The Ionic Model Flashcards
what are the assumptions of the ionic model?
- solids consist of hard, incompressible, non-polarisable charged spheres
- these charges are integer multiples of the elementary (“unit”) charge
- the only interactions between ions are electrostatic
what is the experimental evidence for the ionic model: appearance
- non-volatile
- brittle
- often transparent solids e.g. rock salt
what is the experimental evidence for the ionic model: electrical conductivity
insulating in solid form but conducting when molten or dissolved in polar solvent (e.g. in aqueous solution)
what is the experimental evidence for the ionic model: spectroscopy and magnetism
some ionic compounds show similar absorption spectra and magnetic properties to the free gas-phase ions
what is the experimental evidence for the ionic model: electron density
from x-ray diffraction there has been direct observation of the electron distribution in ionic solids
what are the different ways of determining ionic radius
don’t describe the methods
- Electron density measurements
- Pauling method using Zeff (slater’s rules)
- “Anions-touching” method by Lande
- Thermochemical scale based on Kapustinskii
- Self consistent set by Shannon and Prewitt
Describe the method of determining ionic radii by using electron density measurements
Interatomic distances are determined using electron density maps where the minimum in electron density is used as the point where “one ion stops and the other starts”
Using the lattice parameter the sum of both radii can be determined
i.e. r(cat) + r(an) = 0.5 x a
Describe the pauling method of determining ionic radii
The ions in a crystal lattice are assumed to be perfect spheres in contact with each other. The sum of the radii is therefore equal to the distance between the nuclei.
Assume that the radius of the ion having noble gas configuration is inversely proportional to Zeff.
r = Cn / Zeff where Cn is a constant depending on the principle quantum number, n
Describe the “anions-touching” method by Lande of determining ionic radii
Assume that the anions are touching, allowing calculation of r(an) from the lattice parameter, a. Calculated through geometric means.
Describe the thermochemical scale method of determining ionic radii based on Kapustinskii.
Obtain the lattice enthalpy from thermochemical experiments - can use Born-Haber cycles using the enthalpy of formation and related data.
Assume that the lattice energy is equal to the lattice enthalpy and use Kapustinskii’s equation for lattice energy, subbing in the experimentally determined lattice enthalpy in order to find the sum of the radii.
this is the preferred method for find the radii of molecular ions such as carbonate ions
Describe the self-consistent set by Shannon and Prewitt as a method for determining ionic radii.
It is an empirical approach based on a large dataset of experimentally determined crystal structures - “crystal radii”. By fixing the values of r(O2-) and r(F-), ionic radii for other ions were determined for which would reproduce interionic distances experimentally determined.
enthalpy of formation
enthalpy change when one mole of a compound is formed from its constituent elements in their reference states, all species being present in their standard states
enthalpy of atomisation
energy required to produce one mole of gaseous atoms from the element in its standard state
electron affinity
amount of energy released (or needed) when an electron is added to an atom or ion in the gaseous phase
Lattice energy
amount of energy required to dissociate an ionic soid into a gas of ions at infinite separation (at 0K)
lattice enthalpy
the enthalpy change associated with the dissociated of an ionic solid into a gas of ions at infinite separation (at 298K)
Hess’s Law
enthalpy change is independent of the pathway taken
What were Kapustinskii’s simplifications giving the Kapustinskii equation
- replace Madelung constant, A with 0.87v - A/n is assumed invariant
- replace the interatomic distance, r, with the sum of the ionic radii
- use n=9 as in rocksalt for all structures
What is variation between experimental and calculated lattice enthalpies used as an indication of?
covalent character in ionic compounds
what does agreement between experimental and calculated lattice enthalpies support?
(almost) pure ionic character - but it is not rigid proof.
Even so it does support the use of the ionic model for discussing the thermochemistry of these compounds
What could differences between the experimental and calculate lattice enthalpy be because of?
- covalent character
- van der waals forces
- inter-layer forces like hydrogen bonding
what is polarisation increased by (according to Fajan’s rules)
- high charge and small size of cation
- high charge and large size of anion
- electronic configuration of the cation (shielding effects)
what are the resulting effects of polarisation
- increase in melting and boiling points
- solubility of salts in polar solvents
- bond length shortening (in ionic compounds)
what is the coulomb energy of attraction in an ionic solid
E = (q(+)q(-)A) / (4 π ε(0) r)
ε(0) is vacuum permittivity
A is Madelung constant
r is interionic distance
what is the born repulsion formula
E = B/r^n
B is the born exponent
evaluate the use of the additivity of ionic radii as an indicator to the presence of covalent character
- polarisation does result in bond shortening as a result of the contraction of anion electron density
- accuracy depends on the method used to determine ionic radii
- unreliable for complex structures which arent binary compounds or rocksalt structures
- deviations as a result of other intermolecular forces not accounted for i.e. van der waals
- covalent compounds can mimic interionic distances
define ionic radius
size of an ion with respect to interionic spacing in a lattice of r+ and r- hard sphered which do not overlap
