ﺔﻴﺒﻌﺸﻟﺍ ﺔﻴﻁﺍﺭﻘﻤﻴﺩﻟﺍ ﺔﻴﺭﺌﺍﺯﺠﻟﺍ ﺔﻴﺭﻭﻬﻤﺠﻟﺍ
ﺩﻌﺒ ﻥﻋ ﻥﻴﻭﻜﺘﻟﺍﻭ ﻡﻴﻠﻌﺘﻠﻟ ﻲﻨﻁﻭﻟﺍ ﻥﺍﻭﻴﺩﻟﺍ ﺔﻴﻨﻁﻭﻟﺍ ﺔﻴﺒﺭﺘﻟﺍ ﺓﺭﺍﺯﻭ ﻯﻭﺘﺴﻤﻟﺍ ﻥﺎﺤﺘﻤﺍ ﺏﺍﻭﺠ ﻡﻴﻤﺼﺘ
– ﻱﺎﻤ ﺓﺭﻭﺩ 2011
ﺔﺒﻌﺸﻟﺍﻭ ﻯﻭﺘﺴﻤﻟﺍ :
ﺔﻴﺒﻴﺭﺠﺘ ﻡﻭﻠﻋ ﻱﻭﻨﺎﺜ 3 ﺓﺩﺎﻤﻟﺍ
: ﺔﻴﺌﺎﻴﺯﻴﻓ ﻡﻭﻠﻋ
لﻭﻷﺍ ﻥﻴﺭﻤﺘﻟﺍ :
) ﻁﺎﻘﻨ 8 (
. 1 ﺕﻻﺩﺎﻌﻤﻟﺍ :
ﺓﺩﺴﻜﻷﺍ ﺔﻟﺩﺎﻌﻤ
− :
+ +
=Zn 2e
Zn 2 (aq) )
S
... (
...
0.5
ﺔﻟﺩﺎﻌﻤ ﻹﺍ ﻉﺎﺠﺭ
) :
g 2( )
aq
( 2e H
H
2 + + − =
...
...
0.5
ﺓﺩﺴﻜﻷﺍ ﺔﻟﺩﺎﻌﻤ –
ﻉﺎﺠﺭﺍ :
) aq 2 ( )
g 2( ) aq ) (
S
( 2H H Zn
Zn + + = + +
...
0.5
. 2 ﺕﻻﻭﻤﻟﺍ ﺩﺩﻋ ﺏﺎﺴﺤ :
ﻥﻴﺠﻭﺭﺩﻴﻬﻟﺍ ﺩﺭﺍﻭﺸ ﺕﻻﻭﻤ ﺩﺩﻋ :
mol 02 , 0 04 , 0 5 , 0 CV
n1 = = × =
...
0.5
ﻙﻨﺯﻟﺍ ﻥﺩﻌﻤ ﺕﻻﻭﻤ ﺩﺩﻋ :
mol 015 , 65 0
1 M
n2 = m = = ...
0.5
. 3 لﻋﺎﻔﺘﻟﺍ ﻡﺩﻘﺘ لﻭﺩﺠ :
...
...
1
لﻋﺎﻔﺘﻟﺍ ﺔﻟﺩﺎﻌﻤ 2H+(aq) +Zn(s) =H2(g) +Zn2+(aq) ﺔﻅﺤﻠﻟﺍ
ﻡﺩﻘﺘﻟﺍ ( mol ) ﺓﺩﺎﻤﻟﺍ ﺕﺎﻴﻤﻜ ﺔﻴﺌﺍﺩﺘﺒﻻﺍ
x = 0 n1 n2 0 0
ﺔﻴﺌﺎﻬﻨﻟﺍ
x = xmax n1 – 2xmax n2 – xmax xmax xmax
ﺩﺠﻨ لﻭﺩﺠﻟﺍ ﻥﻤ :
mol 01 , 2 0
02 , 0 2
xmax = n1 = = ﻭ
mol 015 , 0 n xmax = 2 = ...
+ 0.25 0.25
ﻭﻫ ﺩﺤﻤﻟﺍ لﻋﺎﻔﺘﻤﻟﺍ ﻥﺃ ﺩﺠﻨ ﻪﻨﻤ ﻭ H+
ﻭ xmax = 0,01 mol .
...
+ 0.25 0.25
. 4 ﺔﻴﺌﺎﻬﻨﻟﺍ ﻪﺘﻤﻴﻗ ﻑﺼﻨ ﻰﻟﺇ لﻋﺎﻔﺘﻟﺍ ﺎﻬﻴﻓ لﺼﻴ ﻲﺘﻟﺍ ﺔﻅﺤﻠﻟﺍ ﻲﻫ لﻋﺎﻔﺘﻟﺍ ﻑﺼﻨ ﻥﻤﺯ .
...
...
0.5
. 5 ﺔﻗﻼﻌﻟﺍ ﻥﺎﻴﺒﺘ
( )
:2
n n1
H+ t1/2 =
ﺎﻨﻴﺩﻟ ﻡﺩﻘﺘﻟﺍ لﻭﺩﺠ ﻥﻤ :
x 2 n nH+ = 1 − ...
0.25
ﺔﻅﺤﻠﻟﺍ ﻲﻓ t = t ½
ﻥﻭﻜﻴ
( ) ( )
1/22 /
1 1 t
H t n 2 x
n + = − ⋅
ﺩﺠﻨ لﻋﺎﻔﺘﻟﺍ ﻑﺼﻨ ﻥﻤﺯ ﻑﻴﺭﻌﺘ ﺏﺴﺤ
( )
:4 n 2 2 n 2
x x 1
1 t1/2 = max = =
ﺔﻟﺩﺎﻌﻤﻟﺍ ﻲﻓ ﺽﻭﻌﻨ
( ) ( )
1/22 /
1 1 t
H t n 2 x
n + = − ⋅
...
0.25
ﺩﺠﻨﻓ
( )
:2 n 2 n n 4 2 n n
n 1 1 1 1 1
H+ t1/2 = − ⋅ = − = ...
0.25
ﺏﻭﻠﻁﻤﻟﺍ ﻭﻫ ﻭ .
ﺩﺠﻨ ﻥﺎﻴﺒﻟﺍ ﻥﻤ :
t ½ = 270 s )
ﻲﻟﺍﻭﻤﻟﺍ ﻡﺴﺭﻟﺍ ﺭﻅﻨﺃ (
...
0.25
. 6 ﺎﻨﻴﺩﻟ لﻋﺎﻔﺘﻟﺍ ﻡﺩﻘﺘ لﻭﺩﺠ ﻥﻤ :
x 2 n nH+ = 1 − ...
0.25
ﺩﺠﻨ ﻪﻨﻤ ﻭ 2 :
n x n1 − H+ =
ﺩﺠﻨﻓ ﺔﻟﺩﺎﻌﻤﻟﺍ ﻩﺫﻫ ﺎﻓﺭﻁ ﻕﺘﺸﻨ dt :
dn 2 1 dt
v = dx =− H+ ...
0.25
ﺍ ﻭﻫ ﻭ ﺏﻭﻠﻁﻤﻟ .
ﺕﻗﻭﻟﺍ ﺭﻭﺭﻤ ﻊﻤ ﺔﻋﺭﺴﻟﺍ ﻩﺫﻫ ﺹﻗﺎﻨﺘﺘ .
...
0.25
ﻡﺜ ﺔﻔﻠﺘﺨﻤ ﺔﻴﻨﻤﺯ ﺕﺎﻅﺤﻟ ﺩﻨﻋ ﻰﻨﺤﻨﻤﻠﻟ ﺕﺎﺴﺎﻤﻤﻟﺍ ﻥﻤ ﺔﻋﻭﻤﺠﻤ ﻡﺴﺭﻨ ،ﺍﺫﻫ ﺭﻴﺭﺒﺘﻟ ﺞﺘﻨﺘﺴﻨ ﻡﺜ ﺱﺎﻤﻤ لﻜ لﻴﻤ ﺏﺴﺤﻨ
ﺕﻗﻭﻟﺍ ﺭﻭﺭﻤ ﻊﻤ ﺹﻗﺎﻨﺘﺘ ﺔﻋﺭﺴﻟﺍ ﻩﺫﻫ ﻥﺃ ﻅﺤﻼﻨﻓ ﺔﻅﺤﻟ لﻜ ﻲﻓ ﺔﻴﻅﺤﻠﻟﺍ ﺔﻋﺭﺴﻟﺍ ﺔﻤﻴﻗ ﻙﻟﺫ ﺩﻌﺒ .
...
0.25
. 7 ﺏﺴﺤﻨ ﻥﺎﻴﺒﻟﺍ ﻥﻤ ﺩﺠﻨﻓ ﺱﺎﻤﻤﻟﺍ لﻴﻤ
: )
mol 10 ( nH+ −3
) s (
s
t
270 t1/2 =
1
5 t
H 2.10 mol.s
dt dn
2 / 1
−
− −
⎟⎟ =
⎠
⎜⎜ ⎞
⎝
⎛ +
...
0.5
ﺔﻴﻅﺤﻠﻟﺍ ﺔﻋﺭﺴﻟﺍ ﺔﻤﻴﻗ ﺞﺘﻨﺘﺴﻨ ﻪﻨﻤ ﻭ :
1
5 H ( 2.10 5) 1.10 mol.s
2 1 dt
dn 2 1 dt
v=dx =− + =− − − = − −
...
0.5
ﻲﻨﺎﺜﻟﺍ ﻥﻴﺭﻤﺘﻟﺍ )
ﻁﺎﻘﻨ 6 (
. 1 ﻑﻴﺭﻌﺘﻟﺍ :
ﻟ ﻥﻴﺭﻴﻅﻨ ﻲﻨﺤﺸﻟﺍ ﺩﺩﻌﻟﺍ ﺱﻔﻨ ﺎﻤﻬﻟ ﺭﺼﻨﻌﻟﺍ ﺱﻔﻨ
ﻲﻠﺘﻜﻟﺍ ﺩﺩﻌﻟﺍ ﻲﻓ ﻥﺎﻔﻠﺘﺨﻴ ﻭ Z . A
...
0.5
. 2 ﻲﻋﺎﻌﺸﻹﺍ ﻁﺎﺸﻨﻟﺍ ﺔﻟﺩﺎﻌﻤ :
e S
P
1632 101532
→ +
− ...0.5
.3 ﺃ . ﺎﻨﻴﺩﻟ :
⎪⎩
⎪⎨
⎧
⋅ λ
=
−∆
= N P
N P N
...
0.5
ﺎﻤﻟ t 0 ﺩﺠﻨ ∆ →
: 0 dt N
dN+λ =
ﺏ . ﺔﻟﺍﺩﻟﺍ ﻕﺘﺸﻨ ﺩﺠﻨﻓ N(t)
τ :
⋅ −
−τ
=
t
0 e
1N dt
... dN 0.25
ﺔﻟﺍﺩﻟﺍ ﻥﻤ لﻜ ﺔﻴﻠﻀﺎﻔﺘﻟﺍ ﺔﻟﺩﺎﻌﻤﻟﺍ ﻲﻓ ﺽﻭﻌﻨ ﺎﻬﻘﺘﺸﻤ ﻭ N(t)
dt ﺏﺘﻜﻨﻓ dN :
0 e
N e
1N t
0 t
0 ⋅ +λ⋅ ⋅ =
− τ −τ −τ
ﻪﻨﻤ ﻭ : 1 0
e N
t
0 ⎟=
⎠
⎜ ⎞
⎝
⎛
− τ λ
⋅ −τ ...
0.25
) mol 10 ( nH+ −3
) s ( t
لﺠﺃ ﻥﻤ ﺔﻗﻼﻌﻟﺍ ﻩﺫﻫ ﻕﻘﺤﺘﺘ τ :
= λ 1 ...
0.5
. ـﺟ ﺽﻭﻌﻨ t = τ
ﺔﻟﺍﺩﻟﺍ ﻲﻓ : N(t)
τ
−τ
⋅
= N e )
t (
N 0
ﺩﺠﻨ ﻪﻨﻤ ﻭ :
37 , N 0
N
0 t
⎟⎟ =
⎠
⎜⎜ ⎞
⎝
⎛
τ
=
...
0.5
ﺩﺠﻨ ﻥﺎﻴﺒﻟﺍ ﻥﻤ :
τ = 43 ans ...
0.5
ﺩ . ﻲﻋﺎﻌﺸﻹﺍ ﻁﺎﺸﻨﻟﺍ ﺕﺒﺎﺜ 1 :
ans 023 , 43 0
1
1 −
= τ =
= ... λ 0.5
. ـه ﺔﻌﺸﻤﻟﺍ ﺔﻴﻭﻨﻷﺍ ﻥﻤ ﺔﻴﻠﺼﻷﺍ ﺔﻴﻤﻜﻟﺍ ﻑﺼﻨ ﻙﻜﻔﺘﺘ ﻲﻜﻟ ﺔﻤﺯﻼﻟﺍ ﺔﻴﻨﻤﺯﻟﺍ ﺓﺩﻤﻟﺍ ﻲﻫ ﺭﻤﻌﻟﺍ ﻑﺼﻨ ﻥﻤﺯ .
...
0.5
ﺎﻨﻴﺩﻟ
τ :
⋅ −
=
t 0 e N ) t ( N
ﺏﺘﻜﻨ ﻪﻨﻤ ﻭ τ :
= − t 0
N e ) t ( ...N 0.25
ﻲﻓ ﺔﻅﺤﻠﻟﺍ t = t ½
ﺎﻨﻴﺩﻟ ﻥﻭﻜﻴ 2 :
) N t (
N 1/2 = 0
ﻪﻨﻤ ﻭ τ :
= −
2 /
t1
2 e 1 ...
0.25
ﺩﺠﻨﻓ ﻥﺎﻓﺭﻁﻟﺍ ﻰﻠﻋ ﻡﺘﻴﺭﺎﻏﻭﻠﻟﺍ ﻕﺒﻁﻨ :
t ½ = τ.ln2 ...
0.5
ﻲﻁﻌﻴ ﻱﺩﺩﻌﻟﺍ ﻕﻴﺒﻁﺘﻟﺍ :
t ½ = 30 ans .
...
0.5
ﺙﻟﺎﺜﻟﺍ ﻥﻴﺭﻤﺘﻟﺍ )
ﻁﺎﻘﻨ 6 ( N0
N
) ans ( t cm
4 , 15
cm 8 , 6
ans 1 0 ,
43 −
cm 65 , 2
cm 52 , 2
. 2 لﻘﺜﻟﺍ ﺔﻤﻴﻗ ﺏﺎﺴﺤ :
N 10 81 , 9 10 . 012 , 1 g m
P= ⋅ = −4× = −3
...
0.5
ﺱﺩﻴﻤﺨﺭﺃ ﺔﻌﻓﺍﺩ ﺔﻤﻴﻗ ﺏﺎﺴﺤ :
N 10 . 4 , 1 81 , 9 10 10
. 1 , 1 10 . 3 , 1 g V g
m0 ⋅ =ρa ⋅ ⋅ = −3× −7 × 3× = −6
= ... Π 0.25
ﺔﻨﺭﺎﻘﻤﻟﺍ :
10 700 . 4 , 1
10 . 1 P
6 3 ≈
Π = −
... −
0.25
ﻥﺃ ﻅﺤﻼﻨ Π
⋅
≈700 P
ﻡﺴﺠﻟﺍ لﻘﺜ ﻡﺎﻤﺃ ﺔﻠﻤﻬﻤ ﺱﺩﻴﻤﺨﺭﺃ ﺔﻌﻓﺍﺩ ﻥﺃ ﺞﺘﻨﺘﺴﻨ ﻪﻨﻤ ﻭ .
...
0.25
. 3 ﺃ . ﺨﻟﺍ ﻯﻭﻘﻟﺍ لﻴﺜﻤﺘ ﺔﻴﺠﺭﺎ
: ...
...
1
. ﺏ
ﻲﻠﻴﻟﺎﻏ ﺎﻌﺠﺭﻤ ﺭﺒﺘﻌﻴ ﻊﺠﺭﻤﻟﺍ ﺍﺫﻫ ﻥﻷ ﻲﻀﺭﻷﺍ ﻲﺤﻁﺴﻟﺍ ﻊﺠﺭﻤﻟﺍ ﻲﻓ ﺔﻜﺭﺤﻟﺍ ﺱﺭﺩﺘ .
...
0.25
. ـﺟ ﺔﻴﻠﻀﺎﻔﺘﻟﺍ ﺔﻟﺩﺎﻌﻤﻟﺍ ﻥﺎﻴﺒﺘ :
ﺎﻨﻴﺩﻟ
→ :
→= ⋅
∑
F m a...
...
0.25
ﻲﻟﺎﺘﻟﺎﺒ ﻭ
→ :
→
→P+ F = m⋅ a ...
0.25
ﺭﻭﺤﻤﻟﺍ ﻰﻠﻋ ﻁﺎﻘﺴﻹﺎﺒ ﺩﺠﻨ z’z
dt : mdv v
K
mg− ⋅ 2 = ...
0.25
ﻰﻟﺇ لﺼﻨ ﻪﻨﻤ ﻭ
2 : m v g K dt
dv = − ⋅
ﺩ . ﺩﺠﻨ ﻥﺎﻴﺒﻟﺍ ﻥﻤ
1 : s . m 12 vA = − ...
0.25
→O k
' z
z
→P
→F
ﻥﻭﻜﻴ ﺔﻴﺩﺤﻟﺍ ﺎﻬﺘﻤﻴﻗ ﻰﻟﺇ ﺔﻋﺭﺴﻟﺍ لﺼﺘ ﺎﻤﻟ :
dt 0 dv = ...
0.25
ﺔﻴﻠﻀﺎﻔﺘﻟﺍ ﺔﻟﺩﺎﻌﻤﻟﺍ ﺢﺒﺼﺘ ﻪﻨﻤ ﻭ :
0 m v
g− K ⋅ A2 =
ﺩﺠﻨ ﻪﻨﻤ ﻭ :
2 v
g K m
A
= ⋅ ...
0.5
ﻲﻁﻌﻴ ﻱﺩﺩﻌﻟﺍ ﻕﻴﺒﻁﺘﻟﺍ
1 :
6 2
3
2 6,9.10 m.s 12
10 v
g
K = m⋅ = − = − −
A
....
...
0.5
. ـه ﻉﺭﺎﺴﺘﻟﺍ ﺔﻤﻴﻗ ﺩﺠﻨ ﺔﻴﻠﻀﺎﻔﺘﻟﺍ ﺔﻟﺩﺎﻌﻤﻟﺍ ﻥﻤ a0
ﺔﻅﺤﻠﻟﺍ ﻲﻓ t = 0
:
( )
2 t 0 20
0 t v g 9,8m.s
m g K dt
a dv = −
= = − ⋅ = =
⎟⎠
⎜ ⎞
⎝
=⎛ ...
0.5
ﻭ . ﻨ ﻥﺃ ﻡﻠﻌ τ
⋅
=a0 vA ...
...
0.5
ﺩﺠﻨ ﻪﻨﻤ ﻭ
0 : a vA
= τ
ﻲﻁﻌﻴ ﻱﺩﺩﻌﻟﺍ ﻕﻴﺒﻁﺘﻟﺍ :
s 22 , 8 1 , 9 12 a
v
0
=
=
=
τ A
...
0.25
s 1
. m 12 vA= −
