Chem 1711 Born-Haber Cycle, Practice Problems

1. Given the following information for magnesium, oxygen, and magnesium oxide calculate the second electron gainenthalpy for oxygen {i.e. for O— (g) + e— O2— (g)}.

for Mg (s), ΔHsub = +148 kJ/mol bond dissociation energy for O2 = +499 kJ/mol1st ionization energy for Mg = +738 kJ/mol 1st electron gain enthalpy for O = –141 kJ/mol2nd ionization energy for Mg = +1450 kJ/mol for MgO (s), lattice energy = +3890 kJ/mol

for MgO (s), enthalpy of formation = –602 kJ/mol

2. Consider an ionic compound MX2 where M is a metal that forms a cation of +2 charge, and X is a nonmetal that forms ananion of –1 charge. A Born-Haber cycle for MX2 is given below. Each step in this cycle has been assigned a number(1 – 7).

M (s) + X2 (g)

MX2 (s)

M2+ (g) + 2 X- (g)

M (g)

M+ (g)

2 X (g)

1

2

3

4

5

6

7

a. Identify one step (1 - 7) that is endothermic as written. ______________

b. Which step (1 - 7) corresponds to ΔHosub? _____________

c. Which step (1 - 7) corresponds to ΔHof? _____________

d. Use the following energy values to calculate the lattice energy (in kJ/mol) for MX2. ΔHo

sub = 296 kJ/mol; ΔHof = -421 kJ/mol; 1st ionization energy = 378 kJ/mol;

2nd ionization energy = 555 kJ/mol; bond dissociation enthalpy = 310 kJ/mol; electron affinity = -427 kJ/mol.

eh#{B C)\eM lltl

i . ( i ivcrt tho i 'oi io* ' i rrg ir t i 'orrrrt t i icr ir 1'or tr lzigircsi i i l i ' l , t ; ; iygci l , ai i ic l

cn tha lp l lb r oxygen { i . c . fo r O (S) . ' o - + O2 (S) }

Born'Haber CYcle, Practice Problerns

, . - . ' , . ' . . ' . . ; " " . . ' . i . 1 , ' . ' . , l , . r r l , , l r . t l r ! . { , r ' r r t r l r ' l l r ' l l ( t l l u i l l l lt l t ( l l r l L . \ r L r r r l

lbr Mg (s), AH.,,., = +148 k.l/ lr ioll ' ' ion izal ion encrg) ' for Mg = +738 k. l /mol2'r ioniz.ation cnerg_\' l irr Mg = +1-l-50 k.l/rnol

boncl clissociation energy 1'or O. = +-199 kJ/rnol

l" elcctt 'ott gain cnthalpy 1'or O = -l '11 k.l/mcll

I-or MgO (s), leitt icc e Irerg)' = +3890 k.l/ttrol

1'or MgO (s), cnthalpy of' lbnnation = 602 k.l/rnol

aHl = a[l*t lEk + 2^tE n fa(a$uss)r

+ \ s + 8 4 + 2 l A E 4 - L EM 1 ( s ) +a,l"{5u{-

NU 3)ts4 $

ru

*$o-ri*^u0 *

ry'*'J) +

'/z 0e tJ ) -t tt"+

J,r.co*airr) >

o tt)rs\;de

o-Ls )z"[ea

or- rJ )

N.tJo (s) '. 2"te= '+r"rrl,u';:iil^il_,Tt^

tlo= [-uoe +3rqo- rqt -?38-'T;l':#

2 . (lonsiclcr an iouic cornpotrncl MX.anion o1 ' - l chargc. A L lorn-Hatre l( t - 1 ) .

= t Sttt{ Kv-ol

w,hcrc M is a rnct l l that l 'onns a caticln o1'+2 chargc, ancl X is i t t lorttr letal t l tat forms an

c1,clc for MX. is given bclon,. l lacl i stcp in t l i is cycle hi is bcen assi-9ncd r rtutt tbcr

r i . Idcnti l '1 'onc stcp ( l - 7) that is cr ldothcrmrc as wrrtten

b. Which step (1 - 7) corrcspouds to AHu.,,s '?

3, ' l r 5, lo

NL\ : (s )Which stcp ( I - 7) corlcsl.rott t ls to AH"t:, '

L . l se the lb l lo rv ing cncrgy 'va l r rcs to ca lc t t la tc thc la t l i ce cncr .g r ' ( in kJ /n ro l ) f i r r ' l \ ' lX .

AHu.ul, = 296 k. l /nrol; AI ' lu, = - '12 I l t . l /nrol; l ' t iott iz 'at ion etrcrg\ '- 378 k' l /rr tol;

2 ' ) ( l io r r i za t io ' encrgy * -5 -5-5 k . l /n ro l ;bonc l d issoc ia t iop cn tha lp l '= .1 10 k . l /n ro l ;

clectron af l ' inrt1' = -127 k. l lnoI.

+ ls+JE +z"dTE + AHa;s , + 2 ( r4 ) - LE

+ ls l j - t +znA:- ,E +al- la iss +z(€i l -aHl

i \ l ( s )

- li

.j"*'+N l , ( g )

. l+l r t : (g)

Ir l

I

+ X l ( g )

t \" l \* \

z i ( s t \

3

AHr = aHJ"ub

AHj'^b

: $ -q , ,+ 3 -18+sss+ 310+ 2 Gqa- r ) -kL tL ' t tV*o lL-

b

lsfhce tvJJ =. + l lot K{n^ut-=#=-==-