1Åm = 1×10 −10 m

The ångström is often used in natural sciences and technology to express the sizes of atoms, molecules, and microscopic biological structures, the lengths of chemical bonds, the arrangement of atoms in crystals, the wavelengths of electromagnetic radiation, and the dimensions of integrated circuit parts

1Åm = 1×10 −10 m The unit was named after the Svensk physicist Anders Jonas Ångström (1814–1874). Ångström was one of the pioneers in the field of spectroscopy, and is known also for studies of astrophysics, heat transfer, terrestrial magnetism, and the aurora borealis.

1Åm = 1×10 −10 m In 1868, Ångström created a chart of the spectrum of solar radiation that expressed the wavelengths of electromagnetic radiation in the electromagnetic spectrum in multiples of 1×10 −10 m. Since the human eye is sensitive to wavelengths from about 4,000 to 7,000 angstroms, that choice of unit allowed sufficiently accurate measurements of visible wavelengths without resorting to fractional numbers. The unit then spread to other sciences that deal with atomic- scale structures.

Born-Haber cycles

Born and Haber 0 93 years ago, two German scientists Max Born and Fritz Haber first found a means of calculating lattice enthalpies, which cannot be determined directly. 0 They did so by comparing the standard enthalpy change of formation of the ionic compound to the enthalpy required to make gaseous ions from the elements. 0 This is an application of Hess's Law to ionic systems.

Concepts 0 Hess’s law: the enthalpy change for any chemical reaction is independent of the route, providing the starting conditions and final conditions, and reactants and products, are the same

Concepts 0 Lattice enthalpy: the enthalpy change that occurs when 1 mole of a solid ionic compound is separated into gaseous ions under standard conditions. (This endothermic definition is given in Table 13 of the IB booklet) NaCl(s) → Na + (g) + Cl - (g) ΔH lattice O (NaCl)

Concepts 0 Standard enthalpy change of formation: the enthalpy change occurs when 1 mole of the substance is formed from its constituent elements in their standard states under standard conditions. Na(s) + ½ Cl 2 (g) → NaCl(s) ΔH f O (NaCl)

Cycle Na(s) + ½ Cl 2 (g) Na + (g) + Cl - (g) NaCl(s)

From Na(s) + ½ Cl 2 (g) to Na + (g) + Cl - (g) Atomization Step 1 Na(s) + ½ Cl 2 (g) → Na(g) + ½ Cl 2 (g) ΔH atom O (Na) Step 2 Na(g) + ½ Cl 2 (g) → Na(g) + Cl(g) ΔH atom O (Cl) ( ΔH atom O (Cl) = ½ E(Cl-Cl), bond enthalpies are provided in Table 10 of the IB booklet )

Concept 0 Standard enthalpy change of atomization: the enthalpy change that occurs when 1 mole of gaseous atoms are formed from the element in its standard state under standard conditions.

From Na(s) + ½ Cl 2 (g) to Na + (g) + Cl - (g) Electrons being removed and added Step 3 Na(g) + Cl(g) → Na + (g) + e - + Cl (g) ΔH i O (Na) Step 4 Na + (g) + e - + Cl (g) → Na + (g) + Cl - (g) ΔH e O (Cl)

Concepts 0 First ionization energy: the energy required to remove 1 mole of electrons from 1 mole of isolated gaseous atom. 0 First electron affinity: the energy released when 1 mole of electron is added to 1 mole of isolated gaseous atom. (Data provided in Table 7 of the IB booklet)

Born-Haber Cycle H Na + (g) + e - + Cl (g) Na(g) + Cl(g) Na + (g) + Cl - (g) Na(g) + ½ Cl 2 (g) Na(s) + ½ Cl 2 (g) NaCl(s)

Born-Haber cycle H Mg 2+ (g) + O 2- (g) Mg 2+ (g) + 2e - + O(g) Mg(g) + O (g) Mg(g) + ½ O 2 (g) Mg(s) + ½ O 2 (g) MgO(s)

Born-Haber cycle ΔH lat O (ab) = ΔH atom O (a) + ΔH atom O (b) + ΔH i O (a) + ΔH e O (b) - ΔH f O (ab)

0 Second ionization energy 0 Second electron affinity 0 Overall ionization energy & electron affinity

Exothermic/Endothermic processes 0 Atomization is an endothermic process 0 Enthalpies of atomization always have positive values 0 Removing electrons from metal elements is a endothermic process 0 Adding electrons to non-metal element can be exothermic/endothermic

Exothermic/Endothermic processes 0 From the cycle it can be seen that the main reason why the formation of the ionic compound (NaCl) is overall an exothermic process is the large amount of energy given out when the ionic lattice is formed from its gaseous state.

Use of Born-Haber cycles 0 Can be used to calculate the enthalpy change of reactions, both hypothetical and practical.(find an unknown value provided that all the other values are known) 0 To determine the degree of ionic character of a salt ……

To determine the degree of ionic character of a salt Theoretical Lattice enthalpies can be calculated by assuming the crystal is made up from perfect spherical ions and that the only interaction is due to electrostatic forces between the ions (ionic model); it can be calculated from the size, charge and packing of the constituent ions ΔH lat O = Knm/ ( R M n+ +R X m- ) K is a constant which depends on the geometry of lattice.

To determine the degree of ionic character of a salt ΔH lat O = Knm/ ( R M n+ +R X m- ) 0 The energy needed to separate the ions depends on the product of the ionic charges and the sum of the ionic radii. 0 An increase in the ionic radius of one of the ions decreases the attraction between the ions 0 An increase in the ionic charge increases the ionic attraction between the ions

To determine the degree of ionic character of a salt 0 A comparison of theoretical and experimental lattice enthalpies is an indication of the ionic character of a compound. 0 If there is good agreement between the two values obtained, it is reasonable to say that the salt has a high degree of ionic character, which indicates a large difference in electronegativity values between the constituent elements. 0 If there is a appreciable discrepancy between the two value obtained, it indicates that the salt contains an appreciable amount of covalent bonding, and the difference in electronegativity value is relatively low.

To determine the degree of ionic character of a salt 0 The bonding of sodium iodide is stronger than expected from a simple ionic model because the large iodide ion is distorted (polarized) by the smaller sodium ion. This gives the compound some covalent character, which provides an additional contribution to the bonding. 0 A covalent bond can be considered an extreme case od distortion. CompoundΔH lat O (Born-Haber) ΔH lat O (ionic model) % difference NaCl NaBr ,9 NaI AgI

Other uses: to determine if a particular compound is likely to form 0 The enthalpies of formation of some unknown compounds can be calculated by using lattice enthalpy and Born-Haber cycle, this can help chemists to predict the possibility of forming new compounds. 0 The formation of the first noble gas compound, XePtF 6 is a great example. 0 It can also help chemists to understand the existence of particular compounds. 0 Why sodium chloride has the formula NaCl instead of NaCl 2 ?

Bibliography 0 Catrin Brown, Mike Ford: Higher Level Chemistry. Pearson Baccalaureate. 0 Geoffery Neuss: Chemistry Course Companion. Oxford University Press ber.htm %E5%93%88%E4%BC%AF%E5%BE%AA%E7%8E%AF 0 f

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