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Lattice Energy - Practice Questions & MCQ

Edited By admin | Updated on Sep 18, 2023 18:35 AM | #JEE Main

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Lattice Enthalpy

The lattice energy of a compound is a measure of the strength of this attraction. The lattice energy (ΔHlattice) of an ionic compound is defined as the energy required to separate one mole of the solid into its component gaseous ions. For the ionic solid MX, the lattice energy is the enthalpy change of the process:

 

The lattice energy ΔHlattice of an ionic crystal can be expressed by the following equation:

\mathrm{\Delta H_{\text {lattice }}=\frac{\mathrm{C}\left(\mathrm{Z}^{+}\right)\left(\mathrm{Z}^{-}\right)}{\mathrm{R}_{0}}}

in which C is a constant that depends on the type of crystal structure; Z+ and Z are the charges on the ions, and Ro is the interionic distance. Thus, the lattice energy of an ionic crystal increases rapidly as the charges of the ions increase and the sizes of the ions decrease. 

 

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:

  • ΔHf°, the standard enthalpy of formation of the compound

  • IE, the ionization energy of the metal

  • EA, the electron affinity of the nonmetal

  • ΔHs°, the enthalpy of sublimation of the metal

  • D, the bond dissociation energy of the nonmetal

  • ΔHlattice, the lattice energy of the compound

The figure given below shows 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.

 

For Caesium fluoride, the lattice energy can be calculated using the given values as follows:

 

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Lattice Enthalpy

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Lattice Enthalpy

Chemistry Part I Textbook for Class XI

Page No. : 107

Line : 8

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