אאאאאא
3 F L 2010 E 2011
אא W
/1 ﺓﺩﺎﳌﺍ ﺕﺎﻴﻤﻛ :
2
3 ):
(H O+ +Cl− n ،
1 3 :n CaCO
mol g M =40+12+3×16=100 /
mol n1 =2×10−2
،
2
1 2 10
100
2 = × −
=
= M n m
mol n2 =10−2 ،
2 2 =C⋅V =0,1×0,1=10− n
/2 ﻡﺪﻘﺘﻟﺍ ﻝﻭﺪﺟ :
ﻡﺪﻘﺘﻟﺍ
) ( 2 ) ( 2 2
) ( )
( 3 )
(
3s 2H Oaq Ca aq CO g 3H Ol
CaCO + + ⎯⎯→ + + +
ﻞﻋﺎﻔﺘﻟﺍ ﺔﻟﺩﺎﻌﻣ
0 //////
0
0 n2
n1
ﺔﻴﺋﺍﺪﺘﺑﻹﺍ ﺔﻟﺎﳊﺍ
x //////
x x
x n2 −2⋅ x n1− ﺔﻴﻄﺳﻮﻟﺍ ﺔﻟﺎﳊﺍ
xmax
//////
xmax
xmax
max
2 2 x
n − ⋅
max
1 x
n − ﺔﻴﺋﺎﻬﻨﻟﺍ ﺔﻟﺎﳊﺍ
ﻥﺃ ﺽﺮﻔﻧ CaCO3
ﺪﶈﺍ ﻮﻫ :
mol xmax =2×10−2 ⇒
max 0
1−x =
n
ﺓﺩﺎﻣ ﺔﻴﻤﻛ ﰲ ﺽﻮﻌﻧ O+
H3 :
0
10 3 10
2 2 10
2 max 2 2 2
2− ⋅x = − − × × − =− × − <
n
ﻪﻨﻣ ﻭ CaCO3
ﺍﺪﳏ ﺲﻴﻟ .
mol xmax =5×10−3 ،
2 10 2
2 2
max
= −
=n x
⇒ 0 2 max
2 − ⋅x =
n
ﻭ ﻥﻮﻜﻳ ﻞﻋﺎﻔﺘﳌﺍ ﺪﶈﺍ ﻮﻫ : O+
H3
/ ﺃ3 / ﻡﺪﻘﺘﻟﺍ ﻝﻭﺪﺟ ﻦﻣ :
x nCO = ﺯﺎﻏ ﺭﺎﺒﺘﻋﺎﺑ ﻭ ، 2
CO2
ﻥﻮﻜﻳ ، ﺔﺑﺮﺠﺘﻟﺍ ﻁﻭﺮﺷ ﰲ ﺎﻴﻟﺎﺜﻣ ﺍﺯﺎﻏ :
T R
V x P CO
⋅
= ⋅ 2
⇒ T R x V
P⋅ CO = ⋅ ⋅ 2
⇒ T R n V
P⋅ CO = CO ⋅ ⋅
2
2
ﺏ / ﻲﻤﻈﻋﻷﺍ ﻢﺠﳊﺍ :
6 5
3 max
max 121 10
10 02 , 1
298 31 , 8 10
5 − −
×
× =
×
×
= ×
⋅
= ⋅ P
T R V x
⇒ P
T R V = x⋅ ⋅
mL Vmax =121
ﻥﺃ ﻆﺣﻼﻧ ﺕﺎﺳﺎﻴﻘﻟﺍ ﻝﻭﺪﺟ ﻦﻣ
: mL Vf =121
ﺎﻨﻳﺪﻟ ﻭ : mL Vmax =121
ﻥﺫﺇ : Vf
Vmax = ﻪﻨﻣ ﻭ ؛ ﻞﻋﺎﻔﺘﻟﺍ
ﻡﺎــﺗ
/ﺃ4 / ﺔﻴﻤﺠﳊﺍ ﺔﻋﺮﺴﻟﺍ :
dt dx v=V1 ⋅
dt ﲎﺤﻨﻤﻠﻟ ﺱﺎﻤﳌﺍ ﻞﻴﻣ ﻞﺜﳝ dx )
(t ﺔﻴﻤﺠﳊﺍ ﺔﻋﺮﺴﻟﺎﻓ ﻪﻴﻠﻋ ﻭ ، ﺺﻗﺎﻨﺘﻳ ﻞﻴﳌﺍ ﺍﺬﻫ ﻥﺃ ﺎﻴﻧﺎﻴﺑ ﻆﺣﻼﻧ ﻭ ، x
ﺑ ﺔﺼﻗﺎﻨﺘﻣ ﻦﻣﺰﻟﺍ ﺔﻟﻻﺪ .
ﺏ / ﻞﻋﺎﻔﺘﻟﺍ ﻒﺼﻧ ﻦﻣﺯ :
ﺪﳒ ﻥﺎﻴﺒﻟﺍ ﻦﻣ :
50 1 , 1
12 = ×
: t 2 xmax
x=
ﻪﻨﻣ ﻭ : s t 55
12 =
3mol 10−
s 50
) (s t )
(mol x
2 xmax
xmax
12
t
2 1
אא W
–I ﻥﻮﺑﺮﻜﻟﺍ ﺔﺳﺍﺭﺩ : 14
/1 ﻱﻭﻮﻨﻟﺍ ﻞﻋﺎﻔﺘﻟﺍ ﺔﻟﺩﺎﻌﻣ :
X C N
n+147 ⎯⎯→146 +ZA
1
0
⎩
⎨⎧
=
= 1 1 Z A ⇒
⎩
⎨⎧
+
= +
+
= +
Z A 6 7 0
14 14 1
ﻱﻭﻮﻨﻟﺍ ﻞﻋﺎﻔﺘﻟﺍ ﺔﻟﺩﺎﻌﻣ ﻥﻮﻜﺗ ؛ ﻪﻨﻣ ﻭ :
H C N
n 147 146 11
1
0 + ⎯⎯→ +
ﻢﻴﺴﳉﺍ ﻭ ﻥﻮــﺗﻭﺮﺑ ﻮﻫ ﺮﺧﻵﺍ .
/2 ﻚﻜﻔﺘﻟﺍ ﺔﻟﺩﺎﻌﻣ
β
−: e
X C ZA 01
14
6 ⎯⎯→ +−
⎩⎨
⎧
=
= 7 14 Z A ⇒
⎩⎨
⎧
−
= +
= 1 6
0 14
Z A
ﻱﻭﻮﻨﻟﺍ ﻚﻜﻔﺘﻟﺍ ﺔﻟﺩﺎﻌﻣ ﻥﻮﻜﺗ ؛ ﻪﻨﻣ ﻭ :
e N C 147 01
14
6 ⎯⎯→ +−
/3 ﻲﻋﺎﻌﺷﻹﺍ ﻁﺎﺸﻨﻟﺍ ﺖﺑﺎﺛ :
12
12
10 92 , 3600 3 24
25 , 365 5570
69 , 0 2
ln −
×
× =
×
= ×
= t
λ
1
10 12
92 ,
3 × − −
= s
λ
ﻭﺃ :
4
12
10 238 , 5570 1
69 , 0 2
ln −
×
=
=
= t ﻪﻨﻣ ﻭ ،
λ
:1
10 4
238 ,
1 × − −
= an
λ
/ﺃ4 /
: 0
0 N N
t = =
: 1 20
12 1
N N t
t = =
4 : 2
2 2 1 0
12 2
N N N
t
t = ⋅ = =
8 : 2
3 3 2 0
12 3
N N N
t
t = ⋅ = =
16 : 2
4 4 3 0
12 4
N N N
t
t = ⋅ = =
32
: 2
5 5 4 0
12 5
N N N
t
t = ⋅ = =
ﺏ / ﻥﺎﻴﺒﻟﺍ ﻢﺳﺭ :
ﺟ / ﻥﺎﻴﺒﻟﺍ ﺔﻟﺩﺎﻌﻣ :
e t
N N = 0⋅ −λ⋅
–II ﺦـﻳﺭﺄـﺘﻟﺍ :
/ﺃ1 / ﺔﻴﻠﺿﺎﻔﺘﻟﺍ ﺔﻟﺩﺎﻌﳌﺍ :
=0
⋅ + N dt
dN
λ
⇒ dt N
dN = ⋅
−
λ
⇒
⎪⎩
⎪⎨
⎧
⋅
=
−
= N A dt A dN
λ
ﺏ / ﺔﻟﺩﺎﻌﳌﺍ ﻞﺣ ﻦﻣ ﻖﻘﺤﺘﻟﺍ :
=0
⋅ + N dt
dN
λ
⇒ dt N
dN =−
λ
⋅⇒ e t
dt N
dN =−
λ
⋅ 0⋅ −λ⋅⇒ e t
N N = 0⋅ −λ⋅
/ﺃ2 / ﲔﺘﺜﳉﺍ ﺮﻤﻋ :
e t
N
N =ln −λ⋅ ln
0
⇒ e t
N
N − ⋅
= λ
0
⇒ e t
N N = 0⋅ −λ⋅
N N0
t
12
t
4 3
0
1 ln N t = − ⋅ N
λ
⇒
0
ln N t = N
⋅
−
λ
⇒ﺔﺜﳉ ﺔﺒﺴﻨﻟﺎﺑ
"
ﻢﻴﻠﺳ : "
500 9399 , 0 10 ln
238 , 1
1
1 4 × =
×
= − −
t
ans
t1 =500
ﺔﺜﳉ ﺔﺒﺴﻨﻟﺎﺑ
"
ﺩﻮﻌﺴﻣ : "
800 9057 , 0 10 ln
238 , 1
1
2 4× =
×
= − −
t
ans
t2 =800
ﺏ / ﻋ ﲔﺑ ﻕﺮﻔﻟﺍ ﻥﺃ ﻆﺣﻼﻧ ﻮﻫ ﲔﺘﺜﳉﺍ ﻱﺮﻤ
ﺕﻮﻣ ﲔﺑ ﻥﺃ ﻱﺃ ، ﺔﻨﺳ 300
"
ﻢﻴﻠﺳ "
ﺕﻮﻣ ﻭ
"
ﺩﻮﻌﺴﻣ "
ﺔﻨﺳ 300 .
ﻥﻮﻜﻳ ﻥﺃ ﻦﻜﳝ ﻻ ﱄﺎﺘﻟﺎﺑ ﻭ
"
ﺩﻮﻌﺴﻣ "
ﻞﺘﻗ ﺪﻗ
"
ﻢﻴﻠﺳ "
ﺓﺮﺘﻔﻟﺍ ﺲﻔﻧ ﰲ ﺎﺸﻴﻌﻳ ﱂ ﺎﻤﻷ .
אא W
/1 ﲏﻣﺰﻟﺍ ﺖﺑﺎﺜﻟﺍ :
6
3 150 10
10 × × −
=
⋅
=R C τ
s
15 ,
=0
τ
/2 ﺔﻔﺜﻜﳌﺍ ﺔﻨﺤﺷ :
03 , 0 200 10
150× 6× =
=
⋅
=
⋅
=C U C E −
q C
C
q =0,03
/3 ﺔﻧﺰﺨﳌﺍ ﺔﻗﺎﻄﻟﺍ :
3 200 03 , 2 0 1 2
1 2
1⋅ ⋅ = ⋅ ⋅ = × × =
= q U q E
EC C
J
EC =3
/ﺃ4 / ﺕﺎﻨﺤﺸﻟﺍ ﲔﺑ ﺔﻗﻼﻌﻟﺍ :
ﺔﻨﺤﺸﻟﺍ ﻥﺃ ﺎﲟ ﻥﺈﻓ ﲔﺘﻔﺜﻜﳌﺍ ﻰﻠﻋ ﻉﺯﻮﺘﺗ q
:
2
1 q
q q = +
ﺏ / ﲔﺑ ﺔﻗﻼﻌﻟﺍ C1
، C2
، q1
، q2
:
⎪⎪
⎩
⎪⎪⎨
⎧
=
=
2 2 2
1 1 1
C U q
C U q ⇒
⎩⎨
⎧
⋅
=
⋅
=
2 2 2
1 1 1
U C q
U C q
ﻥﺈﻓ ﻉﺮﻔﺘﻟﺍ ﻰﻠﻋ ﻥﺎﺘﻃﻮﺑﺮﻣ ﲔﺘﻔﺜﻜﳌﺍ ﻥﺃ ﺎﲟ :
2
1 U
U = ﻪﻨﻣ ﻭ ، :
2 2 1 1
C q C
q = ﻭﺃ :
2 1 2 1
C C q q =
ﲔﺘﻨﺤﺸﻟﺍ ﺏﺎﺴﺣ :
1 1 1 2
1 C q C q C
q ⋅ = ⋅ − ⋅
⇒
1 1 2
1 C (q q ) C
q ⋅ = − ⋅
⇒
⎩⎨
⎧
−
=
⋅
=
⋅
1 2
1 2 2 1
q q q
C q C
∗ q
C q
C
q C ⋅
= +
2 1
1
1
⇒
1 2
1
1 (C C ) q C
q ⋅ + = ⋅ ⇒
C q C
q C ⋅
= +
2 1
2
2
⇒ C q
C q C q q
q ⋅
− +
=
−
=
2 1
1 1
2
∗
C
q1 =0,018 ،
018 , 0 03 , 100 0 150
150
1 × =
= + q
C
q2 =0,012 ،
012 , 0 03 , 100 0 150
100
2 × =
= + q
ﺟ / ﺔﻗﺎﻄﻟﺍ ﺏﺎﺴﺣ ﺔﻔﺜﻜﻣ ﻞﻛ ﰲ ﺔﻧﺰﺨﳌﺍ
:
J EC1=1,08
08 , 10 1 150
018 , 0 2 1 2
1 2
1
6 2
1 2 1 1
1
1 =
× ×
=
⋅
=
⋅
⋅
= −
C U q
q EC
∗
J
EC2 =0,72
72 , 10 0 100
012 , 0 2 1 2
1
6 2
2 2 2
2 =
× ×
=
⋅
= −
C EC q
∗
ﺩ / ﺔﻧﺭﺎﻘﳌﺍ :
8
, 1 72 , 0 08 ,
2 1
1+ C = + =
C E
E
ﻥﺫﺇ : J E
EC1+ C2 =1,8
ﺎﻨﻳﺪﻟ ﻭ : J EC =3
ﻥﺃ ﻆﺣﻼﻧ :
C C
C E E
E 1+ 2<
ﲑﺴﻔﺘﻟﺍ : ﺔﻔﺜﻜﻣ ﻞﻛ ﻲﺳﻮﺒﻟ ﺔﻣﻭﺎﻘﻣ ﻭ ﻞﻴﺻﻮﺘﻟﺍ ﻙﻼﺳﺃ ﺔﻣﻭﺎﻘﳌ ﺔﺠﻴﺘﻧ ﻝﻮﺟ ﻞﻌﻔﺑ ﺔﻌﺋﺎﺿ ﺔﻗﺎﻃ ﻦﻋ ﺓﺭﺎﺒﻋ ﻕﺮﻔﻟﺍ .
6 5
