1. :
2008 :
. q = 12°C ( H 2O2 )
2 H 2O2( aq) = 2 H 2O( l ) + O2( g ) :
( VM = 24 L.mol -1 )
. [ H 2O2 ]0 = 8, 0 ´10 -2 mol.L-1 VS = 500mL t =0
: (V )
O2
t ( min ) 0 4 8 12 16 20 24 28 32 36 40
VO2 ( mL ) 0 60 114 162 204 234 253 276 288 294 300
[ H 2O2 ] mol.L-1
. .1
. VO2 VM VS [ H 2O2 ]0 : t [ H 2O2 ] .2
. - .3
. [ H 2O2 ] = f ( t ) -
. -
. . t2 = 24 min t1 = 16 min -
. t1 2 -
. . [ H 2O2 ] q ' = 35°C .4
. :
2 H 2O2 (aq ) ® O2 ( g ) + 2 H 2O(l ) . .1
:
( mol )
. n = [ H 2O2 ]0 .VS = 8, 0 ´10-2 ´ 0,5
0 n 0 0
. n = 4 ´ 10-2 mol
x (t ) n - 2x (t ) x (t ) 2x ( t )
[ H 2O2 ] .2
xf n - 2x f xf 2x f
. VO2 VM VS [ H 2O2 ]0 : t
ni ( H 2O2 ) - 2 x ( t ) x (t )
[ H 2O2 ] = = [ H 2O2 ]0 - 2. n( H 2O2 ) ( t ) = ni ( H 2O2 ) - 2 x ( t ) : t
VS VS
2 VO2
. [ H 2O2 ] = [ H 2O2 ]0 - .VO : n ( O2 ) = =x :
VS .VM 2 VM
. - .3
1 2
. [ H 2O2 ] = 8,0 ´ 10-2 - .VO2 : [ H 2O2 ] = 8, 0 ´10-2 - .VO :
6 0, 5 ´ 24 2
1

2. t ( min ) 0 4 8 12 16 20 24 28 32 36 40
[ H 2O2 ] ´10-2 mol.L-1 8,0 7,0 6,1 5,3 4,6 4,1 3,8 3,4 3,2 3,1 3,0
. [ H 2O2 ] = f ( t ) -
. -
1 dx
vvol = . :
VS dt
d [ H 2O2 ] 1 d 2 dx
. = ( n - 2x) = - :
dt VS dt VS dt
1 d [ H 2O2 ]
vvol = - . :
2 dt
d [ H 2O2 ]
.t [ H 2O2 ] = f ( t ) :
dt
. t2 = 24 min t1 = 16 min -
1 ( 7, 0 - 4, 6 ) ´ 10
-3
vvol ( t1 ) = - . = 7, 5 ´10 -4 mol.L-1 .min -1
2 16 - 0
1 ( 7, 0 - 5,5 ) ´ 10
-3
vvol ( t2 ) = - . = 3,1´ 10-5 mol.L-1.min -1
2 24 - 0
.
. t1 2 -
[ H 2O2 ]0 xmax
( ) . [ H 2O2 ] ( t1/2 ) = : x ( t1/ 2 ) = :
2 2
0, 08
.( ) t1/ 2 » 20 min : [ H 2O2 ] ( t1/2 ) = = 40mmol .L-1 :
2
. ( ) q ' = 35°C [ H 2O2 ] .4
,
2008 :
.( )
30mL m = 36mg Mg ( S )
.
. .1
(H (
+
aq ) )
/ H 2( g ) : .2
(
. Mg 2 + ( aq ) / Mg( s ) )
: .3
t ( min ) 0 2 4 6 8 10 12 14 16 18
VH 2 ( mL ) 0 12,0 19,2 25,2 28,8 32,4 34,8 36,0 37,2 37,2
x ( mol )
2

3. . x -
. x = f (t ) -
. t =0 -
. pH = 1 .4
. VM = 24, 0 L.mol -1 M ( Mg ) = 24 g .mol -1 :
. :
. .1
.
.( )
. .2
. Mg( S ) ® Mg 2+ ( aq ) + 2e- :
. 2 H + ( aq) + 2e - ® H 2( g ) :
Mg( S ) + 2 H + ( aq ) ® Mg 2+ ( aq ) + H 2( g ) :
Mg( S ) + 2 H + ( aq ) ® Mg 2+ ( aq ) + H 2( g ) . - .3
:
( mol )
m 36 ´10-3
0 n1 n0 0 0 . n1 = = 1,5 ´10-3 mol
M 24
x (t ) n1 - x ( t ) n0 - 2 x ( t ) x (t ) x (t )
xf n1 - x f n0 - 2 x f xf xf x
t ( min ) 0 2 4 6 8 10 12 14 16 18
. x = n ( H2 ) =
VH 2
:
VM
x ( mmol ) 0 0,50 0,80 1,05 1,20 1,35 1,45 1,50 1,55 1,55
. -
. x = f (t ) -
. t =0 -
dx
: t =0 v= :
dt
17 ´10-4 - 0
.v = = 2,83 ´10-4 mol .min -1
6-0
. .4
. x f = 1,55 ´ 10 -3 mol
. n f ( H + ) = 3 ´ 10-3 mol : n f ( H + ) = é H + ù f .V = 10 - pH .V = 10 -1 ´ 30 ´10 -3 :
ë û H+
n0 ( H + ) = n f ( H + ) + 2 x f : n f ( H + ) = n0 ( H + ) - 2 x f :
6,1´10-3
ë û 0 30 ´10-3 » 0, 2mol.L : n0 ( H ) = 3 ´ 10 + 2 ´ 1,55 ´ 10 = 6,1´ 10 mol :
éH + ù = -1 + -3 -3 -3
3

4. 2008 :
: Mg
Mg( s ) + 2 H 3O + ( aq ) = 2 H 2O( l ) + Mg 2+ ( aq) + H 2( g )
C = 5, 0mol.L-1 V = 60mL m = 1,0 g
.
.
t ( min ) 0 1 2 3 4 5 6 7 8
VH 2 ( mL ) 0 336 625 810 910 970 985 985 985
x ( mol )
. .1
. x .2
. x = f (t ) .3
. xf .4
. ( t = 3min ) ( t = 0 min ) .5
. t1 2 .6
(H O )
3
+
.7
. VM = 24 L.mol -1 M ( Mg ) = 24,3 g.mol -1 :
. :
. .1
+ 2+
Mg( s ) + 2 H 3O ( aq ) = 2 H 2O( l ) + H 2( g ) + Mg ( aq ) : :
( mol ) . n1 =
m
=
1
0 0 0 M 24
n1 n0
n1 » 4,1´ 10-2 mol
x n1 - x n0 - 2 x x x
:
xf n1 - x f n0 - 2 x f xf xf
. n0 = C.V = 5 ´ 60 ´ 10-3 = 0,3mol
t ( min ) 0 1 2 3 4 5 6 7 8
. .2
x ( mmol ) 0 14,0 26,0 33,7 37,9 40,4 41,0 41,0 41,0 x
VH 2
. x = n ( H2 ) = :
VM
. x = f (t ) .3
. xf .4
n0 ( Mg ) n1 ( H 3O + )
= 4,1´10 -2 mol = 0, 3mol :
2 1
n0 ( Mg ) n1 ( H 3O )
+
-2
. Mg x f = 4,1´10 mol : <
2 1
4

5. . :
( t = 3min ) ( t = 0 min ) .5
dnH 2 dx 33, 7 - 17 dnH 2 dx 35 - 0
vH 2 ( 3) = = = » 5, 6mmol.min -1 vH 2 ( 0 ) = = = = 17,5mmol.min -1
dt dt 3-0 dt dt 2-0
. t1 2 .6
x ( t1 2 ) =
xf
. t1 2 = 1,5 min » 20, 05mmol :
2
(H O ) 3
+
.7
n0 - 2 x f xf 4,1´10 -2
é H 3O + ù =
ë ûf =C -2 = 5, 0 - 2 : x f = 4,1´10-2 mol :
V V 60 ´10-3
. é H 3O + ù ; 3, 6mol.L-1 :
ë ûf
2008 :
( S2 ) ( 2K ( +
aq )
+ S2 O82 - ( aq ) ) ( S1 )
. (K ( +
aq )
+ I -( aq ) )
V2 = 50mL C1 = 2, 0 ´ 10-1 mol.L-1 ( S1 ) V1 = 50mL t =0
S 2O82 - . C2 = 1, 0mol.L-1 ( S2 )
. -3-
:
. 2 I -( aq ) + S2O82-( aq) = I 2( aq ) + 2SO4 -( aq)
2
. ox / red .1
. .2
. .3
. t1 .4
2
.5
. t1
2
.6
. t = 10 min
. :
. ox / red .1
. (S O 2
-2
8 / SO4 2 ) :
-
S 2O 8-2(aq ) + 2e - = 2SO 4-2( aq ) :
-2 - -2
(I 2 / I-): 2I - (aq ) = I 2(aq ) + 2e - :
S 2O 8 (aq ) + 2I (aq ) = 2SO 4 ( aq ) + I 2( aq )
. .2
mmol
:
0 n1 = 10 n2 = 50 0 0
n1 = C1.V1 = 0, 2 ´ 50 ´ 10-3 = 10-2 mol
x n1 - x n2 - 2 x 2x x
. n1 = 10mmol :
xf n1 - x f n2 - 2 x f 2x f xf
5

6. . n2 = 50mmol : n2 = C2 .V2 = 1, 0 ´ 50 ´10-3 = 5 ´10-2 mol : I-
. .3
. xmax = n1 = 10mmol n2 - 2 xmax = 0 n1 - xmax = 0 :
. S 2O 8-2 :
. t1 .4
2
n1 10 xf
nS O -2 = = = 5mmol : x ( t1/ 2 ) = :
2 8
2 2 2
. t1/2 = 17,5 min : nS O-2 = 5mmol
2 8
. t1 .5
2
t1
2
2n + n x1/ 2 2 x1/ 2 n - 2x1/2 n -x
éK + ù = 1 2
ë û V +V [I2 ] = é SO4-2 ù = éI - ù = 2
ë û V +V é S2O8-2 ù = 1 1/2
ë û V +V
V1 + V2 ë û V +V
1 2 1 2 1 2 1 2
20 + 50 5 10 50 - 10 10 - 5
= = = = =
100 100 100 100 100
é K ù = 0, 7 mol.L-1
ë û
+
[ I 2 ] = 0, 05mol.L-1 é SO4 ù = 0,1mol.L-1
ë
-2
û é I - ù = 0, 4mol.L-1
ë û é S2O8-2 ù = 0,05mol.L-1
ë û
. t = 10 min .6
dx dnS O-2
. =- 2 8
: nS O-2 = n1 - x :
dt dt 2 8
1 dx 1 dnS2O8-2
vvol = =- :
V dt V dt
dnS O-2
. t = 10 min 2 8
dt
1 6,6 - 9,3
vvol = - = 2,7mmol.L-1.min -1 :
0,1 10 - 0
2009 :
: (I )
-
(S O )
2
2-
8
S 2O82- ( aq) + 2 I -( aq ) = 2SO42- ( aq ) + I 2( aq)
V1 = 100mL (t = 0) (q = 35°C ) .I
V2 = 100mL C1 = 4, 0 ´ 10-2 mol.L-1 ( 2K +
+ S 2O82 - )
. VT = 200mL C2 = 8, 0 ´ 10-2 mol.L-1 (K +
+ I-)
. -
( I2 ) [ I2 ] V2 V1 C1 é S2O82- ù
ë û -
.
(I )
-
(S O )
2
2-
8 (t = 0) é S 2O82- ù
ë û0 -
V0 = 10mL . ti ........ t2 t1 .II
( 2Na +
+ S2 O32 - ) ti
6

7. : V' C ' = 1,5 ´ 10-2 mol.L-1
t ( min ) 0 5 10 15 20 30 45 60
V ' ( ml ) 0 4,0 6,7 8,7 10,4 13,1 15,3 16,7
[ I 2 ] ( mmol / l )
-
. I 2( aq) / I -( aq) S 4O62-( aq) / S 2O32-( aq ) : -
. ·
1 C '´ V '
[ I2 ] = ´ : -
2 V0
. -
. [ I2 ] = f (t ) -
. ( t = 20 min ) -
. :
. - .I
2- - 2-
S 2O 8 ( aq ) + 2I ( aq ) = 2SO 4 ( aq ) + I 2( aq) S 2O 2-
8
( mmol ) . n1 = C1.V1 = 4, 0 ´10-2 ´10-1 :
n1 = 4, 0 ´ 10 -3 mol = 4mmol
0 4 8 0 0
: I-
x (t ) 4 - x (t ) 8 - 2x (t ) 2x ( t ) x (t )
. n2 = C2 .V2 = 8, 0 ´10-2 ´10-1
xf 4-xf 8 - 2x f 2x f xf
n2 = 8, 0 ´ 10-3 mol = 8mmol
. é S2O82- ù
ë û -
n - x C1.V1 x
é S 2O82- ù = 1
ë û = - : ( )
VT V1 + V2 V1 + V2
C .V
é S 2O82- ù = 1 1 - [ I 2 ] :
x
ë û V +V . [ I2 ] = : nI 2 = x :
1 2 V1 + V2
. é S 2O82- ù
ë û0 -
4 ´10-2 ´10-1 C .V
. é S2O82- ù =
ë û0 -1 -1
= 2 ´10-2 mol.L-1 : é S 2O82- ù = 1 1 :
ë û0 V + V
10 + 10 1 2
. ( I2 ) - .II
. -
2- 2- -
. 2 S 2O 3 ( aq ) ® S4 O 6 ( aq ) + 2e :
. I 2(aq ) + 2e - ® 2 I - (aq ) :
2S 2O32-( aq ) + I 2( aq) ® S4O6 - ( aq ) + 2 I - ( aq ) :
2
. -
2S 2O32-( aq ) + I 2( aq) ® S4O6 - ( aq ) + 2 I - ( aq )
2
.
( mol ) n '- 2 xE = 0 n0 - x E = 0 :
0 n' n0 0 0 n'
xE = n0 = :
xE n '- 2 xE n0 - x E xE 2x E 2
7

8. t ( min ) 1 C '.V ' n0
0 5 10 15 20 30 45 60 . [ I2 ] = . : [ I2 ] = :
2 V0
[ I 2 ] ( mmol.L-1 )
V0
0 3,0 5,0 6,5 7,8 9,8 11,5 12,5
. -
1,5 ´10-2 1 C '.V '
( mmol.L-1 [ I2 ] mL V' ) . [ I2 ] = V ' = 0, 75 ´ V ' : [ I2 ] = . :
2 ´10 ´10-3 2 V0
. [ I2 ] = f (t ) -
.
. ( t = 20 min ) -
d æ x ö d [I2 ] 1 dx
. vvol = ç ÷= : vvol = :
dt è VT ø dt VT dt
d [ I2 ]
. t = 20 min vvol =
dt
7,8 - 3, 2
. v vol = = 0, 23mmol .min -1 .L-1 :
20 - 0
2009 :
2,0g . (H +
+ Cl - )
. C = 1,0 ´10-1 mol.L-1 100mL CaCO3
:
t (s) 20 60 100
(1L )
P(CO2 ) ( Pa ) 2280 5560 7170
: T = 25°C
n( CO2 ) ( mol ) :
x ( mol ) . CaCO3( s ) + 2 H + ( aq ) = CO2( g ) + H 2O( l ) + Ca 2+ ( aq )
.1
. ( x) (n )
CO2 .2
. ( P.V = n.R.T ) .3
. 1L = 10-3 m3 R = 8,32SI . x = f (t ) .4
:
: (H )+
t (s) 20 60 100 . (n H + )
( )
.1
é H + ù ( mol.L-1 )
ë û
0,080 0,056 0,040 (n H + ) .2
( )
n H + ( mol ) . ( n0 ) ( x)
( )
x ( mol )
. ( x) .3
x = f (t ) .4
. .5
. t1/ 2 .6
. t = 50s .7
. M ( Ca ) = 40 g .mol -1 M ( C ) = 12 g .mol -1 M ( O ) = 16 g .mol -1
8

9. . :
:
CaCO3( s ) + 2 H + ( aq ) = CO2( g ) + Ca 2+ ( aq ) + H 2O(l )
. .1
( mol ) :
0 n = 2 ´10-2 n0 = 10-2 0 0 n0 = C .V = 0,1´ 0,1
x n- x n0 - 2 x x x . n0 = 10-2 mol :
xmax n - xmax n0 - 2 xmax xmax xmax :
m 2
n= =
M 100
. n = 2 ´ 10-2 mol :
t (s) 20 60 100
. nCO2 = x : .2
n( CO2 ) ( mmol ) 0,92 2,24 2,89
. .3
x ( mmol ) 0,92 2,24 2,89 VCO2
nCO2 = PCO2 : PCO2 .VCO2 = nCO2 .R.T :
R.T
1´10-3
nCO2 = 4, 03 ´10-7.PCO2 : nCO2 = .PCO2 :
8,32 ´ . ( 25 + 273)
. . x = f (t ) .4
:
. (n H + ) .1
( )
. n H + = é H + ù .V = 0,1´ é H + ù :
t (s) 20 60 100 ( ) ë û ë û
n H + ( mmol ) . ( n0 ) ( x ) (n H + )
( )
.2
( ) 8,0 5,6 4,0
. n H + = n0 - 2 x :
x ( mmol ) 1,0 2,2 3,0 ( )
. ( x) .3
1 æ -2 ö 1æ ö
. x= ç 10 - n( H + ) ÷ : x= ç n0 - n( H + ) ÷ : n H + = n0 - 2 x :
2è ø 2è ø ( )
.( ). : . . x = f (t ) .4
. .5
xmax = 5mmol : (H ) + n0 n
< :
2 1
n
1
= 2 ´10-2 mol
n0
2
= 5 ´ 10-3 mol :
. t1/ 2 .6
x ( mmol )
( ) x 5
x t 1 = max = = 2,5mmol :
2 2 2
. t 1 » 70s :
2
( ) = 2,5mmol
x t1
2
. t = 50s .7
dx 1 dx
. t = 50s vvol = :
dt V dt
dx (1,95 - 0, 45 ) ´ 10
-3
= = 3 ´ 10-5 mol.s -1 :
dt 50 - 0
1
t ( s) . vvol = 3 ´10-4 mol.L-1.s -1 : vvol = ´ 3 ´10-5 :
0,1
9

10. 2009 :
. ( H 2O2( aq) )
10L (1L ) (10V )
. Vm = 22, 4 L.mol -1
. 2 H 2O2( aq) = 2 H 2O( l ) + O2( g ) : .1
. C = 0,893mol.L-1 : -
. 100mL V1 -
·
. C1 = 0,1mol.L-1 V1 ·
(K (
+
aq )
+ MnO4-( aq ) ) 20mL (10V ) .2
. VE = 38mL C0 = 0, 02mol.L-1
(O ( ) / H O ( ) ) :
2 g 2 2 aq -
(
. MnO4 ( aq ) / Mn 2 + ( aq )
-
)
. -
. :
. C = 0,893mol.L-1 : - .1
VO2 10
. nO2 = = » 0, 4464mol : (1L )
Vm 22, 4
ni ( H 2O2 ) = 2n f ( O2 ) = 2 ´ 0, 4464 » 0,893mol :
ni ( H 2O2 ) 0,893
.C= = = 0,893mol.L-1 :
VH 2O2 1
. -
. V1 -
0,1 C1
. V1 = .100 = 11, 2mL : V1 = .V : CV1 = C1V :
0,893 C
. - .2
( )
. 2 ´ MnO4 ( aq ) + 8H + ( aq ) + 5e - ® Mn 2 + ( aq ) + 4 H 2O( l ) :
-
. 5 ´ ( H 2O2( aq ) ® O2( g ) + 2 H + ( aq ) + 2e - ) :
. 2MnO4 ( aq ) + 5H 2O2( aq ) + 6 H +( aq) ® 2Mn 2+( aq) + 5O2( g ) + 8H 2O( l ) :
-
. -
n ( MnO4- ) n ( H 2 O2 )
. xmax = = : n ( H 2O2 ) - 5 xmax = 0 n ( MnO4- ) - 2 xmax = 0 :
2 5
5 5
. n ( H 2 O2 )( t ) = C0 .VE : V0 = 20mL n ( H 2 O2 ) n ( H 2 O2 ) = n ( MnO4- )
2 2
5 C .V 5 0, 02 ´ 38
C ' = [ H 2 O2 ] = . 0 E = . = 0, 095mol.L-1 :
2 V0 2 20
10

11. C '.V 0, 095 ´ 100
C '' = = = 0,848mol.L-1 :
V1 11, 2
C '' ¹ C
2009 :
20m3 SO2 . SO2
( S0 ) V = 50mL .( SO2 ) ( S0 ) 1L
. C1 = 2, 0 ´ 10-4 mol.L-1 (K ( +
aq )
+ MnO4-( aq ) )
(
. MnO4 ( aq ) / Mn 2 + ( aq )
-
) ( SO 2-
4 ( aq ) )
/ SO2( g ) : .1
.2
. (C ) VE = 9,5mL (K ( +
aq )
+ MnO4-( aq ) ) .3
. SO2 .4
. 250m g.m -3 SO2 .5
. M ( O ) = 16 g .mol -1 M ( S ) = 32 g .mol -1 :
. :
: .1
(
. 5 ´ SO2( g ) + 2 H 2O( l ) ® SO4 -( aq ) + 4 H + ( aq ) + 2e - :
2
)
(
. 2 ´ MnO4 ( aq ) + 8H +( aq ) + 5e - ® Mn 2 + ( aq ) + 4 H 2 O( l )
-
) :
5SO2( g ) + 2 MnO4-( aq ) + 2 H 2O( l ) ® 5SO4 -( aq ) + 2Mn 2+ ( aq ) + 4 H + ( aq ) :
2
. MnO 4- ( ) .2
. (C ) .3
n0 ( SO2 ) n0 ( MnO4 )
-
C.V C1 .VE
= : = : ( )
5 2 5 2
5 C1.VE 5 2 ´10-4
. C = 10-2 mol.L-1 C= = :
2 V 2 50 ´10 -3
. SO2 .4
Cm = M .C = 64 ´ 10-2 = 0, 64 g .L-1
. .5
SO2 m = 0, 64 g SO2 1L Cm = 0, 64 g .L-1 :
m 0, 64
3, 2 ´ 104 m g .m -3 > 250 m g .m -3 : t= = 3, 2 ´ 10-2 g.m -3 :
Vair 20
.
2010 :
:
Zn( s ) + 2 H + ( aq) = Zn 2+ (aq ) + H 2( g )
V = 40mL m = 1, 0 g t =0
. VM = 25 L.mol -1 : . C = 5, 0 ´ 10-1 mol.L-1
11

12. : VH 2
t (s) 0 50 100 150 200 250 300 400 500 750
VH 2 ( mL ) 0 36 64 86 104 120 132 154 170 200
x ( mol )
. VH 2 x .1
. .2
. 1cm ® 1, 0 ´ 10-3 mol 1cm ® 100s : x = f (t ) .3
. . t2 = 400s t1 = 100 s : .4
. .5
. xmax -
M ( Zn ) = 65 g .mol -1 : . t1/ 2 -
. :
: .1
Zn( s ) + 2 H +( aq) = Zn 2+ ( aq) + H 2( g ) :
1
( mmol ) . n1 =
m
= = 1,54 ´ 10-2 mol
M 65
0 15,4 20 0 0 :
x 15, 4 - x 20 - 2x x x n0 = C.V = 0, 5 ´ 40 ´ 10-3 = 2 ´ 10 -2 mol
xf 15, 4 - x f 20 - 2 x f xf xf . VH 2 x ·
1 VH 2
. x= ´ VH 2 : nH 2 = : nH 2 = x :
25 VM
t (s) 0 50 100 150 200 250 300 400 500 750 . .2
: x = f (t ) .3
x ( mmol ) 0 1,44 2,56 3,44 4,16 4,80 5,28 6,16 6,80 8,00
.
. t2 t1 : .4
dx 1 dx
t2 t1 vvol = . :
dt V dt
t1 = 100 s :
vvol =
1 ( 2,56 - 0, 7 ) ´10-3 :
40 ´ 10-3 100 - 0
. vvol = 4, 6 ´10 -4 mol.L-1 .s -1
t1 = 400 s
vvol =
1 ( 6,16 - 3, 0 ) ´10-3
40 ´ 10-3 400 - 0
. vvol = 2, 0 ´10 -4 mol.L-1 .s -1
.
12