Construct a Born-Haber cycle for the formation of the hypothetical compound NaCl2, where the sodium ion has a 2+ charge (the 2nd ionization energy for sodium is given in Table 7.2 in the textbook).Part AHow large would the lattice energy need to be for the formation of NaCl2 to be exothermic? Part BIf we were to estimate the lattice energy of NaCl2 to be roughly equal to that of MgCl2 (2326 kJ/mol from Table 8.2 in the textbook), what value would you obtain for the standard enthalpy of formation, ΔH∘f, of NaCl2?

Question
Asked Nov 25, 2019
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Construct a Born-Haber cycle for the formation of the hypothetical compound NaCl2, where the sodium ion has a 2+ charge (the 2nd ionization energy for sodium is given in Table 7.2 in the textbook).

Part A

How large would the lattice energy need to be for the formation of NaCl2 to be exothermic?
 

Part B

If we were to estimate the lattice energy of NaCl2 to be roughly equal to that of MgCl2 (2326 kJ/mol from Table 8.2 in the textbook), what value would you obtain for the standard enthalpy of formation, ΔH∘f, of NaCl2?
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Expert Answer

Step 1

The Born-Haber cycle for the formation of hypothetical compound NaCl2 can be constructed as given below.

ΔΗ ,
form
Na (s)
C2(g)
NaCl2 (s)
Dissociation
ΔΗ.
sub
enegy
Lattice
Na(g)
2C1 (g)
energy
Ionization
Electron
affinity
energy
Na2+
(g)
2Cl (g)
help_outline

Image Transcriptionclose

ΔΗ , form Na (s) C2(g) NaCl2 (s) Dissociation ΔΗ. sub enegy Lattice Na(g) 2C1 (g) energy Ionization Electron affinity energy Na2+ (g) 2Cl (g)

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Step 2

The various reactions are given as,

Na(s)+Cl, (g)NaCl, (s) AH?
Na(s)Na (g)
Na (g) Na (g)+e
AH
-108kJ/mol
sub
LE, 496 kJ/mol
Na(g)Na2
Cl, (g) 2C1(g)
Cl(g)e C(g)
(g+2e
LE, 4562kJ/mol
-122 kJ /mol
dissociation
EA -349 kJ /mol
help_outline

Image Transcriptionclose

Na(s)+Cl, (g)NaCl, (s) AH? Na(s)Na (g) Na (g) Na (g)+e AH -108kJ/mol sub LE, 496 kJ/mol Na(g)Na2 Cl, (g) 2C1(g) Cl(g)e C(g) (g+2e LE, 4562kJ/mol -122 kJ /mol dissociation EA -349 kJ /mol

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Step 3

Using Hess&rsqu...

AH2 (NaC AH LE +Dissociation energy + EA - lattice energy
latticeenergy AH LEDissociation energy + EA - AH2 (NaCl
lattice energy 108kJ/mol+ 496KJ /mol+4562kJ /mol + 2188.4 kJ/mol
2x(122KJ/ mol)-(2x349 kJ/ mol)- AH (NaCl)
sub
sub
lattice energy 4712 kJ /mol - AH2 (NaCl
Where, LE Ionization energy
=
E.A Electron affinity
=
help_outline

Image Transcriptionclose

AH2 (NaC AH LE +Dissociation energy + EA - lattice energy latticeenergy AH LEDissociation energy + EA - AH2 (NaCl lattice energy 108kJ/mol+ 496KJ /mol+4562kJ /mol + 2188.4 kJ/mol 2x(122KJ/ mol)-(2x349 kJ/ mol)- AH (NaCl) sub sub lattice energy 4712 kJ /mol - AH2 (NaCl Where, LE Ionization energy = E.A Electron affinity =

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