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Brown's Chemistry Clinic
Equilibria Part 5
"pH, weak-strong acids and bases in aqueous solution"
GCE-AS-A2-IB Advanced Level Theoretical-Physical Chemistry revision notes
GCSE
Notes on reversible reactions-equilibrium *
Advanced Part 1. Equilibrium,
Le Chatelier's Principle-rules * Part 2. Kc and Kp equilibrium expressions and
calculations * Part 3.
Equilibria and industrial processes * 4.
Partition,
solubility product and ion-exchange * Part 5 sub-index:
5.1 Lewis and Bronsted-Lowry acid-base theories * 5.2
self-ionisation of water and pH scale * 5.3 strong acids-examples-calculations *
5.4 weak acids-examples & pH-Ka-pKa calculations * 5.5 strong bases-examples-pH calculations
* 5.6 weak bases- examples & pH-Kb-pKb calculations * Part 6. Salt
hydrolysis,
Acid-base titrations-indicators, pH curves and buffers * Part 7.
Redox equilibria, half-cell electrode potentials,
electrolysis and electrochemical series
*
Part 8. Phase equilibria-vapour
pressure, boiling point and intermolecular forces
* The K and ΔS-ΔG connection with EØcell
will be dealt with via new thermodynamics pages later, but an
example of a ΔS-ΔG calculation is given at the end of
the advanced kinetics pages and
ΔG for cells is
mentioned in Equilibria Part 7.
M = old fashioned shorthand for mol dm-3 *
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5.1
Acid-base theory
-
Basic ideas
on acids, bases and their reactions, pH scale, using indicators and
simple acid-base theory are described on the GCSE notes pages and
are essential reading before tackling parts 5 and 6 of these more
advanced notes, and much of it is not repeated here.
-
The Bronsted-Lowry theory of acids and bases
-
5.1.1: An acid is a
proton donor and a base is a
proton acceptor.
-
Bronsted-Lowry
acids and bases are a 'sub-set' of the general Lewis acid-base
theory, namely acids are electron pair acceptors and
bases are electron pair donors.
-
All bases X:, will have a lone
pair of non-bonding electrons that will except the electron
deficient proton H+ to form a covalent X-H bond.
-
Note: In organic
chemistry mechanisms, nucleophiles are Lewis bases and
electrophiles are Lewis acids and they may fit into the
Bronsted-Lowry definition too e.g. protonation of alcohols and
alkenes via acid.
-
In general, a
Lewis acid - Lewis base interaction involves the formation of a
single dative covalent/co-ordinated bond where the bonding pair of
electrons is donated by the base to the electron pair accepting acid.
-
The oxonium
ion, H3O+(aq) (or more simply,
the aqueous hydrogen ion, H+) is formed by any
acidic substance in water.
-
The hydroxide
ion, OH-(aq), is formed by any soluble
base forming an alkaline solution.
-
5.1.2: Examples of
soluble substances giving aqueous solution acid-base interactions
-
5.1.2a: Conc. sulphuric acid: H2SO4(l)
+ 2H2O(l) ==> 2H3O+(aq)
+ SO42-(aq)
-
Sulphuric
acid, H2SO4,
is the acidic proton donor and H2O is the proton
accepting base.
-
Note the
products are also acids and bases:
-
H3O+
is the conjugate acid of the base H2O
-
SO42-
is the conjugate base of the acid H2SO4
-
The
conjugate acid and original base or the conjugate base and the
original acid are known as a conjugate pair and are
related by proton transfer.
-
5.1.2b: Hydrogen
chloride gas: HCl(g) + H2O(l) ==> H3O+(aq) + Cl-(aq)
-
HCl is the
acid and Cl- is the conjugate base.
-
H2O
is the base and H3O+ is the conjugate acid.
-
The
resulting solution is called hydrochloric acid.
-
5.1.2c: Ammonia:
NH3(aq)
+ H2O(l)
 NH4+(aq) + OH-(aq)
-
Ammonia is
the base and the ammonium ion, NH4+, is
its conjugate acid,
-
and water is
the acid and the hydroxide ion is its conjugate base.
-
5.1.2d: The
hydrogen carbonate ion, HCO3-, can act as
an acid with a base or act as a base with an acid, such behaviour
is described as amphoteric.
-
5.1.2e: Since any
soluble base gives hydroxide ions in aqueous and any soluble acid gives
oxonium/hydrogen ions, they combine to form water. The ionic equation for these
neutralisations is:
-
H3O+(aq)
+ OH-(aq) ==>
2H2O(l)
-
or more
simply: H+(aq)
+ OH-(aq) ==>
H2O(l)
-
More
reactions of H3O+/H+
are given in 5.1.4
-
5.1.3: Acids can be described as monobasic,
dibasic or tribasic etc. depending on the maximum number of protons that
are available for transfer in an acid-base reaction. The terms
mono/di/triprotic are used to mean the same thing, the term then
applies to the maximum number of protons the final conjugate base
can accept.
-
monobasic
acids e.g.
-
dibasic acids
e.g.
-
sulphuric H2SO4,
ethanedioic (COOH)2, and the three isomeric
-
benzene-x,y-dicarboxylic acids
(x,y = 1,1 1,2 and 1,3) C6H4(COOH)2,
-
tribasic
acids e.g.
-
boric acid H3BO3, phosphoric(V)
H3PO4,
-
citric acid  , the middle-left hydrogen
of the HO-C (alcohol) is not acidic in water.
-
5.1.4: Examples of
water
insoluble bases giving acid-base neutralization reactions.
-
5.1.5: Examples of
two solids reacting together in an acid-base reaction.
5.2
The pH
scale and the self-ionisation of water
-
5.2.1 Despite being
essentially covalent, the highly polar water molecule does undergo a minute
amount of self-ionisation.
-
2H2O(l)
H3O+(aq) + OH-(aq)
-
|
Kc =
|
[H3O+(aq)] [OH-(aq)] |
| --------------- |
| [H2O(l)]2
|
-
However, since the
concentration of water is effectively constant for dilute aqueous
solutions,
-
the equilibrium expression is simplified to:
-
Kw
= [H3O+(aq)] [OH-(aq)]
and equals 1 x 10-14 mol2 dm-6
at 298 K.
-
and Kw
is called the ionic product of water and its value will
increase with increase in temperature as the self-ionisation of
water is an endothermic process.
-
pKw
= -log(Kw) = 14, so please note ...
-
log10,
log or lg means to logarithm to base 10
-
pX means
-log10(X/units of X) and allows a wide range of values to be
expressed in a simpler numerical scale and an increase/decrease of
1 pX unit is equal to factorial decrease/increase of 10 of the
value of X. (see pH table below)
-
pH = -log[H+(aq)/mol
dm-3],
which is the formal definition of pH, also ...
-
pOH = -log[OH-(aq)/mol
dm-3], pKw
= pH + pOH,
-
and these will
be explained in more detail later and a
reminder that in associated calculations [x] means
concentration of x in mol dm-3.
-
Note that
mathematically [H+(aq)] = 10-pH
-
Later you will
also come across in weak acid/base quantitative chemistry ...
-
5.2.2
Historically the H of pH is shorthand for the hydrogen
ion, H+ and pH is a mathematical function of its
concentration. The p was used to mean power/potential
in terms of H+ ion concentration, and it is
mathematically -log to the base 10 of a concentration, which in this
case is for the H+ ion concentration. It is the - sign in
the mathematical definition which means that the higher the acid/H+
ion concentration is, the lower the pH.
-
Note: (i) The
scale was devised to give a more 'reasonable' number system because
of the huge range of concentrations possible that can have
measurable chemical effects e.g. 10-14 to 101
(means pH 14 to pH-1). (ii) You can even talk about the pCl of
seawater, which is a function of the concentration of the chloride
ion, Cl-, from the salts in seawater and there are special
electrodes that can measure pH, pCl or p of any other ion.
-
The pH of a
solution is defined as minus log to the base 10 of the hydrogen ion concentration
in mol dm-3.
-
pH = -log( [H3O+(aq)]/mol
dm-3),
and in the 'anti-log' format, [H3O+(aq)]
= 10-pH.
-
log
maybe shown on your calculator as log10 or just lg.
-
pH = -log(
[OH-(aq)]/mol
dm-3),
and in the 'anti-log' format, [OH-(aq)]
= 10-pOH.
-
Therefore: pH
+ pOH = pKw
-
In pure water [H3O+(aq)]
= [OH-(aq)] at pH 7, but if anything is
dissolved to form either hydrogen ions or hydroxide ions, then the
pH will change e.g.
-
if [H3O+(aq)]
> [OH-(aq)] then pH <7, acidic,
-
if [H3O+(aq)]
< [OH-(aq)] then pH >7, alkaline.
-
5.2.3 Using the Kw expression
the relative molarities of hydrogen ions and hydroxide ions in
aqueous solution at
various pH's can be calculated and are shown in the below. In terms
of pH and molar concentrations ...
-
acidic:
pH <7, [H+] > 10-7, [H+(aq)] > [OH-(aq)],
[OH-aq)] < 10-7 mol dm-3
-
neutral:
pH 7, [H+(aq)] = [OH-(aq)] = 10-7
mol dm-3
(at 25oC, 298K)
-
alkaline-basic: pH >7, [H+(aq)] < 10-7, [OH-(aq)]
> [H+(aq)], [OH-(aq)] > 10-7
mol dm-3
| pH |
-1 |
0 |
1 |
2 |
3 |
4 |
5 |
6 |
7 |
8 |
9 |
10 |
11 |
12 |
13 |
14 |
15 |
| [H+] |
10 |
1 |
0.1 |
10-2 |
10-3 |
10-4 |
10-5 |
10-6 |
10-7 |
10-8 |
10-9 |
10-10 |
10-11 |
10-12 |
10-13 |
10-14 |
10-15 |
| [OH-] |
10-15 |
10-14 |
10-13 |
10-12 |
10-11 |
10-10 |
10-9 |
10-8 |
10-7 |
10-6 |
10-5 |
10-4 |
10-3 |
10-2 |
0.1 |
1 |
10 |
5.3
Definition, examples and pH calculations
of strong acids
5.4
Definition, examples and pH, Ka
and pKa calculations
of weak acids
-
5.4.1 Definition
and examples of WEAK ACIDS
-
5.4.2a
Examples include organic
carboxylic acids like ethanoic acid which are just a few % ionized.
-
CH3COOH(aq)
+ H2O(l)
H3O+(aq)
+ CH3COO-(aq)
-
or more simply:
CH3COOH(aq)
H+(aq)
+ CH3COO-(aq)
-
Ethanoic acid is
the B-L acid and the ethanoate ion its conjugate base.
-
Water is the
base and the hydrogen/oxonium ion is its conjugate acid.
-
Since the water
concentration is essentially constant, the equilibrium expression
for a monobasic acid
is written as:
-
|
Ka =
|
[H+(aq)] [A-(aq)]
[H+(aq)] [CH3COO-(aq)]
|
|
------------
= ------------------ |
|
[HA(aq)]
[CH3COOH(aq)] |
-
Ka
is called the acid ionisation or dissociation constant
with units of mol dm-3.
-
Note:
-
Since
water is the solvent, [H2O(l)], it is effectively
constant and omitted from Ka expressions.
-
Ethanoic acid pKa
= 4.76, Ka = 1.74 x 10-5
mol dm-3 and is only about 2% ionised.
-
5.4.2b The
equilibrium can also be expressed as the acid-base reaction of the
conjugate base with water (below) but the above expression is
invariably used in problem solving.
-
e.g. for
ethanoic acid: CH3COO-(aq)
+ H2O(l)
CH3COOH(aq)
+ OH-(aq)
-
|
Kb =
|
[CH3COOH(aq)] [OH-(aq)] |
|
------------------- |
|
[CH3COO-(aq)] |
-
Note that: Ka-acid
x Kb-conj. base = Kw and pKa
+ pKb = pKw, check it out for yourself.
-
5.4.2c Ionic acid-base
equilibrium can be more complicated in the case of dibasic/diprotic
acids.
-
e.g.
 , ethanedioic acid, more simply shown as HOOC-COOH.
-
HOOC-COOH(aq)
H+(aq)
+ HOOC-COO-(aq)
-
HOOC-COO-(aq)
H+(aq)
-OOC-COO-(aq)
-
and Ka1
> Ka2, showing, not surprisingly, the 1st proton is
released more readily than the 2nd.
-
Ka1 =
5.89 x 10-2 mol dm-3 (pKa1 = 1.23),
and Ka2 = 5.24 x 10-5 mol dm-3 (pKa2
= 4.28)
-
5.4.2d There are many examples of inorganic weak acids e.g.
-
(a) Hydrofluoric acid, HF: pKa = 3.25, Ka =
5.6 x 10-4 mol dm-3
-
HF(aq) + H2O(l)
H3O+(aq) + F-(aq)
-
The strong
hydrogen-fluorine bond and the intermolecular HF-H2O
hydrogen bonding are mainly responsible for the lack of dissociation
into ions in dilute solution. HF (562), HCl (431), HBr (366) and HI
(299) have progressively weaker bonds as the halogen atom gets
bigger and the bond length increases, so bar HF they are all very
strong acids and virtually completely ionised and don't hydrogen
bond with water. (endothermic bond enthalpies in kJ mol-1)
-
(b) Hydrocyanic acid, HCN: pKa = 9.31, Ka =
4.9 x 10-10 mol dm-3
-
(c)
Phosphoric(V) acid, H3PO4, is a
tribasic acid.
-
(a1) H3PO4(aq)
H+(aq)
+ H2PO4-(aq)
(Ka1 = 7.9 x 10-3 mol dm-3,
pKa1 = 2.1)
-
(a2) H2PO4-(aq)
H+(aq)
+ HPO42-(aq) (Ka2
= 6.2 x 10-8 mol dm-3, pKa2 =
7.2)
-
(a3) HPO42-(aq)
H+(aq)
+ PO43-(aq) (Ka3
= 4.4 x 10-13 mol dm-3, pKa3 =
12.4)
-
The subsequent
ions H2PO4- and HPO42-
are, not surprisingly, increasingly weak acids.
-
5.4.2e Carbon dioxide
is a weakly acidic gas.
-
It dissolves in water to give 'carbonic acid'
(fizzy 'carbonated water'!). Unpolluted rainwater has a pH of about
5.5 when in equilibrium with the 0.03-0.04% of CO2 in
air.
-
The carbon
dioxide may exist as (a) dissolved CO2 or (b)
'carbonic acid', which complicates matters a bit, but either
should get you the marks in the exam! So the possible equilibria
are:
-
(a) CO2(g)
CO2(aq) and (b)
CO2(g) +
H2O(l)
H2CO3(aq),
-
(c) CO2(aq)
+ 2H2O(l)
HCO3-(aq) + H3O+(aq)
-
or (d) H2CO3(aq)
+ H2O(l)
HCO3-(aq) + H3O+(aq)
-
and more
simply:
-
(c) CO2(aq)
+ H2O(l)
HCO3-(aq) + H+(aq)
-
or (d) H2CO3(aq)
HCO3-(aq) + H+(aq)
-
so the 1st
ionization gives the hydrogencarbonate ion and hydrogen ion.
-
(a) pKa1(CO2(aq))
= 6.4 (very weak acid)
-
(b) pKa1(H2CO3)
= 3.7 (weak acid)
-
HCO3-(aq)
+ H2O(l)
CO32-(aq) + H3O+(aq)
-
more simply:
HCO3-(aq)
CO32-(aq) + H+(aq)
-
The 2nd
ionization gives the carbonate ion and hydrogen ion.
-
pka2
= pKa(HCO3-) = 10.3 (extremely weak acid)
-
Ka2
= [CO32-(aq)] [H+(aq)]
/ [HCO3-(aq)] = 5.0 x 10-11 mol
dm-3
-
5.4.3 Comparison of weak and strong acids in terms of
equimolar aqueous solutions.
-
Due to the difference in the concentration
of H+ ions produced. e.g. say for the sake of argument,
0.1-1.0 molar solutions of hydrochloric acid (100% ionised) and
ethanoic acid (approx. 2% ionised). This means the hydrochloric acid
is effectively about 50x more acidic than the ethanoic acid and
results in the following sorts of observations:
-
5.4.3a pH of
solution and Ka/pKa
-
For equimolar
solutions the pH of HCl(aq) is much lower than for
CH3COOH(aq) (about pH 0.0-1.0 and 2.5-3.0
respectively, and remember 1 pH unit change represents a 10x [H+]
ion change in concentration.
-
The acid
dissociation/ionisation constant show very different numerical value
ranges.
-
The Ka
for strong acids is large, typically >102 to 1010
mol dm-3 and a negative pKa, typically
-2 to -10.
-
The Ka
for weak acids is small, typically 10-2 to 10-10
mol dm-3 and a positive pKa, typically 2 to 10.
-
5.4.3b Chemical
reactivity
-
5.4.3c Electrical
conductivity
-
5.4.3d Differences
in enthalpy of neutralisation ΔHneutralisation
-
Their widely
differing values and simplified explanations.
-
The ΔHneut
for a strong acid and strong base (SA+SB) it is usually
about -57.1 to -57.3 kJ mol-1, because they are fully
ionised to give the H+ and OH- ions
respectively, so the ΔH value essentially corresponds to the ΔH
for the reaction ...
-
H+(aq)
+ OH-(aq) ==>
H2O(l) (ΔH = -57.1 kJ mol-1)
-
e.g. for
the SA/SB pairs: HCl/NaOH, HCl/KOH, HNO3/NaOH, HNO3/0.5Ba(OH)2,
-
The ΔHneut
for a strong acid-weak base (SA+WB) OR a weak
acid-strong base neutralisation is less exothermic than the
SA+SB above, and in some cases considerable less! e.g. reacting
pair and (ΔH),
-
The ΔHneut
for a weak acid and weak base (WA+WB) neutralisation the
ΔH values are even less exothermic.
-
WA/WB: CH3COOH/NH3
(-50.2), HCN/NH3 (-5.4)
-
CH3COOH(aq)
+ NH3(aq)
 CH3COO-(aq) +
NH4+(aq)
-
HCN(aq)
+ NH3(aq)
 CN-(aq) + NH4+(aq)
-
Basically,
the weaker and weaker the acid or base, the less and less the
neutralisation goes to completion, hence the reaction becomes
less and less exothermic.
-
5.4.4: In principle the
full equilibrium expression for any weak acid HA is
-
|
Kc =
|
[H3O+(aq)] [A-(aq)] |
|
-------------- |
|
[HA(aq)] [H2O(l)] |
-
5.4.5:
Weak acid
calculations
5.5
Definition, examples and pH and pKw calculations
of strong
bases
5.6
Definition, examples and pH, Kb, pKb
and Kw calculations of weak
bases |
