QUÍMICA de 2º de BACHILLERATO EL EQUILIBRIO QUÍMICO PROBLEMAS RESUELTOS QUE HAN SIDO PROPUESTOS EN LOS EXÁMENES DE LAS PRUEBAS DE ACCESO A ESTUDIOS UNIVERSITARIOS EN LA COMUNIDAD DE MADRID (1996 − 2010)
VOLUMEN I DOMINGO A. GARCÍA FERNÁNDEZ DEPARTAMENTO DE FÍSICA Y QUÍMICA I.E.S. EMILIO CASTELAR MADRID
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Estos Estos volúm volúmene eness I y II compre comprende nden n 32 proble problemas mas resue resueltos ltos de EQUILIBRIO QUÍMICO que han sido propuestos en 32 exámenes de Química de las Pruebas de acceso a estudios universitarios en la Comunidad de Madrid entre los años 1996 y 2010, en las siguientes convocatorias:
AÑO
2010
1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 Fase General Fase Específica
Modelo
EXAMEN JUNIO 1 1 1
1 1 1 1 1 1 1 1 1
1
1 1 1 1 1 1 1
SEPTIEMBRE 1 1 1 1 1 1 1 1 1 1 1 1
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ENUNCIADOS VOLUMEN I 1−
En un un reac reactor tor de de 1 L, L, a tem temper peratu atura ra const constan ante, te, se est establ ablec ecee el equi equili libri brio: o: NO2 ( g g ) + SO2 ( g g )
→ ←
NO ( g g ) + SO3 ( g g )
siendo las concentraciones concentraciones en el equilibrio: equilibrio: [NO 2] = 0,2 mol∙L −1, [SO2] = 0,6 mol∙L −1, [NO] = 4,0 mol∙L −1 y [SO3] = 1,2 mol∙L −1 . a) Calcule el valor de la constante K c a esa temperatura. b) Si se se añ añaden 0, 0,4 mo moles de de NO NO 2, ¿cuál será la nueva concentración de reactivos y productos cuando se restablezca de nuevo el equilibrio?. Septiembre 2004
2−
Para la reacción: NO2 ( g g ) + SO2 ( g g )
→ ←
NO ( g g ) + SO3 ( g g )
a 350 K las concentracio concentraciones nes en el equilibrio equilibrio son: [NO 2] = 0,2 mol∙L −1, [SO2] = 0,6 mol∙L −1 , [NO] = 4,0 mol∙L −1 y [SO3] = 1,2 mol∙L −1 . a) Calc Calcul ulee el el vval alor or de las las con const stan ante tess de de equ equil ilib ibri rio: o: K c y K p. b) Calcul Calculee las las nueva nuevass conce concent ntrac racio iones nes en el el equil equilib ibrio rio si si a la la mezcl mezclaa ante anterio rior, r, conte contenid nidaa en un recipiente recipiente de 1 litro, se le añade 1 mol de SO 2 manteniendo la temperatura a 350 K. Modelo 2003
3−
Se intro introduc ducen en en un recipi recipien ente te de 3 L, en el que previ previame amente nte se ha hecho hecho el vacío vacío,, 0,04 moles de SO 3 a 900 K. Una vez alcanzado el equilibrio se encuentra que hay presentes 0,028 moles de SO 3. a) Cal Calcul cule, a dic dicha te temp mpeerat ratura, ra, el el val valoor de de K c para la reacción: 2 SO3 ( g g )
→ ←
2 SO2 ( g g ) + O2 ( g g ) .
b) b) Cal Calcul cule, a di dicha te temp mpeerat ratura, ra, el el val valoor de de K p para dicha disociación. −1 −1 Dato Dato:: R = 0,0 0,082 82 atm atm∙L ∙L∙m ∙mol ol ∙K . Modelo 2006
4−
La reacción: CO ( g g ) + H2O ( g g )
→ ←
H2 ( g g ) + CO2 ( g g )
tiene una constante K c de 8,25 a 900 ºC. En un recipiente de 25 litros se mezclan 10 moles de CO y 5 moles de H 2O a 900 ºC. Calcule en el equilibrio:
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Página 3 Ejercicios de acceso a la Universidad − Problemas de Equilibrio químico
5−
Para la reacción: N2 ( g g ) + O2 ( g g )
→ ←
2 NO ( g g )
el valor de la constante constante de equilibrio equilibrio K c es 8,8 x 10 −4 a 1.930 ºC. Si se introducen 2 moles de N2 y 1 mol de O2 en un recipiente vacío de 2 L y se calienta hasta 1.930 ºC, calcule: a) la conc concen entr trac ació iónn de de cad cadaa una una de las las esp espec ecie iess en en equ equil ilib ibri rio; o; b) la presió presiónn parc parcia iall de cada cada espec especie ie y el el vval alor or de de la la con consta stante nte de equil equilib ibrio rio K p. −1 −1 Dato Dato:: R = 0,0 0,082 82 atm atm∙L ∙L∙m ∙mol ol ∙K . Septiembre 2005
6−
La cons consttante nte de equil uilibrio rio K c para la reacción: N2 ( g g ) + O2 ( g g )
→ ←
2 NO ( g g )
vale 8,8 x 10 −4, a 2.200 K. a) Si 2 moles de N 2 y 1 mol de O 2 se introducen en un recipiente de 2 L y se calienta a 2.200 K, calcule los moles de cada especie química en el equilibrio. b) b) Calc Calcul ulee las las nuev nuevas as conc concen entr trac acio ione ness que que se alca alcanz nzan an en el equi equili libr brio io si se añad añadee al recipiente anterior 1 mol de O 2. Septiembre 2002
7−
Se int introdu roduccen 0,1 0,1 mole oles de SbC SbCl 5 en un recipiente de 1 litro, se calientan a 182 ºC y se produce su disociación: SbCl5 ( g g )
→ ←
SbCl3 ( g g ) + Cl2 ( g g )
quedando, cuando se alcanza el equilibrio, 0,087 moles de SbCl 5. Calcule: a) La constante de equilibrio K c. b) b) Las Las conce concent ntra raci cion ones es de los los comp compon onen ente tess en el equi equili libr brio io,, si se aume aument ntaa el volum volumen en de 1 a 3 litros, manteniendo la temperatura constante. c) La pre presi sión ón tot total al de de la mez mezcl claa en las las con condi dici cion ones es fin final ales es del del apa apart rtad adoo b). b). −1 −1 Dato Dato:: R = 0,0 0,082 82 atm atm∙L ∙L∙m ∙mol ol ∙K . Septiembre 2000
8−
Considere la la re reacción: CO2 ( g g ) + H2 ( g g )
→ ←
CO ( g g ) + H2O ( g g ) .
Al mezclar inicialmente 49,3 moles de CO 2 y 50,7 moles de H 2, a la temperatura de 1.000 K, se encuentra una composición en el equilibrio equilibrio de 21,4 moles de CO 2, 22,8 moles de H2, 27,9 moles de CO y 27,9 moles de H 2O. a) Determine el valor de K c. b) b) Calc Calcul ulee la comp compos osic ició iónn de la mezc mezcla la en en el el equ equil ilib ibri rioo cuan cuando do se se par parte te inic inicia ialm lmen ente te de 60 moles de CO 2 y 40 moles de H 2 en las mismas condiciones. Septiembre 2001
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a)
la cantidad de pentacloruro de fósforo que permanece sin disociar, una vez establecido el equilibrio; b) la presió presiónn ttota otall en en el el iint nteri erior or del del matraz matraz en las condic condicio iones nes de equil equilib ibrio rio.. −1 −1 Dato Dato:: R = 0,0 0,082 82 atm atm∙L ∙L∙m ∙mol ol ∙K . Modelo 2001 Página 4 Ejercicios de acceso a la Universidad − Problemas de Equilibrio químico
10 − El pentac pentaclorur loruroo de fósforo fósforo se descom descompone pone con con la tempera temperatura tura dando dando triclor tricloruro uro de fósforo fósforo y cloro. Se introducen 20,85 g de pentacloruro pentacloruro de de fósforo en un recipiente recipiente cerrado de 1 L y se calientan calientan a 250 ºC hasta alcanzar alcanzar el equilibrio. equilibrio. A esa temperatura todas las especies se encuentran en estado gaseoso y la constante de equilibrio K c vale 0,044. a) Form Fo rmul ulee y aju ajust stee la la rea reacc cció iónn quím químic icaa que que ti tien enee lug lugar ar.. −1 b) Obtenga la co concentración en mo mol∙L de cada una de las especies de la mezcla gaseosa a esa temperatura. c) ¿Cuá ¿Cuáll ser seráá la la pre presi sión ón en el inte interi rior or del del rec recip ipie ient nte? e?.. d) Obtenga la presión parci rcial de Cl 2. −1 −1 Datos: Datos: R = 0,082 0,082 atm∙L∙mo atm∙L∙moll ∙K ; masas atómicas (u): P = 31,0 , Cl = 35,5 . Junio 2009
11 −
El equilibrio rio: PCl5 ( g g )
→ ←
PCl3 ( g g ) + Cl2 ( g g )
se alcanza calentando 3 gramos de pentacloruro de fósforo hasta 300 ºC en un recipiente de medio litro, siendo la presión final de 2 atm. Calcule: a) el grad gradoo de de dis disoc ocia iaci ción ón del del pent pentac aclo loru ruro ro de de fós fósfo foro ro;; b) el valor de K p a dicha temperatura. Datos: Datos: R = 0,082 0,082 atm∙L∙mo atm∙L∙moll −1∙K −1 ; masas atómicas (u): P = 31,0 , Cl = 35,5 . Junio 2003
12 − En un recip recipie iente nte cerrad cerrado, o, a la temper temperat atura ura de 490 K, se int introd roduce uce 1 mol de PCl 5 ( g g ) que se descompone parcialmente según la reacción: PCl5 ( g g )
→ ←
PCl3 ( g g ) + Cl2 ( g g ) .
Cuando se alcanza el equilibrio la presión es de 1 atm y la mezcla es equimolecular (igual número de moles de PCl 5, PCl3 y Cl2). a) Dete Determ rmin inee el el valo valorr de de la la con const stan ante te de equi equili libr brio io K p a dicha temperatura. b) Si la la mezcl mezclaa se compr comprim imee hast hastaa 10 atm, atm, cal calcul culee la la nueva nueva compo composi sició ciónn de equil equilibr ibrio. io. Modelo 2005
13 − A 200 200 ºC y pres presió iónn de de 1 atm atmós ósfe fera ra el el PCl PCl 5 se disocia en PCl 3 y Cl2, en un 48,5 %. Calcule: a) K c y K p. b) El grado grado de disoci disociaci ación ón a la misma misma tempe temperat ratura ura pero pero a 10 atmós atmósfe feras ras de presió presión. n. c) Expl Expliq ique ue en func funció iónn de Prin Princi cipi pioo de Le Chât Châtel elie ierr si el resu result ltad adoo obte obteni nido do en b) le parece correcto. Dato R = 0,082 0,082 atm∙L∙mo atm∙L∙moll −1∙K −1 masas atómicas (u): P = 30,97 , Cl = 35,5 .
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siendo el valor de K c = 0,0156. Una muestra de 0,6 moles de HI se introduce en un matraz de 1 L y parte del HI se descompone hasta que el sistema alcanza el equilibrio. a) ¿Cuá ¿Cuáll es es la la con conce cent ntra raci ción ón de cada cada espe especi ciee en en el el equi equili libr brio io?. ?. b) Calcule K p. c) Cal Calcul cule la la pre presi sión ón tota otal en en el el eq equil uilibrio rio. −1 −1 Dato Dato:: R = 0,0 0,082 82 atm atm∙L ∙L∙m ∙mol ol ∙K . Junio 2004 Página 5 Ejercicios de acceso a la Universidad − Problemas de Equilibrio químico
15 − El valo valorr de la la consta constante nte de equil equilibri ibrioo a 700 700 K para la reacc reacción: ión: 2 HI ( g g )
→ ←
H2 ( g g ) + I2 ( g g )
es 0,0183. Si se introducen 3,0 moles de HI en un recipiente recipiente de 5 L que estaba vacío y se deja alcanzar el equilibrio: a) ¿Cuántos moles de I 2 se forman?. b) ¿Cuál es la presión total?. c) ¿Cuá ¿Cuáll será será la la conc concen entr trac ació iónn de HI en el el equi equili libr brio io si a la la mism mismaa temp temper erat atur uraa se aumenta el volumen al doble?. Dato Dato:: R = 0,0 0,082 82 atm atm∙L ∙L∙m ∙mol ol−1∙K −1 . Septiembre 2008
16 − Una Una mezcl mezclaa gaseosa gaseosa consti constitui tuida da inicia inicialme lment ntee por 3,5 moles moles de hidróge hidrógeno no y 2,5 moles moles de yodo se calienta a 400 ºC con lo que al alcanzar el equilibrio se obtienen 4,5 moles de HI, siendo el volumen del recipiente de reacción de 10 litros. Calcule: a) El val valor de de la las con const staante ntes de de eq equil uilibrio rio K c y K p. b) b) La conc concen entr trac ació iónn de los los comp compue uest stos os si el el volum volumen en se red reduc ucee a la mitad mitad mant manten enie iend ndoo constante la temperatura temperatura de 400 ºC. Junio 1998
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Página 6 Ejercicios de acceso a la Universidad − Problemas de Equilibrio químico
VOLUMEN II 17 −
El fosgeno, CO COCl 2, usado en la preparación del poliuretano, se obtiene a partir del: CO ( g g ) + Cl2 ( g g )
→ ←
COCl2 ( g g ) .
Una mezcla en equilibrio a 395 ºC contiene 0,01 moles de CO y 0,02 moles de Cl 2 por litro, así como cierta cantidad de COCl 2. a) Si la Kc de formación del fosgeno a 395 ºC vale 1,23 x 10 3, ¿cuál es la concentración de COCl2?. b) Calcule el valor de K p de la reacción anterior a esa temperatura. c) ¿Cuánto valdrá la constante K c de disociación del fosgeno a esa temperatura?. Dato Dato:: R = 0,0 0,082 82 atm atm∙L ∙L∙m ∙mol ol−1∙K −1 . Septiembre 1996
18 − Se intr introd oduc ucen en 2 mo mole less de COBr COBr 2 en un recipiente de 2 L y se calienta hasta 73 ºC. El valor de la constante K c, a esa temperatura, temperatura, para el equilibrio: equilibrio: COBr 2 ( g g )
→ ←
CO ( g g ) + Br 2 ( g g )
es 0,09. Calcule en dichas condiciones: a) El núme número ro de mo mole less de de las las tres tres sust sustan anci cias as en el equi equili libr brio io.. b) La pr presión to total de del si sistema. c) El valor de la constante K p. Dato Dato:: R = 0,0 0,082 82 atm atm∙L ∙L∙m ∙mol ol−1∙K −1 .
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20 −
Cono Conoccido el vval aloor de de K c para el equilibrio: 3 H2 ( g g ) + N2 ( g g )
→ ←
2 NH3 ( g g )
K c = 783
calcule a la misma temperatura el valor de la constante de equilibrio de las siguientes reacciones: 1 2
N2 ( g g ) +
2 NH3 ( g g )
→ ←
3 2
H2 ( g g )
→ ←
NH3 ( g g )
N2 ( g g ) + 3 H 2 ( g g )
K c (a) K c (b) . Junio 1996
Página 7 Ejercicios de acceso a la Universidad − Problemas de Equilibrio químico
21 − Una mezcla cla de 2 mole oles de N 2 y 6 moles moles de H2 se calienta hasta 700 ºC en un reactor de 100 L, estableciéndose el equilibrio: N2 ( g g ) + 3 H 2 ( g g )
→ ←
2 NH3 ( g g ) .
En estas condiciones se forman 48,28 g de amoníaco en el reactor. Calcule: a) La cantidad de gramos de N 2 y H2 en el equilibrio. b) La constante de equilibrio K c. c) La pres presió iónn tot total al en el reac reacto torr cuan cuando do se ha alca alcanz nzad adoo el equi equili libr brio io.. −1 −1 Dato Dato:: R = 0,0 0,082 82 atm atm∙L ∙L∙m ∙mol ol ∙K ; masas atómicas (u): H = 1 , N = 14. Modelo 2010
22 − En un reci recipi pien ente te de 0,4 0,4 L se intr introd oduc ucen en 1 mo moll de N 2 y 3 moles de H 2 a la temperatura de 780 K. Cuando se establece el equilibrio para la reacción: N2 ( g g ) + 3 H2 ( g g )
→ ←
2 NH3 ( g g )
se tiene una mezcla con un 28 % en mol de NH 3. Determine. a) El núme número ro de mo mole less de de cad cadaa com compo pone nent ntee en en el el equ equil ilib ibri rio. o. b) La pr presión fifinal de del si sistema. c) El val valor de de la const nstant ante de equi quilibri brio K p. −1 −1 Dato Dato:: R = 0,0 0,082 82 atm atm∙L ∙L∙m ∙mol ol ∙K . Junio 2006
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NH3 ( g g )
→ ←
3 2
H2 ( g g ) +
1 2
N2 ( g g ) .
Calcule: a) La pres presió iónn par parci cial al de cada cada uno uno de de los los gase gasess en en el el equ equil ilib ibri rio. o. b) b) El volu volume menn de de la la mez mezcl claa si si se se par parte te de 170 170 g de de amo amoní níac aco. o. c) El valor de la constante K p. d) El valor de la constante K c. Datos: Datos: R = 0,082 0,082 atm∙L∙mo atm∙L∙moll −1∙K −1 ; masas atómicas (u): H = 1 , N = 14. Modelo 2007
Página 8 Ejercicios de acceso a la Universidad − Problemas de Equilibrio químico
25 − A 400 ºC y 10 atmós atmósfera ferass el amoníac amoníacoo contenid contenidoo en un recipie recipiente nte se encuen encuentra tra disoci disociado ado en sus elementos en un 80 %. Calcule: a) El valo valorr de la pres presió iónn en el reci recipi pien ente te si la diso disoci ciac ació iónn fues fuesee del del 50 %, sin sin vari variar ar el volumen ni la temperatura. b) La tempe temperat ratura ura que deberí deberíaa alcan alcanzar zar el recip recipie iente nte para para que la disoci disociac ación ión vol volvi viera era a ser del 80 %, sin variar el volumen ni la presión aplicada en a). Dato Dato:: R = 0,0 0,082 82 atm atm∙L ∙L∙m ∙mol ol−1∙K −1 . Modelo 2000
26 − Un recipi recipiente ente de de 37,5 L, que se encuent encuentra ra a 343 K y 6 atm, contiene contiene una mezcla mezcla en equilibrio con el mismo número de moles de NO 2 y N2O4, según la reacción: 2 NO2 ( g g )
→ ←
N2O4 ( g g ) .
Determinar: a) El núme número ro de mo mole less de de cad cadaa com compo pone nent ntee en en el el equ equil ilib ibri rio. o. b) b) El val valor de de la la co const nstant ante de de equ equiilibri brio K p. c) La fracc fracció iónn mo mola larr de cada cada uno uno de los comp compon onen ente tess de la mezc mezcla la,, si la pres presió iónn se reduce a la mitad. Dato Dato:: R = 0,0 0,082 82 atm atm∙L ∙L∙m ∙mol ol−1∙K −1 . Modelo 2009
27 − En un recipien recipiente te cerrado cerrado de volumen volumen constant constantee igual igual a 22 L y a temperat temperatura ura de 305 K
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a) El volumen del reactor. b) b) El núme número ro de mo mole less de cada cada comp compon onen ente te en el equi equili libr brio io.. c) El val valor de de la const nstant ante de equi quilibri brio K p. d) El val valor de de la const nstant ante de de equ equiilibri brio K c. −1 −1 Datos: Datos: R = 0,082 0,082 atm∙L∙mo atm∙L∙moll ∙K ; masas atómicas (u): N = 14 , O = 16 . Junio 2010 (Fase General)
29 − La const constant antee de equil equilib ibrio rio de la la reacc reacció ión: n: N2O4 ( g g )
→ ←
2 NO2 ( g g )
vale 0,671 a 45 ºC. Calcule la presión total en el equilibrio en un recipiente que se ha llenado con N2O4 a 10 atmósferas y a dicha temperatura. temperatura. −1 −1 Dato Dato:: R = 0,0 0,082 82 atm atm∙L ∙L∙m ∙mol ol ∙K . Junio 1997 Página 9 Ejercicios de acceso a la Universidad − Problemas de Equilibrio químico
30 −
Cons Consid ider eree la reac reacci ción ón:: N2O4 ( g g )
→ ←
2 NO2 ( g g ) .
Calcule: a) K p, a 25 ºC y 1 atm, si el compuesto N 2O4 está disociado en un 50 %. b) b) ΔH de la reac reacci ción ón,, sabi sabien endo do que que las las enta entalp lpía íass de de for forma maci ción ón de NO 2 y N2O4 son: −1 −1 −50,16 kJ∙mol y −96,14 kJ∙mol , respectivamente. Modelo 2002
31 − El N2O4 gas se descompone parcialmente a 45 ºC para dar NO 2 gas. En un recipiente vacío, de un litro de capacidad, capacidad, a 45 ºC se introducen introducen 0,1 moles de N 2O4, alcanzándose alcanzándose en el equilibrio una presión de 3,18 atmósferas. Calcule: a) Las const constant antes es de equil equilib ibrio rio en funci función ón de de las las presi presione oness y de las las conc concent entrac racion iones. es. b) El grado de disociación de del N 2O4. −1 −1 Dato Dato:: R = 0,0 0,082 82 atm atm∙L ∙L∙m ∙mol ol ∙K . Junio 2000
32
A te
rat
el ada un un mol de et
la co
ol d
por de de ácid ácidoo nítric nítric
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Página 10
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Ejercicios de acceso a la Universidad − Examen de septiembre de 2004 − Opción A − Problema 2
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