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7/26/2019 Cape Chemistry
1/28
FURTHER TOPICS ONFURTHER TOPICS ON
CHEMICALCHEMICALEQUILIBRIUMEQUILIBRIUM
KNOCKHARDY PUBLISHINGKNOCKHARDY PUBLISHING 20152015SPECIFICATIONSSPECIFICATIONS
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INTRODUCTION
This Powerpointshow is one of several pro!"e #o help s#!en#s !ners#an
sele"#e #opi"s a# AS an A2 level Che$is#r%& I# is 'ase on #he re(!ire$en#s of
#he A)A an OCR spe"ifi"a#ions '!# is s!i#a'le for o#her e*a$ina#ion 'oars&
Inivi!al s#!en#s $a% !se #he $a#erial a# ho$e for revision p!rposes or i#
$a% 'e !se for "lassroo$ #ea"hin+ if an in#era"#ive whi#e 'oar is availa'le&
A""o$pan%in+ no#es on #his, an #he f!ll ran+e of AS an A2 #opi"s, are
availa'le fro$ #he -NOC-.ARD/ SCIENCE ESITE a#&&&
www.knockhardy.org.uk/sci.htm
Navi+a#ionis a"hieve '%&&&
either "li"in+ on #he +re% arrows a# #he foo# of ea"h pa+e
or !sin+ #he lef# an ri+h# arrow e%s on #he e%'oar
KNOCKHARDY PUBLISHINGKNOCKHARDY PUBLISHING
C.E3ICA4 E)UI4IRIU3 26C.E3ICA4 E)UI4IRIU3 26
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CONTENTS
The E(!ili'ri!$ 4aw
The e(!ili'ri!$ "ons#an# -"
Cal"!la#ions involvin+ -"
Cal"!la#ions involvin+ +ases
3ole fra"#ion an par#ial press!re "al"!la#ions
Cal"!la#ions involvin+ -p
C.E3ICA4 E)UI4IRIU3 26C.E3ICA4 E)UI4IRIU3 26
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Si$pl% s#a#es
7If #he "on"en#ra#ions of all #he s!'s#an"es presen# a# e(!ili'ri!$ are
raise #o #he power of #he n!$'er of $oles #he% appear in #he e(!a#ion,#he pro!"# of #he "on"en#ra#ions of #he pro!"#s ivie '% #he pro!"#
of #he "on"en#ra#ions of #he rea"#an#s is a "ons#an#, provie #he
#e$pera#!re re$ains "ons#an#8
There are several for$s of #he "ons#an#9 all var% wi#h #e$pera#!re&
-" #he e(!ili'ri!$ val!es are e*presse as "on"en#ra#ions in $ol $:;
-p #he e(!ili'ri!$ val!es are e*presse as par#ial press!res
The par#ial press!re e*pression "an 'e !se for rea"#ions involvin+ +ases
T.E E)UI4IRIU3 4AT.E E)UI4IRIU3 4A
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for an e(!ili'ri!$ rea"#ion of #he for$&&&
aA < ' "C < D
#hen a# "ons#an# #e$pera#!re6 =C>"& =D> ? a "ons#an#, -"6
=A>a& =>'
where [ ] eno#es #he e(!ili'ri!$ "on"en#ra#ion in $ol $:;
-" is nown as #he E(!ili'ri!$ Cons#an#
T.E E)UI4IRIU3 CONSTANT -T.E E)UI4IRIU3 CONSTANT -""
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@A4UE OF -"
AFFECTED'% a "han+e of #e$pera#!re
NOTAFFECTED'% a "han+e in "on"en#ra#ion of rea"#an#s or pro!"#s
a "han+e of press!re
ain+ a "a#al%s#
for an e(!ili'ri!$ rea"#ion of #he for$&&&
aA < ' "C < D
#hen a# "ons#an# #e$pera#!re6 =C>"& =D> ? a "ons#an#, -"6
=A>a& =>'
where [ ] eno#es #he e(!ili'ri!$ "on"en#ra#ion in $ol $:;
-" is nown as #he E(!ili'ri!$ Cons#an#
T.E E)UI4IRIU3 CONSTANT -T.E E)UI4IRIU3 CONSTANT -""
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"ons#r!"# #he 'alan"e e(!a#ion, in"l!in+ s#a#e s%$'ols a(6, +6 e#"&
e#er$ine #he n!$'er of $oles of ea"h spe"ies a# e(!ili'ri!$
ivie $oles '% vol!$e in $;6 #o +e# #he e(!ili'ri!$ "on"en#ra#ions in $ol $:;
If no vol!$e is (!o#e, !se a @9 i# will pro'a'l% "an"el o!#6
fro$ #he e(!a#ion "ons#r!"#e in #he firs# s#ep, wri#e o!# an e*pression for -"&
s!'s#i#!#e val!es fro$ #hir s#ep an "al"!la#e #he val!e of -" wi#h an% !ni#s
CA4CU4ATIONS IN@O4@IN -CA4CU4ATIONS IN@O4@IN -""
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"ons#r!"# #he 'alan"e e(!a#ion, in"l!in+ s#a#e s%$'ols a(6, +6 e#"&
e#er$ine #he n!$'er of $oles of ea"h spe"ies a# e(!ili'ri!$
ivie $oles '% vol!$e in $;6 #o +e# #he e(!ili'ri!$ "on"en#ra#ions in $ol $:;
If no vol!$e is (!o#e, !se a @9 i# will pro'a'l% "an"el o!#6
fro$ #he e(!a#ion "ons#r!"#e in #he firs# s#ep, wri#e o!# an e*pression for -"&
s!'s#i#!#e val!es fro$ #hir s#ep an "al"!la#e #he val!e of -" wi#h an% !ni#s
E*a$ple 1
One $ole of e#hanoi" a"i rea"#s wi#h one $ole of e#hanol a# 2B-& hen e(!ili'ri!$ isrea"he i# is fo!n #ha# #wo #hirs of #he a"i has rea"#e& Cal"!la#e #he val!e of -"&
CA4CU4ATIONS IN@O4@IN -CA4CU4ATIONS IN@O4@IN -""
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"ons#r!"# #he 'alan"e e(!a#ion, in"l!in+ s#a#e s%$'ols a(6, +6 e#"&
e#er$ine #he n!$'er of $oles of ea"h spe"ies a# e(!ili'ri!$
ivie $oles '% vol!$e in $;6 #o +e# #he e(!ili'ri!$ "on"en#ra#ions in $ol $:;
If no vol!$e is (!o#e, !se a @9 i# will pro'a'l% "an"el o!#6
fro$ #he e(!a#ion "ons#r!"#e in #he firs# s#ep, wri#e o!# an e*pression for -"&
s!'s#i#!#e val!es fro$ #hir s#ep an "al"!la#e #he val!e of -" wi#h an% !ni#s
E*a$ple 1
One $ole of e#hanoi" a"i rea"#s wi#h one $ole of e#hanol a# 2B-& hen e(!ili'ri!$ isrea"he i# is fo!n #ha# #wo #hirs of #he a"i has rea"#e& Cal"!la#e #he val!e of -"&
C.;COO.l6 < C2.5O.l6 C.;COOC2.5l6 < .2Ol6
CA4CU4ATIONS IN@O4@IN -CA4CU4ATIONS IN@O4@IN -""
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"ons#r!"# #he 'alan"e e(!a#ion, in"l!in+ s#a#e s%$'ols a(6, +6 e#"&
e#er$ine #he n!$'er of $oles of ea"h spe"ies a# e(!ili'ri!$
ivie $oles '% vol!$e in $;6 #o +e# #he e(!ili'ri!$ "on"en#ra#ions in $ol $:;
If no vol!$e is (!o#e, !se a @9 i# will pro'a'l% "an"el o!#6
fro$ #he e(!a#ion "ons#r!"#e in #he firs# s#ep, wri#e o!# an e*pression for -"&
s!'s#i#!#e val!es fro$ #hir s#ep an "al"!la#e #he val!e of -" wi#h an% !ni#s
E*a$ple 1
One $ole of e#hanoi" a"i rea"#s wi#h one $ole of e#hanol a# 2B-& hen e(!ili'ri!$ isrea"he i# is fo!n #ha# #wo #hirs of #he a"i has rea"#e& Cal"!la#e #he val!e of -"&
C.;COO.l6 < C2.5O.l6 C.;COOC2.5l6 < .2Ol6
$oles ini#iall%6 1 1 0 0
$oles a# e(!ili'ri!$6 1 : 2; 1 : 2; 2; 2;
Ini#ial $oles of C.;COO. ? 1 $oles rea"#e ? 2; e(!ili'ri!$ $oles of C.;COO. ? 1;
For ever% C.;COO. #ha# rea"#s9 a si$ilar n!$'er of C2.5O.s rea"# e(!il $oles ? 1 : 2;6
a si$ilar n!$'er of C.;COOC2.5s are pro!"e
a si$ilar n!$'er of .2Os are pro!"e
CA4CU4ATIONS IN@O4@IN -CA4CU4ATIONS IN@O4@IN -""
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"ons#r!"# #he 'alan"e e(!a#ion, in"l!in+ s#a#e s%$'ols a(6, +6 e#"&
e#er$ine #he n!$'er of $oles of ea"h spe"ies a# e(!ili'ri!$
ivie $oles '% vol!$e in $;6 #o +e# #he e(!ili'ri!$ "on"en#ra#ions in $ol $:;
If no vol!$e is (!o#e, !se a @9 i# will pro'a'l% "an"el o!#6
fro$ #he e(!a#ion "ons#r!"#e in #he firs# s#ep, wri#e o!# an e*pression for -"&
s!'s#i#!#e val!es fro$ #hir s#ep an "al"!la#e #he val!e of -" wi#h an% !ni#s
E*a$ple 1
One $ole of e#hanoi" a"i rea"#s wi#h one $ole of e#hanol a# 2B-& hen e(!ili'ri!$ isrea"he i# is fo!n #ha# #wo #hirs of #he a"i has rea"#e& Cal"!la#e #he val!e of -"&
C.;COO.l6 < C2.5O.l6 C.;COOC2.5l6 < .2Ol6
$oles ini#iall%6 1 1 0 0
$oles a# e(!ili'ri!$6 1 : 2; 1 : 2; 2; 2;e(!ili'ri!$ "on"s& 1; @ 1; @ 2; @ 2; @
@ ? vol!$e $;6 of #he e(!ili'ri!$ $i*#!re
CA4CU4ATIONS IN@O4@IN -CA4CU4ATIONS IN@O4@IN -""
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"ons#r!"# #he 'alan"e e(!a#ion, in"l!in+ s#a#e s%$'ols a(6, +6 e#"&
e#er$ine #he n!$'er of $oles of ea"h spe"ies a# e(!ili'ri!$
ivie $oles '% vol!$e in $;6 #o +e# #he e(!ili'ri!$ "on"en#ra#ions in $ol $:;
If no vol!$e is (!o#e, !se a @9 i# will pro'a'l% "an"el o!#6
fro$ #he e(!a#ion "ons#r!"#e in #he firs# s#ep, wri#e o!# an e*pression for -"&
s!'s#i#!#e val!es fro$ #hir s#ep an "al"!la#e #he val!e of -" wi#h an% !ni#s
E*a$ple 1
One $ole of e#hanoi" a"i rea"#s wi#h one $ole of e#hanol a# 2B-& hen e(!ili'ri!$ isrea"he i# is fo!n #ha# #wo #hirs of #he a"i has rea"#e& Cal"!la#e #he val!e of -"&
C.;COO.l6 < C2.5O.l6 C.;COOC2.5l6 < .2Ol6
$oles ini#iall%6 1 1 0 0
$oles a# e(!ili'ri!$6 1 : 2; 1 : 2; 2; 2;e(!ili'ri!$ "on"s& 1; @ 1; @ 2; @ 2; @
@ ? vol!$e $;6 of #he e(!ili'ri!$ $i*#!re
-" ? =C.;COOC2.5> =.2O>
=C.;COO.> =C2.5O.>
CA4CU4ATIONS IN@O4@IN -CA4CU4ATIONS IN@O4@IN -""
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"ons#r!"# #he 'alan"e e(!a#ion, in"l!in+ s#a#e s%$'ols a(6, +6 e#"&
e#er$ine #he n!$'er of $oles of ea"h spe"ies a# e(!ili'ri!$
ivie $oles '% vol!$e in $;6 #o +e# #he e(!ili'ri!$ "on"en#ra#ions in $ol $:;
If no vol!$e is (!o#e, !se a @9 i# will pro'a'l% "an"el o!#6
fro$ #he e(!a#ion "ons#r!"#e in #he firs# s#ep, wri#e o!# an e*pression for -"&
s!'s#i#!#e val!es fro$ #hir s#ep an "al"!la#e #he val!e of -" wi#h an% !ni#s
E*a$ple 1
One $ole of e#hanoi" a"i rea"#s wi#h one $ole of e#hanol a# 2B-& hen e(!ili'ri!$ isrea"he i# is fo!n #ha# #wo #hirs of #he a"i has rea"#e& Cal"!la#e #he val!e of -"&
C.;COO.l6 < C2.5O.l6 C.;COOC2.5l6 < .2Ol6
$oles ini#iall%6 1 1 0 0
$oles a# e(!ili'ri!$6 1 : 2; 1 : 2; 2; 2;e(!ili'ri!$ "on"s& 1; @ 1; @ 2; @ 2; @
@ ? vol!$e $;6 of #he e(!ili'ri!$ $i*#!re
-" ? =C.;COOC2.5> =.2O> ? 2; @ & 2; @ ?
=C.;COO.> =C2.5O.> 1; @ & 1; @
CA4CU4ATIONS IN@O4@IN -CA4CU4ATIONS IN@O4@IN -""
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E*a$ple 2
Consier #he e(!ili'ri!$ P < 2) R < S all spe"ies are a(!eo!s6
One $ole of P an one $ole of ) are $i*e& On"e e(!ili'ri!$ has 'een a"hieve 0&G
$oles of P are presen#& .ow $an% $oles of ), R an S are presen# a# e(!ili'ri!$ H
P < 2) R < S
Ini#ial $oles 1 1 0 0
A# e(!ili'ri!$ 0G 02 0 0
0 rea"#e6 2 * 0 rea"#e6 +e# 1 R an 1 S for ever% P #ha# rea"#s6
1: 0G re$ain 1: 0 re$ain
E*plana#ion J if 0&G $ol of P re$ain of #he ori+inal 1 $ol, 0& $ol have rea"#e
J #he e(!a#ion s#a#es #ha# 2 $oles of ) rea"# wi#h ever% 1 $ol of PJ #his $eans #ha# 0& 2 * 0&6 $ol of ) have rea"#e, leavin+ 0&2 $ol
J one $ol of R an S are pro!"e fro$ ever% $ol of P #ha# rea"#s
J #his $eans 0& $ol of R an 0& $ol of S are presen# a# e(!ili'ri!$
CA4CU4ATIONS IN@O4@IN -CA4CU4ATIONS IN@O4@IN -""
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CA4CU4ATIONS IN@O4@IN ASESCA4CU4ATIONS IN@O4@IN ASES
3e#ho
"arrie o!# in a si$ilar wa% #o #hose involvin+ "on"en#ra#ions
one has #he "hoi"e of !sin+ -"or -
pfor #he e(!ili'ri!$ "ons#an#
when !sin+ -ponl% #ae in#o a""o!n# +aseo!s spe"ies for #he e*pression
!se #he val!e of #he par#ial press!re of an% +as in #he e(!ili'ri!$ $i*#!re
press!re is !s!all% (!o#e in N$:2or Pa : a#$ospheres are so$e#i$es !se
as wi#h -", #he !ni#s of #he "ons#an# -p epen on #he s#oi"hio$e#r% of #he rea"#ion
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CA4CU4ATIONS IN@O4@IN ASESCA4CU4ATIONS IN@O4@IN ASES
3e#ho
"arrie o!# in a si$ilar wa% #o #hose involvin+ "on"en#ra#ions
one has #he "hoi"e of !sin+ -"or -
pfor #he e(!ili'ri!$ "ons#an#
when !sin+ -ponl% #ae in#o a""o!n# +aseo!s spe"ies for #he e*pression
!se #he val!e of #he par#ial press!re of an% +as in #he e(!ili'ri!$ $i*#!re
press!re is !s!all% (!o#e in N$:2or Pa : a#$ospheres are so$e#i$es !se
as wi#h -", #he !ni#s of #he "ons#an# -p epen on #he s#oi"hio$e#r% of #he rea"#ion
USEFU4 RE4ATIONS.IPS
#o#al press!re ? s!$ of #he par#ial press!res
par#ial press!re ? #o#al press!re * $ole fra"#ion
$ole fra"#ion ? n!$'er of $oles of a s!'s#an"e
n!$'er of $oles of all s!'s#an"es presen#
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3O4E FRACTION AND PARTIA4 PRESSURE3O4E FRACTION AND PARTIA4 PRESSURE
E*a$ple A $i*#!re of 1G+ of O2an 2+ of N2, e*er#s a #o#al press!re of
20000 N$:2& ha# is #he par#ial press!re of ea"h +as H
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3O4E FRACTION AND PARTIA4 PRESSURE3O4E FRACTION AND PARTIA4 PRESSURE
E*a$ple A $i*#!re of 1G+ of O2an 2+ of N2, e*er#s a #o#al press!re of
20000 N$:2& ha# is #he par#ial press!re of ea"h +as H
$oles of O2 ? $ass $olar $ass ? 1G+ ;2+ ? 0&5 $ol
$oles of N2 ? $ass $olar $ass ? 2+ 2+ ? 1&5 $ol
#o#al $oles ? 0&5 < 1&5 ? 2&0 $ol
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3O4E FRACTION AND PARTIA4 PRESSURE3O4E FRACTION AND PARTIA4 PRESSURE
E*a$ple A $i*#!re of 1G+ of O2an 2+ of N2, e*er#s a #o#al press!re of
20000 N$:2& ha# is #he par#ial press!re of ea"h +as H
$oles of O2 ? $ass $olar $ass ? 1G+ ;2+ ? 0&5 $ol
$oles of N2 ? $ass $olar $ass ? 2+ 2+ ? 1&5 $ol
#o#al $oles ? 0&5 < 1&5 ? 2&0 $ol
$ole fra"#ion of O2 ? 0&5 2 ? 0&25$ole fra"#ion of N2 ? 1&5 2 ? 0&K5
s!$ of $ole fra"#ions ? 0&K5 < 0&25 ? 1 s!$ sho!l alwa%s 'e 16
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3O4E FRACTION AND PARTIA4 PRESSURE3O4E FRACTION AND PARTIA4 PRESSURE
E*a$ple A $i*#!re of 1G+ of O2an 2+ of N2, e*er#s a #o#al press!re of
20000 N$:2& ha# is #he par#ial press!re of ea"h +as H
$oles of O2 ? $ass $olar $ass ? 1G+ ;2+ ? 0&5 $ol
$oles of N2 ? $ass $olar $ass ? 2+ 2+ ? 1&5 $ol
#o#al $oles ? 0&5 < 1&5 ? 2&0 $ol
$ole fra"#ion of O2 ? 0&5 2 ? 0&25$ole fra"#ion of N2 ? 1&5 2 ? 0&K5
s!$ of $ole fra"#ions ? 0&K5 < 0&25 ? 1
par#ial press!re of O2 ? $ole fra"#ion * #o#al press!re
? 0&25 * 20000 N$:2 ? 5000 N$:2
par#ial press!re of N2 ? $ole fra"#ion * #o#al press!re
? 0&K5 * 20000 N$:2 ? 15000 N$:2
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3O4E FRACTION AND PARTIA4 PRESSURE3O4E FRACTION AND PARTIA4 PRESSURE
E*a$ple A $i*#!re of 1G+ of O2an 2+ of N2, e*er#s a #o#al press!re of
20000 N$:2& ha# is #he par#ial press!re of ea"h +as H
$oles of O2 ? $ass $olar $ass ? 1G+ ;2+ ? 0&5 $ol
$oles of N2 ? $ass $olar $ass ? 2+ 2+ ? 1&5 $ol
#o#al $oles ? 0&5 < 1&5 ? 2&0 $ol
$ole fra"#ion of O2 ? 0&5 2 ? 0&25$ole fra"#ion of N2 ? 1&5 2 ? 0&K5
s!$ of $ole fra"#ions ? 0&K5 < 0&25 ? 1
par#ial press!re of O2 ? $ole fra"#ion * #o#al press!re
? 0&25 * 20000 N$:2 ? 5000 N$:2
par#ial press!re of N2 ? $ole fra"#ion * #o#al press!re
? 0&K5 * 20000 N$:2 ? 15000 N$:2
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CA4CU4ATIONS IN@O4@IN -CA4CU4ATIONS IN@O4@IN -pp
E*a$ple hen ni#ro+en 1 $ole6 an h%ro+en ; $oles6 rea"# a# "ons#an#
#e$pera#!re a# a press!re of * 10GPa, #he e(!ili'ri!$ $i*#!re
was fo!n #o "on#ain 0&K $oles of a$$onia& Cal"!la#e -p&
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CA4CU4ATIONS IN@O4@IN -CA4CU4ATIONS IN@O4@IN -pp
E*a$ple hen ni#ro+en 1 $ole6 an h%ro+en ; $oles6 rea"# a# "ons#an#
#e$pera#!re a# a press!re of * 10GPa, #he e(!ili'ri!$ $i*#!re
was fo!n #o "on#ain 0&K $oles of a$$onia& Cal"!la#e -p&
N2+6 < ;.2+6 2N.;+6
$oles ini#iall%6 1 ; 0
$oles e(!ili'ri!$6 1 : * ; : ;* 2* * $oles of N2rea"#e6
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CA4CU4ATIONS IN@O4@IN -CA4CU4ATIONS IN@O4@IN -pp
E*a$ple hen ni#ro+en 1 $ole6 an h%ro+en ; $oles6 rea"# a# "ons#an#
#e$pera#!re a# a press!re of * 10GPa, #he e(!ili'ri!$ $i*#!re
was fo!n #o "on#ain 0&K $oles of a$$onia& Cal"!la#e -p&
N2+6 < ;.2+6 2N.;+6
$oles ini#iall%6 1 ; 0
$oles e(!ili'ri!$6 1 : * ; : ;* 2* * $oles of N2rea"#e6
$ole fra"#ions 1:*6:2*6 ;:;*6:2*6 2*:2*6 #o#al $oles ? : 2*6
par#ial press!res P&1:*6:2*6 P&;:;*6:2*6 P&2*:2*6 #o#al press!re ? P 6
a# e(!ili'ri!$ #here are 0&K $oles of a$$onia, so 2* ? 0&K an * ? 0&;5
#he #o#al press!re P6 ? * 10G Pa&
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CA4CU4ATIONS IN@O4@IN -CA4CU4ATIONS IN@O4@IN -pp
E*a$ple hen ni#ro+en 1 $ole6 an h%ro+en ; $oles6 rea"# a# "ons#an#
#e$pera#!re a# a press!re of * 10GPa, #he e(!ili'ri!$ $i*#!re
was fo!n #o "on#ain 0&K $oles of a$$onia& Cal"!la#e -p&
N2+6 < ;.2+6 2N.;+6
$oles ini#iall%6 1 ; 0
$oles e(!ili'ri!$6 1 : * ; : ;* 2* * $oles of N2rea"#e6
$ole fra"#ions 1:*6:2*6 ;:;*6:2*6 2*:2*6 #o#al $oles ? : 2*6
par#ial press!res P&1:*6:2*6 P&;:;*6:2*6 P&2*:2*6 #o#al press!re ? P 6
a# e(!ili'ri!$ #here are 0&K $oles of a$$onia, so 2* ? 0&K an * ? 0&;5
#he #o#al press!re P6 ? * 10G Pa&
appl%in+ #he e(!ili'ri!$ law -p ? PN.;62 wi#h !ni#s of Pa:2
PN26 & P.26;
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CA4CU4ATIONS IN@O4@IN -CA4CU4ATIONS IN@O4@IN -pp
E*a$ple hen ni#ro+en 1 $ole6 an h%ro+en ; $oles6 rea"# a# "ons#an#
#e$pera#!re a# a press!re of * 10GPa, #he e(!ili'ri!$ $i*#!re
was fo!n #o "on#ain 0&K $oles of a$$onia& Cal"!la#e -p&
N2+6 < ;.2+6 2N.;+6
$oles ini#iall%6 1 ; 0
$oles e(!ili'ri!$6 1 : * ; : ;* 2* * $oles of N2rea"#e6
$ole fra"#ions 1:*6:2*6 ;:;*6:2*6 2*:2*6 #o#al $oles ? : 2*6
par#ial press!res P&1:*6:2*6 P&;:;*6:2*6 P&2*:2*6 #o#al press!re ? P 6
a# e(!ili'ri!$ #here are 0&K $oles of a$$onia, so 2* ? 0&K an * ? 0&;5
#he #o#al press!re P6 ? * 10G Pa&
appl%in+ #he e(!ili'ri!$ law -p ? PN.;62 wi#h !ni#s of Pa:2
PN26 & P.26;
S!'s#i#!#in+ in #he e*pression +ives -p ? 1&K; * 10:1 Pa:2
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HE
HE
END
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