Chemistry 2810 Lecture Notes
4.3
Dr. R. T. Boeré
Page 44
Brønsted acids and bases
Willy was a chemist's son, and Willy is no more
For what he thought was H2O was H2SO4..
Anonymous
References: K&T section 17.8 Acid-Base properties of Salts: Hydrolysis and 17.10 Molecular structure, bonding and acid-base
behavior (this treatment is VERY cursory and inadequate) Text: S-A-L Chapter 5.1 - 5.8.
Useful as the Lewis and HSAB definitions are, the unique properties of protic acids to a wide variety of disciplines and
applications - biological, environmental, mineralogical - demands that we consider in some detail the inter-relationship of
Br¢nsted-Lowry acidity and basicity of the elements. Again we will focus on the position of the elements in the periodic table to
paint a broad survey of acid/base behavior. Later we will discuss some of the specialized aspects, including how the acids and
bases are made in a more systematic element-by-element treatment. One of the ideas that is important to inorganic chemistry in
general is the recognition that the whole Br¢nsted theory can be extended to solvents other than water. In fact, the sole
requirement of the Br¢nsted definition is that the solvent itself can undergo an auto-ionization reaction. In terms of the broader
application of the chemistry of the elements, this is not so important, because ours is a watery planet, and H2O is the preeminent
solvent for natural systems on planet earth. Nevertheless important chemical transformations are done in non-aqueous protic
solvents such as methanol, ammonia and DMSO, and we will briefly consider this additional aspect of the Br¢nsted acid-base
theory.
4.3.1 The Brønsted definition
Br¢nsted acids and bases are chemicals which alter the [H+ ] of solutions. In the
Br¢nsted definition, each acid and base has a conjugate, as in the following example:
HF(aq) +
H2O
⇔
H3O+
+
F-(aq)
acid
base
conj. acid
conj. base
The actual nature of the proton in water, indicated by the formula H3O+ , is not entirely
understood. It is of course a solvated proton, and the consensus seems to be that the
actual ionic species is H9O4+ , i.e. a proton solvated by four water molecules. Whenever
we write H3O+ , then, we mean merely a representation of a solvated proton in water.
a)
116º
2.50
H
H2O
116º
O
H 2.59
H 105º OH 2
2.59
OH2
Structure of the H 9O4+ ion
Acid (Base) strength
The strength of any acid or base is given by an equilibrium constant which is often called a hydrolysis constant:
[ H O ][ F ] = 35. × 10
=
+
Ka
and, since
[
]
−
3
[ HF ]
−4
pH = − log 10 H3O + , we define the analogous pKa = − log 10 K a and also pK w = − log10 K w , which is the
auto-ionization (also called auto-protolysis) constant of water, for the reaction:
2 H2O ⇔ H3O + + OHIt is precisely this last reaction that is different for other solvent systems, so that for example in pure liquid ammonia, it is:
2 NH3 ⇔ NH4+ + NH2–
From the definition if is obvious that a positive pK a represents a weak acid, while a negative pKa represents a strong acid. As a
general rule, for polyprotic acids, the pK a for a subsequent hydrolysis step is about 5 units greater that the value for the prior
one (100,000 times weaker acid). The manipulation of such constants was treated in detail in General Chemistry; our focus will be
on relating the measured values of pK a's to the chemical identity of the acids involved.
b)
Origin of acidity and basicity
If we look again at the HF equilibrium mentioned above, but now look at isolated molecules in the gas phase, we discover
the following result:
HF( g)
+
H2 O( g )
← 

gas phase
H 3O + ( g)
+
F − (g )
That is, the equilibrium lies extensively to the left. Why then is HF acidic? It turns out that the main component of the energy of
this reaction comes not from the equilibrium above, but rather from the solvation energy of the product ions. Thus the energies
of the reactions:
Chemistry 2810 Lecture Notes
F −(g )
Dr. R. T. Boeré
+ nH2 O →
excess
F − ( aq ) ;
Page 45
H + (g )
+ nH2 O
→
excess
H + ( aq )
are favorable and extremely large. By comparison, acid/base enthalpy, as well as enthalpies of solution (which determine in part
the solubility or insolubility of compounds) are almost negligibly small. It is this solvation energy which tips the balance in
favor of the hydrolysis of HF to release H+ into solution.
4.3.2 Acids and bases across the periodic table
a)
Common acids and bases
It is helpful to consider the well-known acids in terms of their positions in the periodic table. The situation with bases is a
little more restrictive, since the common inorganic bases are all metal hydroxides. Let us therefore consider the metal hydroxides
and some representative acids across the periodic table. Since all the d and f elements form insoluble metal hydroxides which are
weak or non-basic simply because of their extreme insolubility, we start by considering only the s and p block elements. The
remaining elements will be treated in a slightly different manner later. The following periodic table displays the most common
acids and hydroxide bases of these elements:
Main groups bases (shaded) and acids (clear)
1
18
H2O
2
13
14
15
16
17
LiOH
Be(OH)2
B(OH)3
HCO2–
H2O
HF
HOF
NaOH
Mg(OH)2
Al(OH)3
H4SiO 4
polyacids
NH3
HNO3
HNO2
H3PO 2
H3PO 3
H3PO 4
polyacids
H2S
H2S O 3
H2S O 4
polyacids
KOH
Ca(OH)2
Ga(OH)3
Ge(OH)2
H3AsO3
H3AsO4
H2S e
H2SeO 3
H2SeO 4
HCl
HOCl
HClO2
HClO3
HClO4
HBr
HOBr
HBrO 3
HBrO 4
RbOH
Sr(OH)2
In(OH)3
SnO.H 2O
SnO 2.H2O
H3SbO 3
H2Te
H2TeO 3
Te(OH)6
HI
HOI
HIO 3
H5IO 6
CsOH
Ba(OH)2
TlOH
PbO.H2O
Bi(OH)3
H2Po
Po(OH)2
H2PoO 3
?
FrOH
Ra(OH)2
HXeO4–
The acids belong to two main classes: element hydride acids such as HCl and H2S, and the much larger class of the oxo acids. Note that the conventional formulae of the common acids hide the notion that these are oxo -acids, and it would be much
better to rewrite them as follows:
Group 14
O2COH–, for which the parent acid, carbonic acid, is OC(OH)2
Group 15
nitrous acid ONOH
nitric acid O2NOH
Group 16
sulfurous acid, actually a solution of SO2 in water OS(OH)2
sulfuric acid O2S(OH)2
Group 17
hypochlorous acid, HOCl chlorous acid, OClOH
chloric acid, O2ClOH
perchloric acid, O3ClOH
Note also that for the group 13 elements, the formulas of boric acid, B(OH)3 and aluminum hydroxide, Al(OH)3 are identical in
form, so that the formula alone will not tell us which kind of behavior an oxy -acid or hydroxide base will undergo. In fact, it
depends on whether the molecule breaks the E–OH or the EO–H bond on ionizing! If the former, it forms E+ and OH– to give a
basic solution, while the latter yields EO – and H+ to give an acidic solution.
It is therefore immediately obvious that the difference in an acid vs. a base is whether the nature of the element E is one
that stabilizes the E+ compared to the EO – species. In practice, the electronegative elements form acids because they are very
comfortable with a neighboring negatively charged oxygen, while the electropositive elements are less able to stabilize such a
Chemistry 2810 Lecture Notes
Dr. R. T. Boeré
Page 46
negative charge, and therefore prefer to deliver hydroxide and remain as cations in solution. It is also immediately obvious that
this will be very much a matter of degree rather than an absolute cutoff. In support of this notion we find that the acids and/or
hydroxides of the metalloids are neither very acidic nor very basic. These are called the amphoteric elements, from the Greek
word for "both". In practice, the free acids and bases for these elements are rarely found to be stable, so that most discussion
focuses on the character of the oxides, our next topic of discussion.
b)
Oxides of metals and non-metals
The precursors (sometimes in practice, always in theory) of the element hydroxides and the oxo -acids are the corresponding
element oxides. Consider a few common examples:
Na 2O + H2O à 2 NaOH
MgO + H2O à Mg(OH)2
CO2 + H2O ⇔ HCO3– + H+
SO3 + H2O à H2SO4
From these few examples it already appears that the old adage that oxides of the non-metals are the precursors to the oxo-acids,
while oxides of the metals are the precursors of the hydroxide bases holds true. This observation leads to the very valuable
observation that the oxides of the metalloids are amphoteric. An amphoteric oxide is an oxide that reacts readily with both acids
and bases. They are listed in the following periodic table:
Amphoteric oxides
1
2
13
14
15
GeO
GeO2
SnO
SnO 2
PbO
PbO 2
As2O 3
As2O 5
S b2O 3
S b2O 5
Bi 2O 3
Bi 2O 5
16
17
BeO
Al 2O 3
Ga2O 3
In2O 3
For the group 15 element oxides, it is only the E(III) oxidation state that is amphoteric, while the (V) state is acidic. Consider the
reactions of aluminum oxide as examples of amphoteric oxide behavior:
Al2O3 + 6 H+ à 2 Al3+ + 3 H2O
Al2O3 + 2 OH– + 3 H2O à 2 Al(OH)4–
In fact, this tendency is so powerful that a clean metallic
aluminum surface will dissolve in both concentrated acid
and concentrated alkali, liberating H2 in both cases.
We are now able to also consider some of the
properties of the transition metals. Few distinct acids or
bases exist (though there are a few, such as permanganic
acid, HMnO4, which is equivalent in structure and strength
to perchloric acid). The oxides of the transition metals in
their low oxidation states are basic, while the oxides in the
highest oxidation states are acidic. Midrange oxidation
state transition metal oxides are therefore expected to be
amphoteric, and this is observed to be the case. The
diagram at the right shows the relationship of the oxidation
states of the first-row transition element oxides with their
acid, base and amphoteric character. Thus the oxides MO of Ti, V, Cr, Mn and Fe dissolve in water to give basic solutions, so
long as they are protected from oxidizing agents (e.g. dissolved oxygen!) The acidic oxides are CrO3, MnO3, Mn2O7 and FeO3.
The most common oxides are thus all amphoteric, dissolving either in strong acid or strong base to give the metal aqua ions or
hydroxoanions, respectively.
4.3.3 Acid strength and Pauling's rules
This topic is covered both in Kotz and Treichel in Section 17.10 and in SAL p. 194ff. It is a most interesting consideration to
ask why certain elements and different acids of a given element have the variation in pKa that is observed.
Chemistry 2810 Lecture Notes
a)
Dr. R. T. Boeré
Page 47
Strength of oxo-acids by Paulings rules
Linus Pauling stated two empirical rules of oxo -acid strength:
1.
For OpE(OH)q,
pKa ~ 8 - 5p
2.
The successive p Ka values of polyprotic acids (i.e. q >1) increase by 5 units for each successive proton transfer.
This suggests that the dominant factor in determining the strength of oxoacids is the number of terminal oxygen atoms attached
to the central element E. Therefore the structure of the oxoacids becomes important, and these you simply need to learn (once
the connectivity is established, you can get the structure by VSEPR theory.) The table below lists important paradigmatic oxo acids for most of the non-metals. Note how closely the predictions of Pauling's rules are born out by the actual experimental
values. This means that the inductive effect of the terminal oxygen atoms can be thought of as raising the effective
electronegativity of the element E in an oxoacid.
Table of pKa of oxoacids as a function of structure (Pauling's Rules)
p=0
p=1
p=2
p=3
O
HO
O
HO
Cl
Cl
HO
O
OH
I
HO
Cl
HO
O
O
OH
OH
7.2
2.0
1.6, 7.0
Cl
HO
-1.0
O
O
-10
OH
OH
HO
OH
Te
OH
HO
S
Se
HO
HO
O
OH
O
O
OH
7.8, 11.2
2.6, 8.0
-2.0, 1.9
O
P
HO
O
OH
OH
2.1, 7.4, 12.7
OH
HO
P
HO
HO
O
N
OH
H
1.8, 6.6
O
-1.4
OH
C
Si
HO
OH
OH
Legend
10
HO
3.6
OH
B
O
p is # of terminal oxygen atoms
polyprotic acids list pKa for subsequent steps
OH
9.1
Beware of exceptions such as H3PO3, which has one terminal oxygen and one H attached directly to the P! Its acidity is
therefore very close to that of H3PO4, with the first pK actually being more acidic for phosphorous acid, a reversal of the
"normal" trend observed for the halogens. (As seen for the series hypochlorous, chlorous, chloric and perchloric acid, where
the pK grow smoothly with increasing oxidation state of the central atom.)
The weakest oxo -acids are extremely difficult to deprotonate completely. For example, silicate exists in water as SiO2(OH)22–-,
and not as SiO44–. The later ion, known as the orthosilicate anion, is an important species in silicate minerals, about which we
will learn more later. Thus while sodium orthosilicate solutions would be strongly basic, solutions of Na2SiO2(OH)2 are mild
bases, with pKb around +1. Note also the use of silica gel as a chromatographic support: the acidity or basicity of "SiO2" can be
altered over a wide range by treating with strong acids or bases. This has the effect of altering the terminal oxo/hydroxo groups
to give a silicate with the desired pKa .
Chemistry 2810 Lecture Notes
Dr. R. T. Boeré
Page 48
Formation of polyoxo -acids and polyoxoanions is an important process for many oxoacids, and this has an effect on acid
strenght. Thus in diphosphoric acid, P2O72–, the oxygen that bridges between two phosphorus atoms is not considered to be a
terminal oxygen in using Pauling's rules. This simple diphosphate is merely the first in a whole series of chain-like and ring-like
polyphosphates, each of which at least theoretically has a corresponding protonated form. A separation of the anions that coexist, for example, in commercial "polyphosphoric acid" is shown in the paper chromatogram reproduced below:
Polyphosphates are also essential to biochemistry for the important energy storage and usage mechanism involving the
hydrolysis of adenoside triphosphate into phosphate and adenosine diphosphate. This reaction is extremely affected by the
external pH of the solution.
NH 2
N
N
N
O
H
H H2
C
H
b)
3-
N
N
N
H
NH 2
4-
P
O
H
O
O
H
O
O
P
O
O
O
O
P
H
H H2
C
O
H
O
H
ATP4-
P
O
H
O
O
O
O
P
O
O
H
ADP3-
Element hydride acids and the pseudo-halides
The simple element hydride acids reflect both the electronegativity of the element and the strength of the element-hydrogen
bond. Thus we find that NH3 is a base, H2O is amphoteric, while HF is acidic. This classification is only valid, of course, using
the H+ /H2O reference system. In liquid ammonia, water acts as a strong acid! This trend follows directly on the electronegativity
of the element, with F > O > N. More intriguing is the strengths of acids down the groups, where we find:
HI > HBr > HCl >> HF
and
H2Te > H2Se > H2S >> H2O
This series directly reflects the inherent strength of the E–H bond, which are weakest for the heaviest elements simply because
of poor overlap of the orbitals of the small hydrogen atom and the very large heavy atoms. Both water and hydrogen fluoride
are anomalously weak, reflecting not the bond strength, but the high charge density of the OH– and F– ions. In other words,
these ions are very small, so that the unit negative charge is concentrated in a small volume. This makes it difficult to solvate
these ions adequately, and hence the dissociation equilibrium is suppressed in aqueous solution. Pure liquid HF, although a
very corrosive material, is an effective solvent for many ionic solids, and is the next -closest material to liquid water that is known.
Certain element-hydrogen bonds are inert to acid-base reactions, that is they do not hydrolyze in water under normal
conditions. Important examples are the C–H and P–H bond, both of which are unreactive because the electronegativity of C and
P are almost the same as that of H, so the bonds are not polar enough to undergo Br¢nsted equilibria. Notice the anomalous
placement of the P(III) acids in the table of acid pK's below.
Chemistry 2810 Lecture Notes
Dr. R. T. Boeré
Page 49
This is also a good place to mention the closely-related acids of the pseudo-halides. A variety of small inorganic molecular
ions form acids, such as hydrazoic acid: HN3, hydrocyanic acid: HCN, and thiocyanic acid: HNCS. These anions are known as
the pseudo-halides, and their behavior closely mimics mid-size halides and halogen acids such as HCl.
c)
Non-aqueous solvents, solvent leveling and the measurement of acid strength
Although in Chemistry 2810 our focus will be primarily on water as a solvent for
most reactions, inorganic chemistry generally makes wide use of other solvent
systems. In particularly, Brønsted acid-base chemistry can be done in solvents which
differ greatly in inherent acidity or basicity. Such solvents are called protic nonaqueous solvents. They have considerable practical use, but for now we just want to
consider their inherent properties rather than their various uses. Consider a table of
pKa data for some common acids (note that a parallel type of table can be constructed
for base strength).
You were wondering…
What does it mean for an acid to be
stronger than "stong"?
Those acids whose pKa is less than 0 are acids which are inherently stronger than the hydronium ion. Such solvents, when
they are dissolved in water, donate a quantitative amount of H+ to water. In other words, they are the strong acids. This raises
the important question: how can such pKa's be measured in the first place? The answer is quite simply: by using a solvent
reference system that is more acidic than water! For any protic solvent that is capable of undergoing a Brønsted-Lowry
autoionization reaction, the numerical value of the autoionization constant will determine the width of the discrimination window.
However, the relative location of the discrimination window is set by the pKa itself. In other words, the pKa allows the inherent
acidity or basicity of any solvent to be compared. The combination of the width and location of the solvent discrimination
window using the aqueous pH scale for comparison is presented in the very useful graphic shown below.
Note that water has a relatively narrow discrimination window, compared so the acidic solvent HF or the basic solvent
ammonia. Many molecules which are non-basic in water can be protonated simply by dissolving them in a highly acidic solvent
such as hydrofluoric or fluorosulfuric acid.
The principle of solvent leveling is simply that any acid that is a stronger acid than the protonated form of the solvent (e.g.
than H3O+ in water, or H2F+ in liquid HF, etc.) will be leveled to that protonated form, and will thus act as a strong acid in that
solvent. Conversely, any base that is a stronger base than the deprotonated form of the solvent (e.g than OH– in water or
CH3SO2CH2– , in DMSO) will be leveled to that deprotonated form, and will act as a strong base in that solvent. Thus superstrong bases such as the amide ion, NH2– are react completely with water to form ammonia and produce hydroxide ion
quantitatively. But in liquid ammonia, this is the normal basic form. Even stronger bases such as H– react with liquid ammonia to
form H2 and the NH2– ion.
Chemistry 2810 Lecture Notes
Dr. R. T. Boeré
Page 50
4.3.4 Hydrolysis of cations and metal acidity/basicity
It will very be obvious to you by now that the majority of the elements are metals, and that these tend to form cations. It is
therefore important to consider the Brønsted acidity of the metal cations. This is a point that is often ignored in General
Chemistry, and it comes as a surprise to many students that solutions of metal ions are often acidic, since the metal oxides are
closely associated with the hydroxide bases. Now the two phenomena are closely related, insofar as both can be though of as
being due to the reaction of the bare cation with water, a type of reaction which is commonly called hydrolysis. It turns out that
different metal ions, and different oxidation states of metal ions, have very different reactivity with water.
Consider the reaction of the following anhydrous chlorides with an excess of water (effectively a source of the naked metal
cation, since the chloride anion is non-basic and is a spectator ion in water).
Reagent
LiCl
MgCl
AlCl3
TiCl4
Cation radius, Å
0.90
0.86
0.67
0.74
Charge
1+
2+
3+
4+
Electronegativity
0.98
1.31
1.61
1.54
resulting pH
Z2/r
1.11
4.65
13.4
21.6
Note the large difference in solution pH. The means that differing amounts of H3O+ have been created from the original water.
We can break the overall reactions of the metal ions with water into several plausible steps.
1. The metal ion is solvated by water molecules (we can also call this hydration); typically metal ions are surrounded by
about six water molecules in what is known as the primary hydration sphere. Most of the heat liberated in the above
reaction is due to the enthalpy of hydration.
2. The hydrated ion can now undergo step-wise hyrolysis in which it delivers one or more H+ to the bulk solvent. This is
illustrated in the graphic below for the aluminum ion, though the same scheme applies for any element, differing only by
degree. The first step in this diagram shows how a strong attraction of the cation for an oxygen of one of the directlyattached water molecules results in the splitting-off of one H+ :
[Al(H2O)6]3+ + H2O à [Al(H2O)5OH]2+ + H3O+
3. Each step in the hydrolysis reduced the charge as hydroxycations are formed. Eventually a neutral species, a hydrated
metal hydroxide, forms. Form most metal ions of 2+ or higher charge, such neutral species will be insoluble, and a
precipitate will form.
4. In principle, if the effective electronegativity of the element is high enough, this process can continue to produce
hydroxyanions and even oxoanions. This is what happens for the transition metal ions in their highest oxidation states,
which have extremely high effective electronegativity, such as for example Mn(VII) which forms the familiar MnO4– ion in
aqueous solution.
5. Re-acidifying the metal oxoanion does not necessarily return the hydroxide, but often leads to polymerization of the
oxoanions to form polyoxoanions, through an acid-catalyzed condensation, that is, by loss of water between two such
anions.
6. The dehydration of neutral species results in the formation of the anhydrous metal oxide; in principle complete
condensation polymerization of the oxoanions will also lead to the same metal oxide.