Born Haber Cycle

In the Born-Haber Cycle, ionic solids are created through the ionization of elements. 

The Born-Haber Process

Under the Born-Haber Cycle, the formation of an ionic solid is the result of a metal and a gaseous nonmetal combining together. 

Example: The Born-Haber cycle looks mainly at the formation of an ionic compound from gaseous ions. 

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In order for the elements to combine they each must be ionized. Their opposing charges cause them to combine. 

Example: Using the Born-Haber Cycle, demonstrate the formation of cesium chloride, CsCl, and calculate its heat of formation. 

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Born Haber Cycle Additional Practice Problems

Sketch a qualitative enthalpy diagram for the process of dissolving NaI(s) in H2O (exothermic).

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Sketch a qualitative enthalpy diagram for the process of dissolving KCl(s) in H2O (endothermic).

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Use the data given below to construct a Born-Haber cycle to determine the heat of formation of KCl.


\DeltaH °(kJ)
K(g) → K+(g) + e-418
Cl2(g) → 2 Cl(g)244
Cl(g) + e- → Cl-(g)-349
KCl(s) → K+(g) + Cl-(g)717
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Use the data given below to construct a Born-Haber cycle to determine the electron affinity of Br.

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What is the enthalpy of sublimation for K, in kJ/mol?

Given:

Lattice energy of KCl = 699 kJ/mol

First ionization energy of K = 418.7 kJ/mol

Electron affinity of Cl = 349 kJ/mol

Bond energy of Cl-Cl = 242.7 kJ/mol

Enthalpy of formation of KCl = -435.87 kJ/mol

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Use the Born-Haber cycle to calculate the lattice energy of KCl(s) given the following data:

ΔH(sublimation) K = 79.2 kJ/mol

I1 (K) = 418.7 kJ/mol

Bond energy (Cl-Cl) = 242.8 kJ/mol

EA (Cl) = 348 kJ/mol

ΔH°f (KCl(s)) = -435.7 kJ/mol

a. -165 kJ/mol

b. 288 kJ/mol

c. 629 kJ/mol

d. -707 kJ/mol

e. -828 kJ/mol

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Consider an ionic compound, MX, composed of generic metal M and generic, gaseous halogen X.

The enthalpy of formation of MX is ΔH°f = -453 kJ/mol. The enthalpy of sublimation of M is ΔHsub = 127 kJ/mol. The ionization energy of M is IE = 431 kJ/mol. The electron affinity of X is ΔHEA = -301 kJ/mol. The bond energy of X2 is BE = 171 kJ/mol.

Determine the lattice energy of MX.

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Calculate lattice energy. The lattice energy of an ionic compound is the energy change when one mole of ionic solid is separated into its gaseous ions. Given the data below, find lattice energy for AlBr3, which is the ΔH° for the following reaction:

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Use the Born-Haber cycle to calculate the lattice energy of NaCl.

1st Ionization Energy for Na = 495.9 kJ/mol

2nd Ionization Energy for Na = 4,560 kJ/mol

Electron Affinity for Na = 53 kJ/mol

Electron Affinity for Cl = 349 kJ/mol

Energy to dissociate 1/2 mol of Cl2 into Cl atoms = 121.4 kJ

ΔHsublimation (Na) = 108 kJ/mol

ΔHf° (NaCl) = -411 kJ/mol

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Using a Born-Haber cycle, calculate the lattice energy for lithium fluoride, LiF(s), given the following data:

Sublimation energy for Li(s) = 166 kJ ⁄ mol

first ionization energy for Li(g) = 520 kJ ⁄ mol

bond energy for F2(g) = 158 kJ ⁄ mol–1

electron affinity for F(g) = –328 kJ ⁄ mol–1

enthalpy of formation of LiF(s) = –617 kJ ⁄ mol

a) +101 kJ ⁄ mol

b) +180 kJ ⁄ mol

c) –329 kJ ⁄ mol

d) –1054 kJ ⁄ mol

e) –1133 kJ ⁄ mol

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Please refer to the hypothetical Born-Haber cycle below for M(s) + X(s) → MX(s), where M and X are both elements in their standard states. 

The lattice enthalpy (ΔHL) for MX(s) is:

a. 938 kJ     b. 130 kJ     c. - 808 kJ     d. 221 kJ     e. -221 kJ

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Please refer to the hypothetical Born-Haber cycle below for M(s) + X(s) → MX(s), where M and X are both elements in their standard states. 

The enthalpy of formation (ΔH f) for MX(s) is:

a. 938 kJ     b. 130 kJ     c. 808 kJ     d. 221 kJ     e. -221 kJ

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Please refer to the hypothetical Born-Haber cycle below for M(s) + X(s) → MX(s), where M and X are both elements in their standard states.

The atomization energy of M(s) is

a) 351 kJ      b. 130 kJ      c. 481 kJ      d. 221 kJ     e. 702 kJ

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Please refer to the hypothetical Born-Haber cycle below for M(s) + X(s) → MX(s), where M and X are both elements in their standard states. 

The ionization energy of M(s) is

a) 351 kJ      b. 130 kJ     c. 481 kJ      d. 221 kJ      e. 702 kJ

 

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The diagram below is the Born-Haber cycle for the formation of crystalline potassium fluoride KF.

Which energy change (by number) corresponds to the lattice energy of KF?

a. 5

b. 2

c. 4

d. 1

e. 6

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In the Born-Haber cycle for Mg(s) + Cl 2(g)      →       MgCl 2(s), which step(s) is (are) exothermic for the formation of crystalline solid? (the following may not be balanced equations, but describe reaction processes.)

(1) Mg(g) + 2Cl(g)      →       Mg 2+(g) + 2Cl(g)

(2) Mg2+(g) + 2Cl(g)      →       Mg2+(g) + 2Cl - (g)

(3) Mg(s) + Cl2(g)      →       Mg(g) + Cl 2(g)

(4) Mg(s) + Cl2(g)      →       Mg(g) + 2Cl(g)

(5) Mg2+(g) + 2Cl - (g)      →       MgCl 2(g)

a. (1) and (3)

b. (1), (3), and (4)

c. (5)

d. (2) and (5)

e. (1), (2), and (5)

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When setting up the steps of the Born-Haber cycle for K 2O, how many ionization energies (IE) and how many electron affinities (EA) do you need, i.e., non-, first and second?

 

A) 2 IE, 0 EA

B) 2 IE, 1 EA

C) 1 IE, 2 EA

D) 1 IE, 1 EA

E) 0 IE, 2 EA

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Use the data given below to construct a Born-Haber cycle to determine the lattice energy of KBr.

      ΔH°(kJ)

K(s) → K(g)                                             89

K(g) → K+(g) + e-                                   419

½ Br2(l) → Br(g)                                      96

Br(g) + e- → Br-(g)                                 -325

K(s) + ½ Br2(g) → KBr(s)                       -394

 

A) -885 kJ

B) -673 kJ

C) +367 kJ

D) -464 kJ

E) +246 kJ

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