The \"Born-Haber cycle\" (Lecture Notes section 3.2.2) can be used to find the \

Question

The "Born-Haber cycle" (Lecture Notes section 3.2.2) can be used to find the "Lattice Energy" of ionic compounds. For the alkalimetal halide salts, we have data for the Enthalpy of Formation (Delta H degree) of the salt, the Enthalpy of Vapourization of the metal (Delta H_yop), the enthalpy of dissociation halogen of the (Delta H_diss), the Ionization Energy (IE) of the in the gas phase, and the Electron Affinity (EA) of the halogen atom. These data can be found in Atkins Appendix Tables 2.7, 13a, 10.3 and 10.4. Using the data from Atkins, calculate the Lattice Energy of (each student to be assigned a different salt!). In your calculation, be careful with the sign and with the coefficients. For instance, IE and EA are always defined as positive, but in your calculation using the cycle think of the sign for EA! Similarly, realize that Delta H_diss is for the halogen X_2(gas, liquid or solid!).

Explanation / Answer

Let us do the calculation of Lattice energy for NaCl(s)

Na(s) --> Na(g)                 enthalpy of vaporization (dHvap) = +107 kJ/mol

Na(g) --> Na+(g)               first ionization energy (IE) = +496 kJ/mol

1/2Cl2(g) ---> Cl(g)           enthalpy of dissociation (dHdiss) = +122 kJ/mol

Cl(g) ---> Cl-(g)                 Electron affinity (EA) = -349 kJ/mol

Na(s) + 1/2Cl2(g) ---> NaCl(s)    Enthapy of formation (dHof) = -411 kJ/mol

let LE be the lattice energy

then,

dHof = dHvap + IE + dHdiss - EA + LE

-411 = 107 + 496 + 122 - 349 + LE

Thus,

lattice energy for NaCl (LE) = 349 - 411 - 107 - 496 - 122

                                            = -787 kJ/mol

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