Respuesta :
Answer : The lattice energy per mole of Li(s) formed is -1016.6 kJ
Explanation :
The formation of lithium fluoride is,
[tex]Li^{1+}(g)+\frac{1}{2}F_2(g)\overset{\Delta H_f}\rightarrow LiF(s)[/tex]
[tex]\Delta H_f^o[/tex] = enthalpy of formation of lithium fluoride = -594.1 kJ
The steps involved in the born-Haber cycle for the formation of [tex]LiF[/tex]:
(1) Conversion of solid lithium into gaseous lithium atoms.
[tex]Li(s)\overset{\Delta H_s}\rightarrow Li(g)[/tex]
[tex]\Delta H_s[/tex] = sublimation energy of lithium = +155.2 kJ
(2) Conversion of gaseous lithium atoms into gaseous lithium ions.
[tex]Li(g)\overset{\Delta H_I}\rightarrow Li^{+1}(g)[/tex]
[tex]\Delta H_I[/tex] = ionization energy of lithium = +520 kJ
(3) Conversion of molecular gaseous fluorine into gaseous fluorine atoms.
[tex]\frac{1}{2}F_2(g)\overset{\Delta H_D}\rightarrow F(g)[/tex]
[tex]\Delta H_D[/tex] = dissociation energy of fluorine = +75.3 kJ
(4) Conversion of gaseous fluorine atoms into gaseous fluorine ions.
[tex]F(g)\overset{\Delta H_E}\rightarrow F^-(g)[/tex]
[tex]\Delta H_E[/tex] = electron affinity energy of fluorine = -328 kJ
(5) Conversion of gaseous cations and gaseous anion into solid lithium iodide.
[tex]Li^{1+}(g)+F^-(g)\overset{\Delta H_L}\rightarrow LiF(s)[/tex]
[tex]\Delta H_L[/tex] = lattice energy of lithium fluoride = ?
To calculate the overall energy from the born-Haber cycle, the equation used will be:
[tex]\Delta H_f^o=\Delta H_s+\Delta H_I+\Delta H_D+\Delta H_E+\Delta H_L[/tex]
Now put all the given values in this equation, we get:
[tex]-594.1kJ=+155.2kJ+520kJ+75.3kJ+(-328kJ)+\Delta H_L[/tex]
[tex]\Delta H_L=-1016.6kJ[/tex]
Therefore, the lattice energy per mole of Li(s) formed is -1016.6 kJ
The lattice energy of LiF is -1017 KJ.
From the information available in the complete question;
Li(g) ΔH°sublimation (ΔH°s) = + 155.2 kJ
ΔH°ionization-energy (IE)= + 520 kJ
ΔH°bond-energy(BE) = + 75.3 kJ
ΔH°electron-affinity(EA) = – 328 kJ
ΔH°formation (ΔH°f) = – 594.1 kJ
Lattice energy(U) = ?
From Hess law of constant heat summation;
ΔH°f = ΔH°s + BE + IE + EA + U
U = ΔH°f - [ΔH°s + BE + IE + EA]
U = ( – 594.1 kJ) - [ 155.2 kJ + 75.3 kJ + 520 kJ + (– 328 kJ)]
U = -1017 KJ
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The missing part of the question is;
The Process Of Forming An Ionic Salt From Its Constituent Metallic And Nonmetallic Elements Is Called The Born-Haber Cycle, Which Is A Series Of Thermochemical Processes, Each With A ΔH, That Add Up (Think Of Hess’s Law) To Complete A 5+ Step Process For The Formation Of The Salt. Given The Following Data, Calculate The Lattice Energy Per Mole Of LiF(S)
The process of forming an ionic salt from its constituent metallic and nonmetallic elements is called the Born-Haber cycle, which is a series of thermochemical processes, each with a ΔH, that add up (think of Hess’s Law) to complete a 5+ step process for the formation of the salt.
Given the following data, calculate the lattice energy per mole of LiF(s) formed.
Li(s) → Li(g) ΔH°sublimation = + 155.2 kJ
Li(g) → Li+(g) + e- ΔH°ionization-energy = + 520 kJ
½ F2(g) → F(g) ½ ΔH°bond-energy = + 75.3 kJ
F(g) + e- → F– ΔH°electron-affinity = – 328 kJ
Li(s) + ½ F2(g) → LiF(s) ΔH°rxn = – 594.1 kJ
