Gases

T



T!mp!ra'&ra ab%ol&'a

R



Con%'an'! d! propor(onaldad* llamada (on%'an'! d! lo% ga%!% d!al!%

LA CONSTANTE R DE LOS GASES IDEALES La (on%'an'! d! propor(onaldad d! lo% ga%!% d!al!% adop'a d%'n'o% -alor!% +&! d!p!nd!n d! la% &ndad!% (on +&! %! r!pr!%!n'a la pr!%"n* !l -ol&m!n # la '!mp!ra'&ra ab%ol&'a* alg&no% -alor!% (om&n!% para !%'a (on%'an'! p&!d!n %!r, R  R  3!l-n ? R  R  R  R  R  R 

K.KHK= 9 l'ro  a'm ? 2 9 mol  3!l-n ? .1> 9 m!'ro   a%(al ? 2 9 mol  .1> 6o&l!% 2 9 mol  3!l-n ? 1.; Calor$a% 2 9 mol  3!l-n ? 1.; 7TU 2 9 lbra  Ran3n! ? K.K1> 9 l'ro  bar ? 2 9 mol  3!l-n ? =H.= 9 l'ro  mm 8g ? 2 9 mol  3!l-n ? K.;KH 9p!   a'm ? 2 9 lbra  Ran3n! ?

La r!pr!%!n'a("n B7TU * !% la abr!-a'&ra d! la &ndad ngl!%a para !n!rg$a* d!nomnada Undad T5rm(a #r'/n(a. LA DENSIDAD DE LOS GASES La d!n%dad d! &n ga% p&!d! (al(&lar%! &'l)ando la r!la("n, ρ

Dond!,

ρ

M  R T

    

 . M . RT

D!n%dad Ma%a mol!(&lar d!l ga% 9 gramo% 2 mol ? r!%"n Con%'an'! d! lo% ga%!% d!al!% T!mp!ra'&ra ab%ol&'a

LE" DE DALTON C&ando %! 'raba0a (on m!)(la% d! ga%!%* la pr!%"n +&! (ada &no d! lo% ga%!% !0!r(! d!n'ro d!l r!(p!n'! !% d!nomnada !'esió( !a'ial) El !%'&do d!l 7

(ompor'am!n'o d! &na m!)(la d! ga%!% &! r!al)ado por 6on Dal'on !n !l ao 1K1* orm&lando la d!nomnada l!# d! Dal'on d! la% pr!%on!% par(al!%. La l!# !%'abl!(! +&!, La presión total de una mecla de gases es en realidad la suma de las presiones !ue cada gas e"ercería si estuviera solo.

En '5rmno% alg!bra(o%* !%'a l!# %! p&!d! !%(rbr (omo, T   A  7  C  . . . Dond!,

T  r!%"n 'o'al  A * 7 * C * . . .  pr!%on!% par(al!% d! lo% (ompon!n'!% A* 7 # C d! la m!)(la

LA PRESIÓN PARCIAL En &na m!)(la ga%!o%a* la pr!%"n par(al d! &n ga% p&!d! (al(&lar%! por m!do d! la !@pr!%"n,  A  P A T Dond!,

 A  r!%"n par(al d!l (ompon!n'! A P A  Fra(("n molar d!l (ompon!n'! A T  r!%"n 'o'al d! la m!)(la ga%!o%a

LA *RACCIÓN MOLAR La ra(("n molar d! &n ga% A* !n &na m!)(la ga%!o%a (on N (ompon!n'!%* %! p&!d! (al(&lar por la r!la("n, P A  .

dond!,

n A . n A  n7  . . . nN

P A   Fra(("n molar d!l ga% A n A   n4m!ro d! mol!% d!l ga% A n7  n4m!ro d! mol!% d!l ga% 7 nN  n4m!ro d! mol!% d!l !n5%mo (ompon!n'! ga%!o%o

8

Ob%5r-!%! +&! la ra(("n molar* !% &na (an'dad adm!n%onal* +&! !@pr!%a la r!la("n d!l n4m!ro d! mol!% d! &n (ompon!n'! !n r!la("n al n4m!ro d! mol!% d! 'odo% lo% (ompon!n'! pr!%!n'!% !n la m!)(la ga%!o%a. La %&ma'ora d! 'oda% la% ra((on!% molar!% !n &na m!)(la ga%!o%a %!mpr! %!r/ apro@madam!n'! g&al a B1 . CONDICIONES NORMALES DE PRESIÓN " TEMPERATURA Lo +&! %! d!n! (omo (ond(on!% normal!% d! pr!%"n # '!mp!ra'&ra* (orr!%pond! a u(a a'm"%!ra d! pr!%"n # +,-)./  3!l-n. G!n!ralm!n'!* (&ando %! abla d! !%'a% (ond(on!% %! &'l)an la% abr!-a'&ra% C.N 9 Cond(on!% Normal!% ? T..N 9 T!mp!ra'&ra # r!%"n Normal ? T..E. 9 T!mp!ra'&ra # r!%"n E%'/ndar ? o %& !+&-al!n'! d!r-ada d!l nombr! !n ngl5% S.T.. 9S'andard T!mp!ra'&r! and r!%%&r! ?. &OLUMEN MOLAR DE UN GAS IDEAL EN CONDICIONES T)P)E) E@p!rm!n'alm!n'! %! a !n(on'rado +&!* !l -ol&m!n o(&pado por 1 mol d! ga% d!al !n (ond(on!% T..E. !% d! apro@madam!n'! HH.>1= l'ro%. RECOLECCIÓN DE UN GAS SO#RE UN L01UIDO En alg&na% o(a%on!%* lo% ga%!% prod&('o d! &na r!a(("n +&$m(a* %on r!(ol!('ado% %obr! ag&a l$+&da +&! po%!! &na d!'!rmnada pr!%"n d! -apor a la '!mp!ra'&ra d! 'raba0o* !%'o a(! n!(!%aro r!al)ar &na (orr!(("n !n la pr!%"n d!l ga%* d!bdo a +&! !l ga% !%'ar/ %a'&rado (on !l -apor d! ag&a !0!r(!ndo 'amb5n &na pr!%"n 9 pr!%"n par(al ?. La (orr!(("n %! r!al)a %&%'ra#!ndo d! la pr!%"n 'o'al 9 pr!%"n d!l ga% m/% pr!%"n d! -apor d!l ag&a?* la pr!%"n d! -apor d!l ag&a* ob'!n5ndo%! a%$ la -!rdad!ra pr!%"n !0!r(da por !l ga% r!(ol!('ado, r!%"n d!l ga%  r!%"n 'o'al ag&a LA ESTE1UIOMETR0A DE GASES

 r!%"n d! -apor d!l

La !%'!+&om!'r$a d! %&%'an(a% !n !%'ado ga%!o%o* %! &ndam!n'a !n !l -ol&m!n d! lo% ga%!% +&! n'!r-!n!n !n d!'!rmnada r!a(("n +&$m(a. El prn(po +&! g!n!ralm!n'! %! apl(a !% !l +&! !%'abl!(! la l!# d! Ga#  L&%%a( d! lo% -ol4m!n!% d! (ombna("n. 9

LE" DE GA" % LUSSAC DE LOS &OL2MENES DE COM#INACIÓN La l!# !%'abl!(! +&!, B  # temperatura y presión constantes, los volúmenes de los gases !ue reaccionan o se forman en una reacción !uímica pueden ser  e$presados en proporciones de números enteros sencillos ”.

or !0!mplo* la r!a(("n d! orma("n d! (lor&ro d! dr"g!no 9 8Cl ? a par'r d! dr"g!no # o@$g!no ga%!o%o%, 8H 9g?  OH 9g?

→

H8Cl 9g?

D! a(&!rdo a la l!# d! Ga#  L&%%a(, 1 -ol&m!n d! 8 H  1 -ol&m!n OH

→

H -ol4m!n!% d! (lor&ro d! dr"g!no

E3EMPLO 4 .: Q&5 pr!%"n* !@pr!%ada !n p%* !0!r(! &na m!)(la d! H gramo% d! dr"g!no ga%!o%o* 8H #  gramo% d! n'r"g!no ga%!o%o* N H* % %! !n(&!n'ran a (!ro grado% C!l%&% d!n'ro d! &n r!(p!n'! d! 1K l'ro% SOLUCIÓN: La pr!%"n !0!r(da por lo% do% ga%!% d!p!nd! d!l n4m!ro d! mol!% d! (2& pr!%!n'!% !n la m!)(la* por (on%g&!n'! %! d!b! (on-!r'r (2ma%a d! gramo% a mol!%, Pa'a N+:

 g NH @ 1 mol NH  K.H= mol!% NH H g NH

Pa'a $+:

H g 8H  @ 1 mol 8H H g 8H

 1 mol 8H

Lo% mol!% 'o'al!% !n la m!)(la %! ob'!n!n por ad("n, n  n8H  nNH n  1 mol  K.H= mol!%  1.H= mol!%  Aora* (on la !(&a("n d!l ga% d!al* %! p&!d! (al(&lar la pr!%"n !0!r(da por la m!)(la d! ga%!%, V  nRT ara K oC !l !+&-al!n'! !n !l-n !% H;* # (on R  K.KH1 L.a'm 2 mol.   91.H= mol!% @ K.KH1 L.a'm2mol. @ H;  ?

 H. a'm 10

1K L Fnalm!n'! %! (on-!r'! la pr!%"n a p%, H. a'm

@

1>.; p% 1 a'm E3EMPLO 4 +:



5+)-5 !si

C&/n'o% l'ro% d! dr"g!no # o@$g!no ga%!o%o% !n (ond(on!% S.T.. p&!d!n ob'!n!r%! '!"r(am!n'! a par'r d! la d!%(ompo%("n d! 1 lbra d! ag&a. Con%d!r! la %g&!n'! !@pr!%"n, 8HO → 8H  OH SOLUCIÓN: ara pod!r !%'abl!(!r la (an'dad dr"g!no # o@$g!no !% n!(!%aro &'l)ar la !@pr!%"n dada* !%'o a(! n!(!%aro !%'abl!(!r % la !@pr!%"n r!pr!%!n'a &na !(&a("n +&$m(a o no. or %mpl! n%p!(("n %! p&!d! -!r +&! !% n!(!%aro balan(!arla* !%'o %! logra (olo(ando !l n4m!ro H (omo (o!(!n'! !%'!+&om5'r(o d!l ag&a # d!l dr"g!no ga%!o%o, +8HO → +8H  OH  Aora %! (on-!r'! a mol!% la (an'dad d! ag&a dada !n la norma("n, 1 lbra 8HO @ >:> g 8HO @ 1 mol 8HO  H:.HH mol!% 8HO 1 g 8HO  A par'r d! lo% mol!% d! 8 HO* &'l)ando la% r!la(on!% !%'!+&om5'r(a% d! la !(&a("n +&$m(a %! !%'abl!(! !l n4m!ro d! mol!% d! dr"g!no # o@$g!no +&! %! orman, H:.HH mol!% 8 HO @ H mol!% 8H   H:.HH mol 8 H   H mol 8HO H:.HH mol!% 8 HO @ 1 mol!% OH  1H.=1 mol OH H mol 8HO Como la r!a(("n pro(!d! !n (ond(on!% S.T..* %! p&!d! &'l)ar !l -ol&m!n molar d! &n ga% !n !%'a% (ond(on!%* !% d!(r HH.> l'ro% 2 mol , H:.HH mol!% 8 H @ HH.> l'ro% 8H  /65)7- lit'os $+ 1 mol 8H 1H.=1 mol!% O H @ HH.> l'ro% OH  +8+)56 lit'os O+ 1 mol 8H 11

E3EMPLO 4 -: C&/n'o% m!'ro% (4b(o% d! amon$a(o* N8 * p&!d! ob'!n!r%! a par'r d! H: m!'ro% (4b(o% d! dr"g!no ga%!o%o* 8 H* d! a(&!rdo a la %g&!n'! !@pr!%"n, NH  8H → N8 Q&5 -ol&m!n d! N H r!a((ona 9Con%d!r! +&! 'odo% lo% -ol4m!n!% !%'/n m!ddo% a la m%ma pr!%"n # '!mp!ra'&ra ?. SOLUCIÓN: La !@pr!%"n +&! r!pr!%!n'a la r!a(("n +&$m(a %! d!b! balan(!ar #a balan(!ada* %! p&!d! n'!rpr!'ar !n '5rmno% d! mol!% # d! -ol4m!n!% molar!%, NH 1 mol 1 -ol&m!n molar

-8H



 mol!%  -ol4m!n!% molar!%

+N8

→

H mol!% H -ol4m!n!% molar!%

D!bdo a +&! %olam!n'! !% (ono(do !l -ol&m!n d! dr"g!no +&! r!a((ona* r!%&l'a mpo%bl! !%'abl!(!r !l n4m!ro d! mol!% d! dr"g!no +&! r!a((onan* a m!no% +&! %! %&ponga +&! !l pro(!%o o(&rr! a TE. Sn !mbargo* !n !l !n&n(ado d!l probl!ma %! m!n(ona +&! 'odo% lo% -ol4m!n!% !%'/n m!ddo% a la m%ma '!mp!ra'&ra # pr!%"n # %ab!ndo +&! !l -ol&m!n d! &n ga% !% dr!('am!n'! propor(onal al n4m!ro d! mol!% pr!%!n'!%* # +&! la l!# d! A-ogadro !%'abl!(! +&! -ol4m!n!% g&al!% (on'!n!n !l m%mo n4m!ro d! mol5(&la%* !l -ol&m!n d! n'r"g!no +&! r!a((ona %!r/ la '!r(!ra par'! d!l -ol&m!n d! dr"g!no. E%'o %! d!d&(! d! la !(&a("n +&$m(a +&! !%'abl!(! +&! 1 mol d! n'r"g!no r!a((ona (on  mol!% d! dr"g!no. D! orma %!m!0an'! %! p&!d! !%'abl!(!r  +&! !l -ol&m!n d! amon$a(o ormado %!r/ la% H '!r(!ra% par'!% d!l dr"g!no +&! r!a((ona. E%'a% %'&a(on!% no% (ond&(!n a, Vol&m!n ormado d! amon$a(o, H: m 8H  @ H -ol4m!n!% d! N8   .6)6, 9- de N$H -ol4m!n!% d! 8 H Vol&m!n d! n'r"g!no +&! r!a((ona, H: m 8H @ 1 -ol&m!n d! NH  .+)/ 9- de N+ H -ol4m!n!% d! 8 H 12

E3EMPLO 4 5: C&/l %!r/ la pr!%"n !n p% * +&! !0!r(!r/n =KK gramo% d! n'r"g!no ga%!o%o* NH * +&! !%'/n alma(!nado% !n &n r!(p!n'! d! : galon!% a m!no% 1: grado% C!l%&% SOLUCIÓN: En prm!r l&gar* !% n!(!%aro (on-!r'r lo% galon!% a l'ro%, : galon!% @ .;: l'ro%  1.H: l'ro% 1 gal"n En %!g&da %! (on-!r'! la '!mp!ra'&ra a 3!l-n,     1:  H;.1:  H:.1:

o

C  H;.1:

 Aora %! (on-!r'! lo% =KK gramo% d! N H * a mol!%, =KK g NH  @ 1 mol NH   H1.> mol!% N H H g NH Fnalm!n'!* %! %&%''&#! la norma("n !n la !(&a("n d!l ga% d!al,   nRT 2 V   9H1.> mol ?9K.KH1 l'ro%  a'm 2 mol  3!l-n ?9H:.1: 3!l-n ? 1.H: l'ro%   H.

≈ 

H> a'm"%!ra%

H> a'm @ 1>.; p%  -/+)8 !si 1 a'm E3EMPLO 4 /: Una m&!%'ra d! H.H; gramo% d! &n ga% m!ddo a H; grado% C!l%&% # K mm d! 8g* o(&pa &n -ol&m!n d! 1>KK ((. Cal(&lar !l Bp!%o mol!(&lar d!l ga%. SOLUCIÓN: ara pod!r &'l)ar !l -alor d! R  K.KH1 l'ro%  a'm 2 mol  3!l-n * !% n!(!%aro !@pr!%ar la% (an'dad!% dada% !n la% &ndad!% ad!(&ada%, K mm 8g @ 1 a'm"%!ra  1.1;1 a'm ;=K mm 8g 1>KK (( @ 1 l'ro 1KKK ((

 1.> l'ro%

  H; oC  H;.1:  KK.1: 3!l-n 13

Con la norma("n an'!ror* %! p&!d! (al(&lar !l n4m!ro d! mol!% d! ga% !n !%'a% (ond(on!%, n  V 2 RT n  .

91.1;1 a'm?91.> l'ro%? .  K.K==: mol!% 9K.KH1 l'ro%  a'm 2 mol  3!l-n ?9KK.1: 3!l-n? Fnalm!n'! %! r!la(ona la ma%a (on !l n4m!ro d! mol!%, Bp!%o mol!(&lar 

H.H; gramo%  -5)., g  9ol K.==: mol!%

E3EMPLO 4 6: D! a(&!rdo a !%'&do% amb!n'al!%* %! a !%'mado +&! an&alm!n'! %! lb!ra a la a'm"%!ra K.1: gga'on!lada% m5'r(a% d! mon"@do d! (arbono ga%!o%o* CK 9g? . a?

C&/l !% !l -ol&m!n !@pr!%ado !n m!'ro% (4b(o% +&! o(&pa !%'a (an'dad d! ga% !n (ond(on!% ST

b?

C&/n'a% mol5(&la% d! CO !%'/n (on'!nda% !n !%'! -ol&m!n

SOLUCIÓN: En prm!r l&gar* %! d!b! (on-!r'r la% 'on!lada% m5'r(a% d! CO a mol!%, K.1: Gga'on m5'r(a% @ 1@1K  'on m5'r(a%  1 Gga'on m5'r(a

 1:K KKK KKK Ton m5'r(a%

1:K KKK KKK Ton m5'r(a% @ 1KKK 3g @ 1KKK g @ 1 mol CO  :.=P1K 1H 1 Ton m5'r(a 1 g H g CO a?

En (ond(on!% ST* &n mol d! (&al+&!r ga% o(&pa &n -ol&m!n apro@mado d! HH.> l'ro%* &'l)ando !%'a r!la("n %! p&!d! !n(on'rar !l -ol&m!n +&! o(&pa !l CO,

:.= @ 1K1H mol!% CO @ HH.> l'ro% CO @ 1 m!'ro (4b(o CO  .) +; < .;.. 9- CO 1 mol CO 1KKK l'ro% CO b?

El n4m!ro d! mol5(&la% d! CO %! p&!d! (al(&lar &'l)ando !l n4m!ro d!  A-ogadro,

:.= @ 1K1H mol!% CO P =.KHH@1K H mol5(&la% CO  -)+-<.;-6 9ol=ulas CO 1 mol CO 14

PRO#LEMA 4 ,: Una m!)(la d! :K g d! o@$g!no ga%!o%o 9 K H ? # :K g d! !lo 9 8! ? '!n! &na pr!%"n 'o'al d! : a'm"%!ra%. C&/l !% la pr!%"n par(al d! (ada ga% !n la m!)(la SOLUCIÓN: En prm!r l&gar* %! d!b! (on-!r'r la ma%a d! (ada ga% a mol!%, ara !l o@$g!no ga%!o%o,

:K g K H @ 1 mol KH   H g KH

1.:=H: mol K H

ara !l 8!lo,

:K g 8! @ 1 mol 8!  > g 8!

1H.: mol 8!

 Aora %! p&!d! !%'abl!(!r lo% mol!% 'o'al!% !n la m!)(la, Mol!% 'o'al!% Mol!% 'o'al!%

 

mol!% d! o@$g!no  mol!% d! !lo 1.:=H: mol!%  1H.: mol!%  1>.K=H: mol!%

Con la norma("n !n(on'rada* %! p&!d! (al(&lar la ra(("n molar d! (ada ga%, P o@$g!no  mol!% o@$g!no 2 mol!% 'o'al!%  1.:=H: mol 2 1>.K=H: mol  K.11 P!lo

 mol!% !lo 2 mol!% 'o'al!%  1H.: mol 2 1>.K=H: mol  K.

Fnalm!n'! %! p&!d! (al(&lar la pr!%"n par(al d! (ada ga% &'l)ando la ra(("n molar d! (ada &no # la pr!%"n 'o'al d! : a'm"%!ra%. La !@pr!%"n +&! p!rm'! !l (/l(&lo !%,   9P ?9'o'al? r!%"n par(al d!l o@$g!no,  o@$g!no  K.11 @ : a'm  ;)// at9 r!%"n par(al para !l 8!lo,  !lo

 K. @ : a'm  5)5/ at9

PRO#LEMA 4 8: Una m&!%'ra d! =KK mL d! o@$g!no %! r!(og" %obr! ag&a a K grado% C!l%&% # pr!%"n d! 1.: a'm"%!ra%* Q&5 -ol&m!n o(&par$a la m&!%'ra %!(a a TE 9 La pr!%"n d! -apor d!l ag&a a K C!l%&% !% K.K>1 a'm"%!ra% ? SOLUCIÓN: 15

Como !l ga% &! r!(ol!('ado !n ag&a* la pr!%"n m!dda d! 1.: a'm (ompr!nd! la pr!%"n d!l -apor d! ag&a # la pr!%"n d!l o@$g!no* por (on%g&!n'! %! a(! n!(!%aro (al(&lar la pr!%"n d!l o@$g!no %!(o* la !@pr!%"n +&! r!la(ona la% pr!%on!% !%, r!%"n 'o'al  pr!%"n -apor d! ag&a  pr!%"n d!l o@$g!no %!(o S&%''&#!ndo la norma("n, 1.: a'm  K.K>1 a'm  pr!%"n d!l o@$g!no %!(o r!%"n o@$g!no %!(o

 1.: a'm  K.K>1 a'm  1.>:1 a'm

La% (ond(on!% n(al!% para !l o@$g!no %on, r!%"n  1.>:1 a'm T!mp!ra'&ra  K C!l%&%  K !l-n Vol&m!n  =KK mll'ro%  %! l! d!%!a ll!-ar a (ond(on!% TE* +&! (orr!%pond!n a, r!%"n  1 a'm T!mp!ra'&ra  H; 3!l-n Vol&m!n   La !@pr!%"n alg!bra(a +&! r!la(ona la% 'r!% -arabl!% !% la l!# (ombnada, V   V  T T   Al %&%''&r la norma("n* %! !n(&!n'ra +&!, 91.>:1 a'm?9=KK mll'ro%?  K 3!l-n

9 1 a'm ? 9 V   ? H; 3!l-n

Vnal  ,88 ) +5 9ililit'os PRO#LEMA 4 7: C&/l !% la d!n%dad d!l (loro ga%!o%o 9 Cl H ? a TE SOLUCIÓN: La ma%a molar d!l (loro ga%!o%o 9 Cl H ? !%, ;K. gramo% 2 mol Con la !@pr!%"n para d!n%dad* %&%''&#!ndo la norma("n propor(onada* %! ob'!n! , ρ  . M . RT ρ



9 ;K. gramo% 2 mol ? @ 9 1 a'm ? 9 K.KH1 L.a'm 2 mol. ?9 H;  ? 16

ρ

 -).6 g  lit'o

Instruye al joven en su camino, y aun cuando fuere viejo no se apartará de él. Prov. 22 , 6

gared

17