+ ion, denoted as [H+] (or
more accurately written, [H3O+]), measured in moles per litre (also known
as molarity). Therefore, it is often convenient to define pH as:
For both definitions, log10 denotes the base-10 logarithm, therefore pH defines
a logarithmic scale of acidity. For example, if one makes a lemonade with
a H+ concentration of 0.0050 moles per litre, its pH would be:
A solution of pH = 8.2 will have an [H+] concentration of 10−8.2 mol/L, or
about 6.31 × 10−9 mol/L. Thus, its hydrogen activity αH+ is around 6.31 ×
10−9. A solution with an [H+] concentration of 4.5 × 10−4 mol/L will have
a pH value of 3.35.
In solution at 25 °C, a pH of 7 indicates neutrality (i.e. the pH of pure
water) because water naturally dissociates into H+ and OH− ions with equal
concentrations of 1×10−7 mol/L. A lower pH value (for example pH 3) indicates
increasing strength of acidity, and a higher pH value (for example pH 11)
indicates increasing strength of basicity. Note, however, that pure water,
when exposed to the atmosphere, will take in carbon dioxide, some of which
reacts with water to form carbonic acid and H+, thereby lowering the pH to
about 5.7.
Neutral pH at 25 °C is not exactly 7. pH is an experimental value, so it
has an associated error. Since the dissociation constant of water is (1.011
± 0.005) × 10−14, pH of water at 25 °C would be 6.998 ± 0.001. The value is
consistent, however, with neutral pH being 7.00 to two significant figures,
which is near enough for most people to assume that it is exactly 7. The pH
of water gets smaller with higher temperatures. For example, at 50 °C, pH
of water is 6.55 ± 0.01. This means that a diluted solution is neutral at
50 °C when its pH is around 6.55 and that a pH of 7.00 is basic.
Most substances have a pH in the range 0 to 14, although extremely acidic
or extremely basic substances may have pH less than 0 or greater than 14.
An example is acid mine runoff, with a pH = –3.6. Note that this does not
translate to a molar concentration of 3981 M; such high activity values are
the result of the extremely high value of the activity coefficient while concentrations
are within a "reasonable" range. E.g. a 7.622 molal H2SO4 solution
has a pH = -3.13, hydrogen activity αH+ around 1350 and activity coefficient
γH+ = 165.4 when using the MacInnes convention for scaling Pitzer single ion
activity coefficient.
Arbitrarily, the pH is − log10([H + ]). Therefore,
pH = − log10[H + ]
or, by substitution,
.
The "pH" of any other substance may also be found (e.g. the potential
of silver ions, or pAg+) by deriving a similar equation using the same process.
These other equations for potentials will not be the same, however, as the
number of moles of electrons transferred (n) will differ for the different
reactions.
CALCULATTION OF pH FOR WEAK AND STRONG ACIDS
Values of pH weak and strong acids can be approximated using certain assumptions.
Under the Brønsted-Lowry theory, stronger or weaker acids are a relative
concept. But here we define a strong acid as a species which is a much stronger
acid than the hydronium (H3O+) ion. In that case the dissociation reaction
(strictly HX+H2O↔H3O++X− but simplified as HX↔H++X−) goes to completion, i.e.
no unreacted acid remains in solution. Dissolving the strong acid HCl in water
can therefore be expressed:
HCl(aq) → H+ + Cl−
This means that in a 0.01 mol/L solution of HCl it is approximated that there
is a concentration of 0.01 mol/L dissolved hydrogen ions. From above, the
pH is: pH = −log10 [H+]:
pH = −log (0.01)
which equals 2.
For weak acids, the dissociation reaction does not go to completion. An equilibrium
is reached between the hydrogen ions and the conjugate base. The following
shows the equilibrium reaction between methanoic acid and its ions:
HCOOH(aq) ⇌ H+ + HCOO−
It is necessary to know the value of the equilibrium constant of the reaction
for each acid in order to calculate its pH. In the context of pH, this is
termed the acidity constant of the acid but is worked out in the same way
(see chemical equilibrium):
Ka = [hydrogen ions][acid ions] / [acid]
For HCOOH, Ka = 1.6 × 10−4
When calculating the pH of a weak acid, it is usually assumed that the water
does not provide any hydrogen ions. This simplifies the calculation, and the
concentration provided by water, 1×10−7 mol/L, is usually insignificant.
With a 0.1 mol/L solution of methanoic acid (HCOOH), the acidity constant
is equal to:
Ka = [H+][HCOO−] / [HCOOH]
Given that an unknown amount of the acid has dissociated, [HCOOH] will be
reduced by this amount, while [H+] and [HCOO−] will each be increased by this
amount. Therefore, [HCOOH] may be replaced by 0.1 − x, and [H+] and [HCOO−]
may each be replaced by x, giving us the following equation:
Solving this for x yields 3.9×10−3, which is the concentration of hydrogen
ions after dissociation. Therefore the pH is −log(3.9×10−3), or about 2.4.
MEASUREMENT OF pH
Representative pH values Substance pH
Hydrochloric acid, 10M -1.0
Lead-acid battery 0.5
Gastric acid 1.5 – 2.0
Lemon juice 2.4
Cola 2.5
Vinegar 2.9
Orange or apple juice 3.5
Tomato Juice 4.0
Beer 4.5
Acid Rain <5.0
Coffee 5.0
Tea or healthy skin 5.5
Urine 6.0
Milk 6.5
Pure Water 7.0
Healthy human saliva 6.5 – 7.4
Blood 7.34 – 7.45
Seawater 7.7 – 8.3
Hand soap 9.0 – 10.0
Household ammonia 11.5
Bleach 12.5
Household lye 13.5
pH can be measured:
by addition of a pH indicator into the solution under study. The indicator
color varies depending on the pH of the solution. Using indicators, qualitative
determinations can be made with universal indicators that have broad color
variability over a wide pH range and quantitative determinations can be made
using indicators that have strong color variability over a small pH range.
Precise measurements can be made over a wide pH range using indicators that
have multiple equilibriums in conjunction with spectrophotometric methods
to determine the relative abundance of each pH-dependent component that make
up the color of solution, or
by using a pH meter together with pH-selective electrodes (pH glass electrode,
hydrogen electrode, quinhydrone electrode, ion sensitive field effect transistor
and others).
by using pH paper, indicator paper that turns color corresponding to a pH
on a color key. pH paper is usually small strips of paper (or a continuous
tape that can be torn) that has been soaked in an indicator solution, and
is used for approximations.
The lowest and highest ends of the pH scale do not oxidize. The middle of
the scale is what oxidizes, such as water and blood.
As the pH scale is logarithmic, it does not start at zero. Thus the most
acidic of liquids encountered can have a pH as low as −5. The most alkaline
typically has pH of 14. Measurement of extremely low pH values has various
complications. Calibration of the electrode in such cases can be done with
standard solutions of concentrated sulphuric acid whose pH values can be calculated
with the Pitzer model.
As an example of home application, the measurement of pH value can be used
to quantify the amount of acid in a swimming pool.
pOH
There is also pOH, in a sense the opposite of pH, which measures the concentration
of OH− ions, or the basicity.
INDICATORS OF pH
The Hydrangea macrophylla blossoms in pink or blue, depending on soil pH.
In acidic soils, the flowers are blue; in alkaline soils, the flowers are
pink.An indicator is used to measure the pH of a substance. Common indicators
are litmus paper, phenolphthalein, methyl orange, phenol red, bromothymol
blue, bromocresol green and bromocresol purple. To demonstrate the principle
with common household materials, red cabbage, which contains the dye anthocyanin,
is used.
