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4.13 Incomplete Electron Transfer in Ionic Compounds
4.13.1. Theoretical values of lattice enthalpy
Lattice enthalpy: The enthalpy change when one mole of an ionic crystal is formed from its constituent ions in the gaseous state under standard conditions (在標準條件下，由相
互分離的氣態陽離子和氣態陰離子生成一摩爾離子晶體時所釋放的能量。)
mAn+(g) + nBm–(g) → A
mBn(s) ΔH = ∆ Hlattice (in kJmol–1)
It is a measure of the strength of ionic bonds in an ionic compound. Based on the principles of electrostatics, we have,
− + − + + ∝ r r Z Z E = π ε − + r 4 e Z Z N k E o 2 A
Z+ and Z–: Charge of cation and anion
r+ and r–: Internuclear distance = sum of radii of cation and anion (r = r+ + r–)
Such calculation is actually based on two assumptions:
The ionic crystal is made up of perfectly spherical ions with uniform distribution of charge (離子是完全球體，電荷均勻分佈).
The ions are just touching with each other with electrostatic interactions in between
(i.e. no sharing of electrons) (陽離子和陰離子剛剛互相接觸).
Basically, we assumed that the compound is purely ionic.
4.13.2. Comparison of experimental and theoretical values of lattice
enthalpies
However, the reality is always not that simple.
The following table shows the comparison of experimental and theoretical values of lattice enthalpies of some ionic compounds:
Compound Theoretical value / kJmol–1 (From
the pure ionic model) Experimental value / kJmol
–1
(From Born-Haber cycle)
NaCl –770 –781 NaBr –735 –742 NaI –687 –705 KCl –702 –711 KBr –674 –679 KI –636 –643 AgCl –770 –905 AgBr –758 –891 AgI –736 –876 ZnS –3427 –3615
There is good agreement between the theoretical and experimental values of L.E. for the
This close agreement provides evidence that the simple model of an ionic lattice
composed of discrete spherical ions with evenly distributed charges would be a satisfactory one in the case of alkali metal halides.
However, there are great discrepancies between the theoretical values and the experimental
values of silver halides and zinc sulphide.
For examples, the theoretical values for silver halides are approximately 130 kJ mol-1
(i.e. about 15%) less negative than the experimental values.
This suggests that the bonding in silver halides is stronger than the prediction based on
the ionic model.
Besides, the differences also imply that these compounds seem unlikely to be made up
of separate, individual ions. Instead, a significant amount of covalent character might be present in these compounds.
In other words, the bonding in silver halides is not pure ionic but is an intermediate between ionic and covalent.
Therefore, we should not make hard and fast generalization about the nature of bonding in compounds such as silver halides.
Take silver iodide (AgI) as an example, it has a high melting point (558°C) and it
conducts electricity when molten. Both are consistent with the common properties of ionic compound.
However, the values in L.E. show that AgI has a considerable covalent character.
The partly covalent nature of the ionic bonds in zinc sulphide and silver halides can be
interpreted by the idea that electrons are incompletely transferred in forming the ionic compounds and such phenomenon is called polarization of ions (離子的極化).
4.13.3. Polarization of ions
The polarization of ion represents the emergence of covalent character in ionic compounds
due to incomplete transfer of electrons.
It is assumed that the transfer of electron in an ionic compound is complete.
However, in reality, when an ionic bond is formed between the cation X+ and anion Y–,
owing to its charge, the X+ ion would tend to attract the outer electrons in the charge
cloud of Y–.
This causes a displacement of the outer electrons of Y– back to X+. The electronic
clouds of the ions are distorted.
For this reason, the outer electron of X is not completely transferred to Y. The electrons
in one ion are not only confined to the charge cloud of that ion, but shared with the neighboring ions.
This effect can be represented diagrammatically as in the following figure:
The degree of polarization is a measure of covalent character of an ionic compound. In the polarization of ions, the cations take the active role (∵ they attract electrons):
The tendency for a cation to attract electrons and distort an anion (i.e. polarize an
anion) is called polarizing power (極化能力).
Polarizing power of a cation increases as its charge density ( 電 荷 密 度 )
(charge/volume ratio) increases.
For anions, they are considered as “being polarized”:
The ease with which an electron cloud of the anion is distorted by adjacent cation is
called polarizability (極化性 / 被極化能力).
Polarizability of an anion increases as its size increases.
If the electrons are far from the nucleus, they will experience less nuclear control ⇒
Easier to be attracted towards the cation ⇒ More polarizable
Take AgI as an example, the iodide ion is the largest among the halides ions. It is said
to be highly polarizable as its outer electrons are far away from the nuclear control.
Thus, a silver ion might attract the electron cloud around the iodide ion, thus producing
a certain amount of covalent character.
There are some general rules concerning the polarization of ionic bonds to be considered
(called Fajan’s rules):
The polarizing power of a cation is increased as the ionic size is reduced. ♦ Example: Polarizing power of ions of Group II metals:
Be2+ > Mg2+ > Ca2+ > Sr2+ > Ba2+
♦ In this series, beryllium ion is the smallest cation with the greatest polarizing
power. Therefore, when comparing the chlorides of these five elements, BeCl2
has the greatest covalent character.
♦ This can be indicated by their melting points:
BeCl2 (405°C), MgCl2 (714°C), CaCl2 (772°C), SrCl2 (872°C), BaCl2 (960°C) The polarizing power of a cation is increased as the ionic charge is increased.
Al3+ > Mg2+ > Na+
♦ In this series, aluminium ion is the cation with the highest charge so its
polarizing power will be the highest. Therefore, when comparing the chlorides of these elements, NaCl is predominantly (mainly) ionic while AlCl3 is
predominantly covalent.
An ionic compound will have appreciable covalent character if the anion is large
(polarizability of anion increases as the ionic size increases).
♦ Polarizability of halide ions:
I– > Br– > Cl– > F–
♦ Similarly, for ions of Group VI elements S2– > O2–
Transition metal ions such as Zn2+ and Ag+ appear to have higher polarizing power ♦ This is because the d electrons do not effectively shield the nuclear charge.
♦ As a result, ions of transition metal are usually much smaller than the ions of
main group metals and hence these cations have higher charge density (⇒ higher polarizing power).
There exist other evidences which show that some ionic compounds contain some covalent
characters. For example:
Ionic compounds with large degree of polarization may be soluble in organic solvent
(have low solubility in water).
♦ LiCl (quite covalent) is very soluble in ethanol and diethyl ether, but NaCl
(nearly purely ionic) is insoluble.
♦ For the silver halides, the higher the covalent character, the less soluble in water.
AgF > AgCl > AgBr > AgI
The melting points and boiling points of ionic compounds with high degree of
polarization are usually quite low because these compounds are very similar to simple molecular substances.
In contrast, compounds which are predominantly ionic usually have high melting and
boiling points.
Example 1
Arrange and explain the following compounds in increasing order of boiling points AlF3, AlCl3, AlBr3 and AlI3
AlI3 < AlBr3 < AlCl3 < AlF3. Going down the Group VII from F– to I–, the size of anion increases
and the electron cloud becomes easier to be distorted. It results in more polarization and the compound will have more covalent characters. The greater the covalent character of the compound and the lower the b.p. Thus AlI3 would have the highest degree of covalent character
4.14 Polarity of Covalent Bonds
4.14.1.
Electronegativity
( 電負性
/ 電負度
) revisited
Electronegativity is a measure of tendency of an atom in a stable molecule to attract electrons within a bond (原子在分子中吸引鍵合電子的相對能力).
One commonly used method to measure the electronegativity is the Pauling scale of electronegativity (鮑林電負性標度).
Pauling defined the electronegativity of an atom as the power of that atom in a molecule to attract electrons. In contrast with electron affinity, it is a measure of the
power of a single gaseous atom to attract electrons.
The scale is from 0 to 4, electronegativity of monoatomic molecules (i.e. noble gases)
is set as 0, while 4 (maximum) is assigned to the most electronegative atom, fluorine. In general, electronegativity values increase from left to right across each period
This can be explained in term of the increase in effective nuclear charge across a
period. Although an extra electron is also added for each element, this does not fully shield the effect of the increase nuclear charge. An increase in effective nuclear charge makes the attraction for the bonded electrons increase.
Electronegativity decreases when going down each group
This occurs because, in moving down a group, the screening of the atoms increases and
4.14.2.
Polarization of covalent bonds
A covalent bond is said to be “pure” if there is an equal electron sharing between the bonded
atoms. Examples include diatomic molecules like H2 and Cl2.
In some covalent bonds, there may be unequal sharing of the bonded electron pairs. Take
HCl molecule as an example.
This leads to distortion of electron cloud. Such phenomenon is called polarization of covalent bond (or simply “bond polarization”) (鍵極化).
It is caused by a difference in electronegativity between the bonded atoms.
For example, in HCl molecule, since chlorine is more electronegative than hydrogen, the
bonding electrons will be drawn closer to the chlorine atom as shown above.
The resulting covalent bond is called a polar covalent bond (極性共價鍵).
This type of bonding has a partial positive charge (δ+) ( 部 份 正 電 荷 ) on the less electronegative atom and a partial negative charge (δ–) ( 部 份 負 電 荷 ) on the more electronegative atom due to unequal sharing of electron. The Greek letter δ (Delta) is used
to indicate that the charges are small.
It can be generalized that polarity of a chemical bond is related to the difference in
electronegativity between the two bonded atoms. The larger the difference in
electronegativity, the more polar a bond would be (more ionic character).
The following table shows the relationship between bond nature and difference in
electronegativity between the two bonded atoms.
Molecule Bond Difference in electronegativity Bond nature
H2 H–H 2.1 – 2.1 = 0 Purely covalent
(Equal electron sharing)
CCl4 C–Cl 3.0 – 2.5 = 0.5 Polar covalent
(Unequal electron sharing)
HCl H–Cl 3.0 – 2.1 = 0.9
NH3 N–H 3.0 – 2.1 = 0.9
H2O O–H 3.5 – 2.1 = 1.4
BeF2 Be–F 4.0 – 1.5 = 2.5 Predominantly ionic
(Almost complete electron transfer)
It should be noted that pure ionic or covalent bonds are extreme cases. Actually there are
many compounds having intermediate types of bonding.
In general, the bond can be regarded as predominantly ionic when the difference in
electronegativity is greater than 1.7.
The plot showing the relationship between nature of bonding and
4.15 Polarity of Molecules
4.15.1.
Measuring bond polarization – Dipole moments (
偶極矩
)
Bond polarization results in the formation of a dipole ( 偶 極 ) with two equal opposite
charges (+q and –q) (i.e. δ+ and δ– mentioned in the previous part) separated by a distance d.
The product between the charge (q) and the distance between the two charges gives a
quantity called dipole moment (μ). That is,
µ = q × d (Mathematical treatments are not required in AL)
Dipole moments are usually expressed in Debye unit (D). For example, the dipole
moment of HCl molecule is 1.1D.
Dipole moment can be used as a measure of the extent of bond polarization. In other
words, it reflects the polarity of a molecule (偶極矩是分子極性大小的指標). It should be noted that dipole moment is a vector quantity (偶極矩是一向量).
The arrow points from +q towards –q.
For a molecule with more than one polar bond, the dipole moment is given by the vector sum of the dipole moments of various polar bonds.
If the vector sum is zero, the dipole moment of the molecule is zero, and the
molecule will be described as non-polar.
The greater the resultant dipole moment, the more polar the molecule is. The magnitude of dipole moment of a molecule is determined by three factors:
The difference in electronegativity between the bonded atoms and thus the degree of
ionic character of individual bonds. Take the hydrogen halides as examples:
Molecule HF HCl HBr HI
μ (D) 1.91 1.05 0.80 0.42
Shape of molecules.
Bond angle
Bond length (this affects value of d). For example:CH3Cl (1.87 D) and CH3F (1.81 D)
4.15.2.
Polar and non-polar molecules (Important)
Dipole moment is a key factor for determining whether a molecule is polar or non-polar. Based on the fact dipole moment is a vector quantity, the shape of the molecule will
determine whether a molecule has a net dipole moment or not.
Sometimes the dipoles may cancel out each other, giving a zero dipole moment.
For example, for molecules in form of ABx (x 2), the following shapes will give a≧ zero dipole moment.
Shape Molecule Cancelling out of the
dipole moments Linear CO2, BeCl2 Trigonal planar SO3, BF3 Tetrahedral CH4, CCl4 Trigonal bipyramidal PCl5 Octahedral SF6
On the other hand, there are some shapes which the dipole will not be cancelled out. The
molecules will have net dipole moments. For example:
Shape Molecule Dipole moment of
individual polar bond Net dipole moment
V-shaped H2O
Trigonal
pyramidal NH3
Tetrahedral CHCl3
Dipole moments can provide important structural information about a molecule.
On the other hand, existence of a net dipole moment for SO2 molecule indicates that the
molecule contains polar bonds which are not linearly arranged.
Dipole moments also affect the strength of intermolecular forces.
The interactions between polar molecules (called dipole-dipole interactions) will be stronger than that between non-polar molecules (to be discussed later).
For this reason, polar molecules often have higher melting and boiling points than
non-polar molecules with similar sizes.
4.15.3.
Experimental evidence showing polarity of molecules
The phenomenon of polarization of covalent bonds may be readily demonstrated with the
apparatus shown below.
The glass rod acquires positive charges by rubbing it with polythene sheet. A jet of polar liquid can be deflected by an electric field.
The results obtained with a series of liquids are given below:
Molecules with marked deflection Molecules showing no (or slight) deflection
Trichloromethane (CHCl3) Ethanol (CH3CH2OH) Propanone Water (H2O) Tetrachloromethane (CCl4) Benzene (C6H6)
Hexane (slight deflection)
The effect of E-field can be explained by the following diagrams:
Slight deflection of liquid benzene can be explained by the polarization of π electron clouds by the electric field.
Dipole moments are induced in benzene molecules by the electric field.
