Chemistry 2810 Lecture Notes
4.3
Dr. R. T. Boeré
Page52
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 nonaqueous 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) +
H2 O
⇔
H 3 O+
+
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
H
105º
2.59
OH2
2.59
OH2
Structure of the H9O4+ 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 pH = − log 10 H 3 O
+
−
3
[HF ]
], we define the analogous pK
a
−4
= − log10 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 H2 O ⇔
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 pKa represents a weak acid, while a negative pKa represents a strong acid. As
a general rule, for polyprotic acids, the pKa 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 pKa'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 )
+
H 2 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)
+
nH 2 O
Dr. R. T. Boeré
  →
excess
Page53
F − ( aq ) ;
H + ( g)
+
nH 2 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
H2 O
2
13
14
15
16
17
LiOH
Be(OH)2
B(OH)3
HCO2–
H2 O
HF
HOF
NaOH
Mg(OH)2
Al(OH)3
H4SiO4
polyacids
NH3
HNO3
HNO2
H3PO2
H3PO3
H3PO4
polyacids
H2 S
H2SO3
H2SO4
polyacids
KOH
Ca(OH)2
Ga(OH)3
Ge(OH)2
H3AsO3
H3AsO4
H2Se
H2SeO3
H2SeO4
HCl
HOCl
HClO2
HClO3
HClO4
HBr
HOBr
HBrO3
HBrO4
RbOH
Sr(OH)2
In(OH)3
SnO.H2O
SnO2.H2O
H3SbO3
H2Te
H2TeO3
Te(OH)6
HI
HOI
HIO3
H5IO6
CsOH
Ba(OH)2
TlOH
PbO.H2O
Bi(OH)3
H2Po
Po(OH)2
H2PoO3
?
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 oxoacids. 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
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
Chemistry 2810 Lecture Notes
Dr. R. T. Boeré
Page54
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:
Na2O + 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 oxoacids, 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
SnO2
PbO
PbO2
As2O3
As2O5
Sb2O3
Sb2O5
Bi2O3
Bi2O5
16
17
BeO
Al2O3
Ga2O3
In2O3
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.
a)
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
Chemistry 2810 Lecture Notes
2.
Dr. R. T. Boeré
Page55
The successive pKa 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
Cl
OH
I
HO
HO
OH
O
O
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
O
O
OH
OH
7.8, 11.2
2.6, 8.0
-2.0, 1.9
O
O
P
P
OH
HO
OH
2.1, 7.4, 12.7
OH
HO
HO
O
HO
N
OH
H
1.8, 6.6
O
-1.4
OH
C
Si
OH
HO
OH
10
HO
Legend
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.
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 ringlike polyphosphates, each of which at least theoretically has a corresponding protonated form. A separation of the anions that
co-exist, for example, in commercial "polyphosphoric acid" is shown in the paper chromatogram reproduced below:
Chemistry 2810 Lecture Notes
Dr. R. T. Boeré
Page56
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 H2
C
H
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
O
P
O
H
ATP4-
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 elementhydrogen 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.
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.
Chemistry 2810 Lecture Notes
c)
Dr. R. T. Boeré
Page57
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
non-aqueous 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 BrønstedLowry 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
super-strong 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
Page58
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
directly-attached 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.