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The born-haber cycle

It is not possible to measure lattice energies directly. However, the lattice energy can be calculated using the equation given in the previous section or by using a thermochemical cycle. The Born-Haber cycle    is an application of Hess’s law that breaks down the formation of an ionic solid into a series of individual steps:

  • Δ H f ° , the standard enthalpy of formation of the compound
  • IE , the ionization energy of the metal
  • EA , the electron affinity of the nonmetal
  • Δ H s ° , the enthalpy of sublimation of the metal
  • D , the bond dissociation energy of the nonmetal
  • Δ H lattice , the lattice energy of the compound

[link] diagrams the Born-Haber cycle for the formation of solid cesium fluoride.

A diagram is shown. An upward facing arrow is drawn to the far left of the chart and is labeled “H increasing.” A horizontal line is drawn at the bottom of the chart. A downward-facing, vertical arrow to the left side of this line is labeled, “Overall change.” Beside this arrow is another label, “capital delta H subscript f, equals negative 553.5 k J per mol, ( Enthalpy of formation ).” Three horizontal lines, one above the other, and all above the bottom line, are labeled, from bottom to top, as: “C s ( s ), plus sign, one half F subscript 2, ( g ),” “C s ( g ), plus sign, one half F subscript 2, ( g ),” and “C s, superscript positive sign, ( g ), plus sign, one half F subscript 2, ( g ).” Each of these lines is connected by an upward-facing vertical arrow. Each arrow is labeled, “capital delta H subscript 1, equals 76.5 k J per mol, ( Enthalpy of sublimation ),” “capital delta H subscript 2, equals 375.7 k J per mol, ( ionization energy ),” and “capital delta H subscript 3 equals 79.4 k J / mol ( one half dissociation energy ).” Another horizontal line is drawn in the center top portion of the diagram and is labeled “C s, superscript positive sign, ( g ), plus sign, F, ( g ).” There is one more horizontal line drawn to the right of the overall diagram and located halfway down the image. An arrow connects the top line to this line and is labeled, “capital delta H equals negative 328.2 k J / mol ( electron affinity ).” The line is labeled, “C s superscript positive sign ( g ) plus F superscript negative sign ( g ).” The arrow connecting this line to the bottom line is labeled, “negative capital delta H subscript lattice equals negative 756.9 k J / mol.” The arrow points to a label on the bottom line which reads, “C s F ( s ).”
The Born-Haber cycle shows the relative energies of each step involved in the formation of an ionic solid from the necessary elements in their reference states.

We begin with the elements in their most common states, Cs( s ) and F 2 ( g ). The Δ H s ° represents the conversion of solid cesium into a gas, and then the ionization energy converts the gaseous cesium atoms into cations. In the next step, we account for the energy required to break the F–F bond to produce fluorine atoms. Converting one mole of fluorine atoms into fluoride ions is an exothermic process, so this step gives off energy (the electron affinity) and is shown as decreasing along the y -axis. We now have one mole of Cs cations and one mole of F anions. These ions combine to produce solid cesium fluoride. The enthalpy change in this step is the negative of the lattice energy, so it is also an exothermic quantity. The total energy involved in this conversion is equal to the experimentally determined enthalpy of formation, Δ H f ° , of the compound from its elements. In this case, the overall change is exothermic.

Hess’s law can also be used to show the relationship between the enthalpies of the individual steps and the enthalpy of formation. [link] shows this for cesium chloride, CsCl 2 .

Enthalpy of sublimation of Cs( s ) Cs ( s ) Cs ( g ) Δ H = Δ H s ° = 76.5 kJ
One-half of the bond energy of Cl 2 1 2 Cl 2 ( g ) Cl ( g ) Δ H = 1 2 D = 122 kJ
Ionization energy of Na( g ) Na ( g ) Na + ( g ) + e Δ H = I E = 496 kJ
Negative of the electron affinity of Cl Cl ( g ) + e Cl ( g ) Δ H = E A = −368 kJ
Negative of the lattice energy of NaCl( s ) Na + ( g ) + Cl ( g ) NaCl ( s ) Δ H = −Δ H lattice = ?
Enthalpy of formation of NaCl( s ), add steps 1–5 Δ H = Δ H f ° = Δ H s ° + 1 2 D + I E + ( E A ) + ( Δ H lattice ) Na ( s ) + 1 2 Cl 2 ( g ) NaCl ( s ) = −411 kJ

Thus, the lattice energy can be calculated from other values. For cesium chloride, using this data, the lattice energy is:

Δ H lattice = ( 411 + 109 + 122 + 496 + 368 ) kJ = 770 kJ

The Born-Haber cycle may also be used to calculate any one of the other quantities in the equation for lattice energy, provided that the remainder is known. For example, if the relevant enthalpy of sublimation Δ H s ° , ionization energy (IE), bond dissociation enthalpy (D), lattice energy Δ H lattice, and standard enthalpy of formation Δ H f ° are known, the Born-Haber cycle can be used to determine the electron affinity of an atom.

Lattice energies calculated for ionic compounds are typically much higher than bond dissociation energies measured for covalent bonds. Whereas lattice energies typically fall in the range of 600–4000 kJ/mol (some even higher), covalent bond dissociation energies are typically between 150–400 kJ/mol for single bonds. Keep in mind, however, that these are not directly comparable values. For ionic compounds, lattice energies are associated with many interactions, as cations and anions pack together in an extended lattice. For covalent bonds, the bond dissociation energy is associated with the interaction of just two atoms.

Questions & Answers

what a hydrocarbon?
Laura Reply
hydrocarbons are compounds that are made up of hydrogen and carbon only
Kinsley
what is hybridization
Laura Reply
the mixing of atomic orbitals to form molecular of similar energy called hybrid orbitals
Cffrrcvccgg
who are the alchemist?
Victor Reply
alchemy science of transmutation. typically it is aim at tranforming lead to or other base metals to gold and the creation of the philosophers stone which in reality isn't a stone it's something priceless something we all need for coming times. don't be fooled
Kendrick
read Corinthians 5 verses 50 to the end of the chapter then read revelations chapter 2 verse 17
Kendrick
The word "Alchemy" comes from the forgotten name for Ancient Egypt, Khemmet. Khem was the name for the Egyptian Empire, but the actual land of Egypt was called Khemmet because the "T" on the end of a word denoted a physical location on Earth and not just an idea.
Michael
Wow!
mendie
What's the mass number of carbon
Charlie Reply
first Faraday's law
Akinbola
mass number of carbon is 12.
Nnenna
wat d atomic number of oxygen
safiya
atomic number of oxygen is 8
Nnenna
which quantum number divides shell into orbitals?
Tomiwa Reply
azimuthal
Emmanuel
hi
Charlie
azimuthal
reinhard
azimuthal
Charlie
what is atom
Desmond Reply
an atom is a smallest indivisible part of an element
Henry
an atom is the smallest part of an element that takes part in a chemical reaction
Nana
wat is neutralization
Dubem Reply
when any acid reacts with base to decrease it's acidity or vice-versa to form salt and solvent.. which is called neutralization
Santosh
explain buffer
Organic
buffer is a solution which resists changes in pH when acid or alkali added to it..
Santosh
hello, who is online
UTHMAN
buffer is the solution which resist the change in pH by addition of small amount of acid or alkali to it
KAUSIK
neutralisation is the process of mixing of a acid and a base to form water and corresponding salt
KAUSIK
how to solve equation on this
Princewill Reply
what are the elent of ionic and covalent bonding
Princewill
what is gases
Wesike Reply
Its one of the fundamental sate of matter alone side with liquid, solid and plasma
John
What is chemical bonding
John
To my own definitions. It's a unit of measurement to express the amount of a chemical substance.
Ozoaniehe Reply
What is mole
TAMIL Reply
It's the unit of measurements used to express the amount of chemical substance.
Ozoaniehe
What is pressure
Stellamaris Reply
force over area
Jake
force applied per unit area
john
force applied per unit area
Prajapati
Why does carbonic acid don't react with metals
Aditya Reply
Why does carbonic acid don't react with metal
Aditya
Some metals will react depending on their Standard Electrode Potential. Carbonic acid is a very weak acid (i.e. a low hydrogen ion concentration) so the rate of reaction is very low.
Paul
sample of carbon-12 has a mass of 6.00g. How many atoms of carbon-12 are in the sample
Emokiniovo Reply
a sample of carbon-12 has a mass of 6.00g. How many atoms of carbon-12 are in the sample
Sharmin Reply
Practice Key Terms 3

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Source:  OpenStax, Chemistry. OpenStax CNX. May 20, 2015 Download for free at http://legacy.cnx.org/content/col11760/1.9
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