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Construct a Born-Haber cycle and calculate the lattice energy of CaC2 (s). Note that this solid contains the diatomic ion C2 Useful Information: AH (CaC2(s)) -60 kJ/mol + 178 kJ/mol +717 kJ/mol AHsub (Ca (s)) AHsub (C (s)) Bond dissociation energy of C2 (g) First ionization energy of Ca (g) Second ionization energy of Ca (g) First electron affinity of C2 (g) Second electron affinity of C2 (g) = +614 kJ/mol +590 kJ/mol = +1 143 kJ/mol -315 kJ/mol +410 kJ/mol

Explanation / Answer

Heat of formation of CaC2 is given as -60 KJ/mol

Ca (s) + 2C (s) -------> CaC2 (s) ......delta H = -60 KJ/mol .....(1)

1 mole of CaC2 can be prepared from the following series of steps

sublimation of Ca(s)
Ca (s) ---------> Ca (g) ......delta H = 178 KJ/mol ......(2)

gaseous Ca are ionized twice
Ca (g) --------> Ca+ (g) + e-........delta H = 590 KJ/mol ....(3)

Ca+ (g) ---------> Ca2+ (g) + e- ....delta H = 1145 KJ/mol....(4)

2 moles of C(s) are sublimed ...so delta H will be twice that for 1 mol
2C (s) ---------> 2C (g)....delta H = 2*717 = 1434 KJ/mol....(5)

then, a bond is fomed between them

It will be negative of bond breaking (dissociation ) energy...
2C(g) --------> C2 (g) .....delta H = -614 KJ/mol......(6)

than an e- was added to this C2 molecule ....
C2(g) + e- ---------> C2- (g) ......delta H = -315 KJ/mol ....(7)

again an e- was added ....
C2- (g) + e- --------> C22- (g) .....delta H = 410 KJ/mol.......(8)

now we have made Ca2+ (g) and C22- (g)

lattice enrgy is defined for the following process
Ca2+ (g) + C22- (g) -------> CaC2 (s) ....delta H = U


now adding (2) + (3) + (4) + (5 )+ (6) + (7) + (8)

Ca(s) + 2C(s) -----> Ca2+ (g) + C22- (g) ....delta H = 178 + 590 + 1145 + 1434 + -614 + -315 + 410

Ca(s) + 2C(s) -------> Ca2+ (g) + C22- (g) ....delta H = 2828

Here 2828 is the enthalpy change for making of Ca2+ (g) and C22- (g) ......

Further we know that,
Ca2+ and C22- combines to give CaC2 and deltaH = U, so an extra -U term has to be added above ...
Ca(s) + 2C(s) -----> Ca2+ (g) + C22- (g) ....delta H = 2828 - U

now delta H of process (1) should be equal to delta H of above process

-60 = 2828 - U

U = 60+2828 = 2888 KJ/mol

This is the lattice energy of CaC2.

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