The document discusses the history and development of encryption techniques. It describes how early encryption methods involved transposing or substituting letters in a message to make it unreadable to those without the encryption key. Modern encryption uses more complex mathematical algorithms to encrypt messages and ensures only authorized parties can decrypt them. The document provides examples of different encryption algorithms throughout history that increased in complexity over time for keeping messages secure.

1. 
‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬
FFEE
١٦٧١٦٧

2. ‫א‬ ١٦٧ 
 
‫א‬‫א‬‫א‬‫א‬‫א‬FE 
 
،،‫א‬‫א‬،‫א‬W 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W‫א‬
‫א‬‫א‬K 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
   ‫א‬        ،‫א‬ ‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
‫א‬        ‫א‬   ،‫א‬ ‫א‬‫א‬  
 ‫א‬ ‫א‬ ‫א‬‫א‬  ‫א‬ ‫א‬ ‫א‬  ‫א‬ ‫א‬  ‫א‬ ‫א‬
‫א‬‫א‬،‫א‬‫א‬
‫א‬‫א‬،‫א‬K 
 ‫א‬ ‫א‬   ? ‫א‬ ‫א‬FE ?  ?‫א‬
 ?‫א‬ ‫א‬‫א‬ ‫א‬     ‫א‬ ‫א‬ ‫א‬ 
‫א‬K 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
،‫א‬     ،‫א‬ ‫א‬ ‫א‬‫א‬      
‫א‬‫א‬‫א‬‫א‬‫א‬K 
‫؛‬‫א‬‫א‬‫א‬‫א‬
‫א‬K 
‫א‬‫א‬‫א‬‫א‬ 
 

3. ‫א‬ ١٦٧ 
 
‫א‬‫א‬‫א‬‫א‬‫א‬FE 
 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K،
‫א‬  ‫א‬     ،  ‫א‬   ‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬
‫א‬‫א‬K‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬W‫א‬‫א‬
،‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 

4. ‫א‬ ١٦٧ 
 
‫א‬‫א‬‫א‬‫א‬‫א‬FE 
‫א‬‫א‬‫א‬‫א‬ 
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K‫א‬‫א‬W 
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬E‫א‬
K‫א‬‫א‬‫א‬K
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
 J‫א‬‫א‬‫א‬‫א‬‫א‬K
 J‫א‬‫א‬‫א‬‫א‬‫א‬K
 J‫א‬‫א‬‫א‬،‫א‬،
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
 J‫א‬‫א‬‫א‬‫א‬K
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
 J‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬K
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬K 
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
 
 
 

5. ‫א‬ ١٦٧ 
 
‫א‬‫א‬‫א‬‫א‬‫א‬FE 
‫א‬‫א‬ 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
 ‫א‬‫א‬ ‫א‬  ‫א‬ ‫א‬‫א‬‫א‬      
‫א‬K‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬KW 
١.‫א‬‫א‬W‫א‬‫א‬‫א‬K 
٢.‫א‬W‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬K
٣.‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬
K
٤.‫א‬W‫א‬‫א‬‫א‬‫א‬K‫א‬
‫א‬‫א‬K
٥.‫א‬‫א‬W‫א‬‫א‬
‫א‬K‫א‬‫א‬‫א‬K
٦. ‫א‬ ‫א‬W ‫א‬   ‫א‬   
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬
 ‫א‬  ‫א‬       K 
‫א‬‫א‬‫א‬‫א‬K 

6. ‫א‬ ١٦٧ 
 
‫א‬‫א‬‫א‬‫א‬‫א‬FE 
‫א‬ 
‫א‬‫א‬W 
‫א‬W 
‫א‬W 
‫א‬W 
‫א‬‫א‬F‫א‬‫א‬‫א‬E 
‫א‬W 
‫א‬W 
‫א‬   
‫א‬‫א‬‫א‬‫א‬‫؟‬   
‫؟‬‫א‬   
‫א‬‫؟‬   
‫א‬‫א‬‫؟‬‫א‬   
‫א‬K‫א‬‫؟‬‫א‬   
‫א‬‫א‬F‫א‬‫א‬EZ  
‫א‬W 
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.............................................................................................................................
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‫א‬‫א‬W 
‫א‬W 
‫א‬W 

8. ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬FFEE
‫א‬‫א‬‫א‬
١

10. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬FE‫א‬‫א‬‫א‬
-١-
 
‫א‬‫א‬W،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
 
‫א‬‫א‬W 
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
 
‫א‬‫א‬‫א‬W١٢ 
 
‫א‬‫א‬W‫א‬‫א‬‫א‬F١١٠KE 
 
 
 
 
 
 
 
 

11. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬FE‫א‬‫א‬‫א‬
-٢-
١K‫א‬
 J‫א‬‫א‬‫א‬ 
‫א‬‫א‬W‫א‬‫א‬KdL٣
(gm/cm3)

W 
v
m
d = 
mv‫א‬K 
 J‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬W 
١KF‫א‬pyknometerEK
٢K١٠٠K
٣K‫א‬K
٤K‫א‬FKE
‫א‬‫א‬W 
١K‫א‬‫א‬‫א‬‫א‬K 
٢K‫א‬w1K 
٣K‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬‫א‬E
‫א‬‫א‬K‫א‬‫א‬K 
٤K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
٥K‫א‬‫א‬‫א‬‫א‬K 
٦K‫א‬،w2K 
٧K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
FW‫א‬‫א‬E 
‫א‬‫א‬W 
‫א‬w3w3 = w2- w1،‫א‬V‫א‬
‫א‬W 
‫א‬Z
V
W3
L٣
 

12. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬FE‫א‬‫א‬‫א‬
-٣-
 J 
‫א‬‫א‬‫א‬W 
١KK٢K‫א‬K٣KK 
‫א‬‫א‬W 
١K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬wgK 
٢K‫א‬‫א‬W
 J‫א‬‫א‬‫א‬‫א‬v1٣
K
 J‫א‬‫א‬‫א‬‫א‬‫א‬v2٣
K
‫א‬W 
 J‫א‬‫א‬W v =v2-v1K 
‫א‬‫א‬Z
v
wg
L٣
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

13. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬FE‫א‬‫א‬‫א‬
-٤-
٢K‫א‬‫א‬‫א‬‫א‬‫א‬Viscometer
‫א‬W 
 ‫א‬‫א‬K
‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬،‫א‬‫א‬K‫א‬
‫א‬‫א‬‫א‬‫א‬K 
‫א‬W 
 ‫א‬‫א‬‫א‬‫א‬١٢
١L
‫א‬‫א‬١K 
‫א‬W
vl
fr
t
8
4
π
η ×= 
WtW‫א‬‫א‬،fW‫א‬‫א‬،l :‫א‬،rW‫א‬
‫א‬،vW‫א‬‫א‬K 
‫א‬‫א‬‫א‬‫א‬F1E‫א‬F2E
21 ,tt 
22
11
2
1
tf
tf
=∴
η
η
 
‫א‬‫א‬vl
r
8
4
π
K‫א‬W 
hdgf ××=
gW‫א‬‫א‬،dW‫א‬،hW‫א‬‫א‬K 
‫א‬‫א‬‫א‬W 
22
11
2
1
2
1
2
1
dt
dt
t
t
hdg
hdg
×
×
=×
××
××
=
η
η

22
11
2
1
dt
dt
×
×
=
η
η
∴

14. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬FE‫א‬‫א‬‫א‬
-٥-
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬K 
‫א‬‫א‬‫א‬‫א‬‫א‬W 
١K‫א‬‫א‬‫א‬‫א‬K 
٢K‫א‬‫א‬‫א‬K 
٣K‫א‬K 
‫א‬‫א‬W 
١K‫א‬‫א‬K
٢KF١٥٣
E‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
٣K‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬K
٤K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬K
٥K‫א‬‫א‬F‫א‬‫א‬‫א‬KE
٦K‫א‬‫א‬K
٧K‫א‬‫א‬‫א‬K
‫א‬‫א‬W 
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
 J‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
‫א‬W 
‫א‬‫א‬о
poiseL2η
2010.06
258.93
308.00
357.20
 
W‫א‬poiseK 

15. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬FE‫א‬‫א‬‫א‬
-٦-
٣K‫א‬‫א‬ 
‫א‬W 
 ‫א‬‫א‬
‫א‬‫א‬‫א‬،،W 
RT
M
W
nRTPV == 
W 
PW ‫א‬ 
VW ‫א‬ 
WW‫א‬
MW‫א‬‫א‬
TW‫א‬‫א‬‫א‬
RW‫א‬‫א‬ 
‫א‬‫א‬‫א‬‫א‬W 
١K٢٥٠K
٢KK
٣KK
٤K‫א‬K
٥K‫א‬‫א‬‫א‬،‫א‬،‫א‬‫א‬K
٦KK
٧KK
٨K٥٠٠K
٩K‫א‬K
‫א‬‫א‬W 
١ J‫א‬‫א‬‫א‬‫א‬W1K
٢ J‫א‬٣‫א‬‫א‬‫א‬‫א‬‫א‬K

16. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬FE‫א‬‫א‬‫א‬
-٧-
٣ J‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬‫א‬E
‫א‬‫א‬‫א‬T‫א‬‫א‬
‫א‬‫א‬‫א‬KK
٤ J‫א‬‫א‬‫א‬‫א‬‫א‬K
٥ J‫א‬‫א‬W2K
٦ J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬VK
‫א‬W 
 J‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬W 
 
( ) ( )
V1
T082.0WW
PV
RTWW
M 2212
×
×−
=
−
= 

17. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬FE‫א‬‫א‬‫א‬
-٨-
٤K‫א‬‫א‬‫א‬ 
‫א‬W 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W 
‫א‬‫א‬‫א‬‫א‬Z‫א‬‫א‬‫א‬‫א‬ 
W 
١K‫א‬‫א‬‫א‬?QW?
TWCQ ∆××= 
C‫א‬‫א‬‫א‬،W،T∆‫א‬‫א‬‫א‬K 
٢K‫א‬‫א‬‫א‬W
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
٣K‫א‬‫א‬‫א‬W
‫א‬‫א‬‫א‬١‫א‬‫א‬‫א‬K 
٤K‫א‬W
‫א‬‫א‬‫א‬١‫א‬‫א‬‫א‬‫א‬١٥°
K 
 
‫א‬‫א‬‫א‬W 
‫א‬‫א‬W 
١ J١٠٠‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬E‫א‬‫א‬T1،
‫א‬‫א‬‫א‬WK
٢ J‫א‬‫א‬‫א‬١٠٠‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬T2K

18. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬FE‫א‬‫א‬‫א‬
-٩-
‫א‬W 
‫א‬‫א‬‫א‬‫א‬‫א‬Z‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 
 
( ) ( ) ( )21212 T100100TT100TTWC −=−+−× 
 
cal/k/g
( ) ( )
( ) WTT
TT100T100100
C
12
122
×−
−−−
=∴ 
‫א‬‫א‬‫א‬‫א‬W 
‫א‬‫א‬W 
١ J‫א‬F‫א‬٢٠٠‫א‬E‫א‬‫א‬WK
٢ J‫א‬‫א‬F‫א‬‫א‬٩٠°
E‫א‬‫א‬‫א‬
‫א‬T1K
٣ J‫א‬١٠٠‫א‬‫א‬‫א‬‫א‬T2K
٤ J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬T3K
‫א‬W 
‫א‬‫א‬‫א‬‫א‬Z‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
Cal/k/g
( ) ( )
( )31pb
2323calcal
pb
TTW
TT100TTWC
C
−
−+−
= 
 
W 
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬K 
 
 
 
 

19. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬FE‫א‬‫א‬‫א‬
-١٠-
٥K‫א‬‫א‬‫א‬‫א‬ 
 
‫א‬W 
 ‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 

nF
ItA
W = 
 I‫א‬‫א‬t‫א‬A‫א‬
‫א‬‫א‬nW‫א‬‫א‬‫א‬F‫א‬‫א‬٩٦٥٠٠
LK 
‫א‬‫א‬W 
100
W
W
%I
theo
exp
×= 
 I%‫א‬‫א‬‫א‬Wexp‫א‬‫א‬
‫א‬Wtheo‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
‫א‬‫א‬‫א‬W 
١KW 
 J‫א‬
F‫א‬‫א‬KE 
 J‫א‬
‫א‬F‫א‬‫א‬KE 
٢KF1M CuSO4 + 1.5M H2SO4EF1M NiSO4 + 1.5M H2SO4KE 
٣KK
٤KFKE
٥KK
‫א‬‫א‬W 
١ J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
٢ J‫א‬‫א‬‫א‬K
٣ J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬W
I = 5, 10, 50, 100 mA/cm2

20. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬FE‫א‬‫א‬‫א‬
-١١-
٤ J‫א‬FE‫א‬‫א‬FE‫א‬
‫א‬‫א‬‫א‬K
٥ J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬FE‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬Wexp.K 
‫א‬W
 J‫א‬‫א‬‫א‬‫א‬W
    ( )
965002
54.636030I
nF
AtI
W
Cu
theo
×
×××
=
××
= 
 J‫א‬‫א‬W 
       
theo
exp
W
W
%I = 

22. ‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬FFEE
‫א‬
٢

24. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-١٢-
‫א‬‫א‬W‫א‬‫א‬K 
 
‫א‬‫א‬W 
 J‫א‬‫א‬‫א‬K 
 J‫א‬‫א‬‫א‬K 
 J‫א‬‫א‬‫א‬K 
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
 
‫א‬‫א‬‫א‬W١٦ 
 
‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
‫א‬‫א‬K 
 

25. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-١٣-
٦K‫א‬‫א‬‫א‬ 
‫א‬W 
‫א‬‫א‬W 
CH3COOC2H5 + OH-
→ CH3COO-
+ C2H5OH
 ‫א‬‫א‬،‫א‬‫א‬‫א‬
‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬FaE
‫א‬‫א‬‫א‬‫א‬W 
)xa(a
x
t
1
k
−
×= 
k‫א‬‫א‬‫א‬x‫א‬‫א‬‫א‬
‫א‬tK 
‫א‬‫א‬‫א‬W 
١K‫א‬F0.05 MKE
٢K‫א‬F0.05 MEK
٣K‫א‬F0.025 MKE
٤K‫א‬F0.025 MKE
٥K‫א‬K
‫א‬‫א‬‫א‬W 
١KK
٢K١٠K
٣K٥٠K
٤KK
‫א‬‫א‬W 
١K‫א‬٥٠‫א‬،
‫א‬٥٠NaOH،‫א‬‫א‬٢٥K
٢K‫א‬‫א‬‫א‬‫א‬
‫א‬K

26. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-١٤-
٣K‫א‬٥١٠‫א‬١٠٠
١٠HClF0.025 MEF‫א‬E
‫א‬K
٤K‫א‬HClNaOHF0.025MEK
٥K‫א‬‫א‬‫א‬F٣٠{٢٥{٢٠{١٥{١٠E
‫א‬FxEK
‫א‬W 
١K‫א‬aHCl‫א‬‫א‬‫א‬‫א‬‫א‬
x‫א‬‫א‬‫א‬HCltFa-xE‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬K
 
10 ml≡a
xa
x
−
a-xxNaOH /ml t/min 
5
10
15
20
25
30
a = 0.025 MK 
٢K‫א‬‫א‬
xa
x
−
tW
‫א‬ZaK ×K 
٣K‫א‬‫א‬‫א‬
2
1t

aK
1
t
2
1
×
=
 

27. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-١٥-
٧K‫א‬‫א‬ 
‫א‬W 
 ‫א‬‫א‬‫א‬F‫א‬E‫א‬W 
K2S2O8 + 2KI → 2K2SO4 + I2
‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬Pseduo-first order،‫א‬‫א‬‫א‬‫א‬W 
xa
a
log
t
303.2
K
−
×= 
a‫א‬‫א‬‫א‬‫א‬x‫א‬‫א‬‫א‬‫א‬‫א‬K 
‫א‬‫א‬‫א‬W 
١K‫א‬F0.2 MKE
٢K‫א‬F0.005 MEK
٣K‫א‬F0.01 MKE
٤K‫א‬K
٥KK
‫א‬‫א‬‫א‬W 
١KFKE
٢KK
٣KK
٤K١٠K
٥KK
٦K‫א‬K
٧K٥٠K
٨KK

28. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-١٦-
‫א‬‫א‬W 
١K‫א‬٥٠‫א‬F0.2 ME‫א‬٥٠
‫א‬‫א‬‫א‬‫א‬
‫א‬K
٢K٥‫א‬١٠‫א‬
‫א‬٢٠‫א‬‫א‬‫א‬K
٣K‫א‬‫א‬‫א‬‫א‬F0.01 ME‫א‬
‫א‬Vt‫א‬‫א‬xK
٤K‫א‬‫א‬‫א‬F٣٥{٣٠{٢٥{٢٠{١٥{١٠E
‫א‬VtK
٥K‫א‬‫א‬‫א‬٦٠١٥
‫א‬‫א‬،‫א‬‫א‬K
٦K‫א‬١٠‫א‬‫א‬V∞
‫א‬‫א‬‫א‬‫א‬aK
‫א‬W 
١KVtF‫א‬tE‫א‬‫א‬
xV∞F‫א‬‫א‬‫א‬‫א‬aE
‫א‬‫א‬‫א‬‫א‬‫א‬W
tVV
V
log
k
303.2
t
−
×=
∞
∞
 
٢K‫א‬W
V∞= mL
tVV
V
−∞
∞
log
tVV
V
−∞
∞V∞-VtVtt/ min 
5
10
15
20
25
30
35

29. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-١٧-
٣K‫א‬‫א‬
tVV
V
−∞
∞
logF‫א‬‫א‬E‫א‬tF‫א‬‫א‬KE
٤K‫א‬‫א‬‫א‬‫א‬‫א‬kK 
303.2kslope = 
٥K‫א‬
2
1tW 
    k693.0t
2
1 =
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

30. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-١٨-
٨K‫א‬‫א‬‫א‬ 
‫א‬W 
‫א‬‫א‬‫א‬W 
H2O2 → H2O + ½O2
‫א‬‫א‬MnO2،‫א‬
‫א‬‫א‬K 
‫א‬‫א‬‫א‬W 
١KH2O2F0.125 MKE
٢KKMnO4F0.05 MKE
٣K(1 M)H2SO4K
٤KMnO2F0.05 gKE
‫א‬‫א‬‫א‬W 
١K٢٥٠K
٢K١٠K
٣KK
٤KK
٥K٢٥٠K
٦KK
‫א‬‫א‬W 
١K‫א‬١٥٠‫א‬٢٥٠K
٢KF٠{٠٥EMnO2‫א‬‫א‬
‫א‬K
٣K٣١٠‫א‬‫א‬
١٠H2SO4‫א‬KMnO4
‫א‬K
٤K‫א‬‫א‬
‫א‬K

31. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-١٩-
٥K‫א‬‫א‬‫א‬‫א‬١٠
H2SO4 (1 M)K
‫א‬W 
١K‫א‬‫א‬‫א‬H2O2
Fa-xKE 
٢K‫א‬‫א‬F٥E‫א‬‫א‬‫א‬(a)K
٣K‫א‬W
a = ml.
( )xa
a
−
log
( )xa
a
−
(a-x)t/ min
٤K‫א‬‫א‬
( )xa
a
−
logFEtFEK 
٥K‫א‬FkE‫א‬Ft1/2EW
303.2
k
slope= 
k
693.0
t
2
1 = 

32. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٢٠-
٩K‫א‬ 
‫א‬W 
 ‫א‬‫א‬W 
CH3COCH3 + I2
H+
CH2ICOCH3 + HI
 ‫א‬‫א‬‫א‬
،‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K 
x = k t
x‫א‬‫א‬tK 
‫א‬‫א‬‫א‬W 
١KK
٢K١٠٪K
٣K١K
٤K٠{١‫א‬K
٥K٠{٥L‫א‬١٠٪‫א‬K
٦K‫א‬K
٧KK
‫א‬‫א‬‫א‬W 
١K٢٥K
٢KK
٣K٢٥٠K
٤KF‫א‬E٥٠٠K
٥KK
٦KF٢٥،٢٥٠E

33. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٢١-
‫א‬‫א‬W 
١K‫א‬‫א‬W٢٥١٠‫א‬١٩٠
‫א‬‫א‬٢٢٥K 
٢K‫א‬٢٥‫א‬‫א‬K 
٣K‫א‬‫א‬٢٥‫א‬‫א‬١٠
‫א‬‫א‬‫א‬F‫א‬E‫א‬K 
٤K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬VK 
٥K‫א‬F٤{٣EF٣٥{٣٠{٢٥{٢٠{١٥{١٠EK 
٦K‫א‬‫א‬‫א‬‫א‬FV◦EW 
٥‫א‬٤٥‫א‬‫א‬٥٠ 
‫א‬٢٥‫א‬‫א‬V◦K 
‫א‬W 
xVV◦ 
VVx −≡ ° 
‫א‬‫א‬(V◦-V)t‫א‬kK 
 V ≡ a 
/mlxVV ≡−°mlLxaV −≡t/min 
5
10
15
20
25 
30
35
 
 
 
 

34. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٢٢-
١٠K 
‫א‬W 
‫א‬‫א‬‫א‬W 
KBrO3 + 5KBr + 3H2SO4 3Br2 + 3K2SO4 +3H2O
‫א‬‫א‬‫א‬‫א‬‫א‬W 
O H O H
B rB r
B r
+ B r 2
+ 3 H B r
 
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬W 
⎟
⎠
⎞
⎜
⎝
⎛
t
1
Rate α 
‫א‬‫א‬‫א‬W 
RTEa
AeRate /−
= 
A،Ea‫א‬‫א‬‫א‬T/K،‫א‬W 
RTEa
eA
t
/1 −
′= 
C+−
RT
Ea
Z⎟
⎠
⎞
⎜
⎝
⎛
t
1
ln 
C 
‫א‬⎟
⎠
⎞
⎜
⎝
⎛
t
1
ln⎟
⎠
⎞
⎜
⎝
⎛
T
1
‫א‬
R
E a

‫א‬K 
‫א‬‫א‬‫א‬W 
١KF0.01 MKE
٢K‫א‬0.16M)E‫א‬F0.08ME
‫א‬K 

35. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٢٣-
٣K‫א‬F0.3ME 
٤K‫א‬‫א‬K
‫א‬‫א‬‫א‬W 
١K٥٠١٠KK
٢K‫א‬K
٣KK
٤KK
‫א‬‫א‬W 
١ J٥٠‫א‬‫א‬‫א‬W 
١٠H١٠‫א‬‫א‬H‫א‬‫א‬K
٢ J‫א‬‫א‬٥‫א‬K
٣ J‫א‬‫א‬‫א‬‫א‬٢٠‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
٤ J‫א‬‫א‬‫א‬‫א‬F٣٠،٥٠{٤٠KE
٥ J‫א‬‫א‬⎟
⎠
⎞
⎜
⎝
⎛
t
1
ln⎟
⎠
⎞
⎜
⎝
⎛
T
1
‫א‬‫א‬K 
 
T
1( )t
1ln
t
1t/ minKT
20 + 273
30 + 273
40 + 273
50 + 273

37. ‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬FFEE
‫א‬
٣

39. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٢٤-
‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
 
‫א‬‫א‬W 
 J‫א‬‫א‬‫א‬‫א‬K 
 J‫א‬‫א‬‫א‬‫א‬‫א‬K 
 J‫א‬‫א‬‫א‬‫א‬‫א‬K 
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
 
‫א‬‫א‬‫א‬W١٦ 
 
‫א‬‫א‬W 
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
 J‫א‬‫א‬F‫א‬‫א‬‫א‬E 

40. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٢٥-
١١K‫א‬‫א‬ 
‫א‬W 
‫א‬‫א‬F∆HE‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K‫א‬
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬،
K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬KHXBOH
W 
HX + BOH → H2O + BX + ∆H
H+
+ X-
+ B+
+ OH-
→ H2O + B+
+ X-
‫א‬‫א‬‫א‬W 
١ J٠{١‫א‬K 
٢ J٠{١‫א‬K 
٣ J٠{١‫א‬K 
٤ J٠{١‫א‬K 
‫א‬‫א‬‫א‬W 
١ J‫א‬K 
٢ JF‫א‬E٢٥٠K 
٣ J٢٥٠K 
‫א‬‫א‬W 
١ J١٠٠‫א‬١٠٠‫א‬K‫א‬‫א‬
‫א‬‫א‬FTiKE 
٢ J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬FTfKE 
٣ J‫א‬‫א‬‫א‬‫א‬‫א‬K 

41. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٢٦-
‫א‬W 
‫א‬‫א‬‫א‬Z‫א‬‫א‬‫א‬‫א‬H‫א‬‫א‬‫א‬‫א‬ 
( ) TWCWCQ solsolcalcal ∆×+×=
Ccal‫א‬‫א‬‫א‬Csol‫א‬‫א‬‫א‬F‫א‬EWcal
‫א‬Wsol‫א‬F‫א‬‫א‬E∆T‫א‬‫א‬Tf
TiK‫א‬Ti‫א‬K
 
‫א‬‫א‬W 
∆H = Q x 100 cal/mol
‫א‬ ‫א‬ TiTf Q ∆H 
HClNaOH    
CH3COOH NaOH    
HCl NH4OH    

42. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٢٧-
١٢K‫א‬‫א‬ 
 J‫א‬‫א‬‫א‬ 
‫א‬W 
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬KNO3, NH4Cl, KNO3‫א‬‫א‬‫א‬
‫א‬Na2SO4, KOH, NaOHK‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬K 
‫א‬‫א‬W 
 J‫א‬‫א‬‫א‬‫א‬W1K
 J٢٠٠‫א‬‫א‬‫א‬‫א‬‫א‬٥K
 J‫א‬٥KNO3NH4ClNa2SO4‫א‬‫א‬‫א‬‫א‬
١٠FKE
 J‫א‬‫א‬‫א‬‫א‬‫א‬W2K
‫א‬W 
 ‫א‬‫א‬‫א‬?Q?W 
( ) TWCWCQ solsolcalcal ∆×+×=
 
=1W2-W1),CsolEZWsol,T∆‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
‫א‬‫א‬‫א‬∆ΗW 
Cal/mol
( )
( )salt
salt
M
W
Q
×=∆Η
W(salt)M(salt)‫א‬‫א‬K

43. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٢٨-
 J‫א‬‫א‬‫א‬ 
‫א‬W 
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬١٠٠‫א‬
‫א‬K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
١‫א‬‫א‬K 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
Hofft‘Van 
const
T
1
R
Sln +
∆Η
−= 
S‫א‬∆Η‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬K 
‫א‬‫א‬‫א‬W 
 JW(NH4)2SO4, NH4Cl, KBr, KClK
 JK
‫א‬‫א‬‫א‬W 
١K‫א‬٢٠٢٣K
٢K‫א‬K 
٣KK 
٤KK 
٥K‫א‬K 
٦K٦٠٠K
‫א‬‫א‬W 
١K‫א‬٣٠٠‫א‬٦٠٠‫א‬K
٢K‫א‬W1٥‫א‬‫א‬‫א‬
‫א‬W2‫א‬‫א‬FW= W2- W1KE

44. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٢٩-
٣K‫א‬‫א‬٣‫א‬‫א‬،‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬١
‫א‬‫א‬‫א‬‫א‬‫א‬K
٤K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬TK
٥K‫א‬F٤E‫א‬‫א‬TK
٦K‫א‬١‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬F٤EF٥E‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K
٧K١‫א‬‫א‬‫א‬٥
‫א‬K‫א‬‫א‬‫א‬‫א‬
٢‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
KW 
saltMV
W
S
×
×
=
1000
٨K‫א‬‫א‬‫א‬W 
T
1ln SS , mol kg-1
T/KV/ml
ln S
T
1
‫א‬‫א‬‫א‬‫א‬‫א‬ 
 Cal/mol‫א‬×-2Z‫א‬×−=∆ RH 
GveH +=∆‫א‬‫א‬K 
GveH −=∆‫א‬‫א‬‫א‬K 

45. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٣٠-
١٣K‫א‬‫א‬‫א‬‫א‬ 
‫א‬W 
 ‫א‬‫א‬K
‫א‬‫א‬Salting out‫א‬‫א‬‫א‬F(So‫א‬
‫א‬(S)‫א‬CW 
KC
S
S
=⎟
⎠
⎞
⎜
⎝
⎛ ο
log 
K‫א‬،‫א‬‫א‬⎟
⎠
⎞
⎜
⎝
⎛
S
Sο
‫א‬‫א‬‫א‬‫א‬
‫א‬،⎟
⎠
⎞
⎜
⎝
⎛
S
Sο
ZfKf‫א‬‫א‬Activity coefficient
f‫א‬W 
⎟
⎠
⎞
⎜
⎝
⎛
=
S
S
KC ο
logZlog f 
⎟
⎠
⎞
⎜
⎝
⎛
S
Sο
log،C‫א‬‫א‬K
‫א‬‫א‬fC 
‫א‬‫א‬‫א‬W 
١K‫א‬(0.03N)K
٢K‫א‬K 
٣K‫א‬FKE 
٤K‫א‬ 
‫א‬‫א‬‫א‬W
١K٢٥٠K
٢KK
٣KK
٤K١٠K
‫א‬‫א‬W 
١ J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬F٥٠WE
[BaCl2.2H2O]= ( 0.1, 0.3, 0.5, 1.0) M   

46. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٣١-
٢ J‫א‬F‫א‬١{٥E
‫א‬٦٠‫א‬‫א‬٣٥K
٣ J‫א‬F‫א‬E‫א‬‫א‬١٠‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬،‫א‬
‫א‬‫א‬،‫א‬‫א‬K
 J‫א‬W
f
S
S ο
log
S
S οSS°CVNaOH‫א‬
 
‫א‬W 
( )
10
V03.0
SorS NaOH×
=ο 

S
S ο
logCK‫א‬،Kf
W
( )KC
f 10= 

47. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٣٢-
١٤K‫א‬‫א‬‫א‬ 
F‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬E 
‫א‬W 
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬Freundlich‫א‬‫א‬W 
n
KCX
1
= 
X‫א‬‫א‬‫א‬‫א‬،C‫א‬‫א‬‫א‬‫א‬K,n
K 
‫א‬‫א‬‫א‬W 
١ J‫א‬1.0 M)E
٢ J‫א‬F0.1MKE 
٣ J‫א‬K 
٤ J‫א‬K 
٥ JK 
‫א‬‫א‬‫א‬W 
١K٢٥٠K 
٢K‫א‬K
٣KK 
٤KK
٥KK
٦KK
٧KK
‫א‬‫א‬W 
١ J‫א‬‫א‬١٠٠‫א‬‫א‬
‫א‬‫א‬W
Mb =( 0.5, 0.4, 0.3, 0.2, 0.1) M oxalic acid 

48. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٣٣-
٢ J١{٠٠‫א‬‫א‬‫א‬‫א‬
K 
٣ J‫א‬‫א‬‫א‬‫א‬F٣E
K
٤ JFE‫א‬١٠‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬FMaKE
 J‫א‬W
log Xlog CC/ g L-1
X/gMa / mol
L-1

Mb/mol L-1
V/mL NaOHBottle
 
 
( )
210
NV
2NM NaOH
aa
×
== 
  
( )
10
126MM
X ab ×−
= 
   126MC a ×= 
log Clog X‫א‬K,nW 
 
 
 

49. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٣٤-
١٥K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 
‫א‬W 
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
Langmiur isotherm‫א‬W 
KC
KC
+
=
1
θ 
θ‫א‬‫א‬‫א‬‫א‬،C‫א‬‫א‬‫א‬F‫א‬‫א‬E،K
‫א‬‫א‬‫א‬‫א‬K 
‫א‬θ‫א‬W 
mN
N
=θ 
N‫א‬‫א‬‫א‬‫א‬‫א‬Nm‫א‬‫א‬‫א‬
=1θ،W 
KC
KC
N
N
m +
=
1
 
‫א‬‫א‬‫א‬‫א‬W 
mm N
C
KNN
C
+=
1
 
‫א‬‫א‬K ,NmK 
‫א‬‫א‬‫א‬W 
١KF0.5MKE
٢K‫א‬F0.1MKE
٣K‫א‬K
٤K‫א‬K
‫א‬‫א‬‫א‬W
١K٢٥٠K
٢KK
٣KK
٤KK

50. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٣٥-
٥KK
٦K١٠K
‫א‬‫א‬W 
١ J‫א‬‫א‬١٠٠‫א‬‫א‬
‫א‬‫א‬WMb =( 0.2, 0.15, 0.12, 0.09, 0.06) M CH3COOH 
 J١{٠٠‫א‬‫א‬‫א‬‫א‬
K
٢ J‫א‬‫א‬‫א‬‫א‬F٣E
K
٣ JFE‫א‬٢٥‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬FMaKE
٤ J‫א‬W 
NC
⎟
⎠
⎞
⎜
⎝
⎛ −
=
10
ab MM
NaMC =bM‫א‬
NCC،‫א‬Z
mN
1
‫א‬Z
mKN
1

‫א‬‫א‬W‫اﻟﻘﺎﻃﻊ‬
‫اﻟﻤﻴﻞ‬
K= 
K∆GºW∆Gº= -RT ln K 
Nm‫א‬‫א‬‫א‬FSE‫א‬W 
COOHCHm aNS 3
23
1002.6 ×××= 
COOHCHa 3
‫א‬

51. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٣٦-
١٦K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 
‫א‬W 
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬KW 
C
k
c
1000×
=Λ=Λ ∞ 
Λc‫א‬‫א‬‫א‬CF‫א‬EΛ∞‫א‬
‫א‬‫א‬‫א‬‫א‬
 
−
∞
+
∞∞ λ+λ=Λ 
k‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬
E 
     ..wtEqCS ×= 
‫א‬‫א‬‫א‬K 
‫א‬‫א‬‫א‬W 
١K‫א‬(0.01 M KCl = 0.0014 S cm-1
)K
٢K‫א‬‫א‬WPbSO4, AgCl, BaSO4K
٣KK
‫א‬‫א‬‫א‬W 
١K‫א‬K
٢KK
٣KK

52. ‫א‬١٦٧‫א‬‫א‬
‫א‬‫א‬‫א‬FE‫א‬
-٣٧-
‫א‬‫א‬W 
١ J‫א‬‫א‬‫א‬‫א‬٠{٠١
‫א‬‫א‬٠{٠٠١٤١٣ J١
 J١
٢٥K
٢ J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
kwaterK
٣ J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K
٤ J‫א‬‫א‬‫א‬‫א‬٢٥k saltK‫א‬
‫א‬‫א‬W
k = k salt – k water 
‫א‬‫א‬‫א‬‫א‬‫א‬W 
−
∞
+
∞ λ+λ
×
=
1000k
C 
‫א‬W
wt.EqCS ×= 
‫א‬‫א‬W 
    ( )2
sp
wt.MSK = 
‫א‬‫א‬MXWBaSO4, AgCl, PbSO4 
‫א‬‫א‬‫א‬‫א‬‫א‬٢٥ 
 
Cl1-
= 76.35 cm2
Ω-1
equ.Ag+
= 61.90 cm2
Ω-1
equ.
SO4
2-
= 80.02 cm2
Ω-1
equ. ½Ba2+
= 63.63 cm2
Ω-1
equ. ½
Pb2+
= 73.01 cm2
Ω-1
equ. ½
Ca2+
= 59.50 cm2
Ω-1
equ. ½

54. 
‫א‬‫א‬‫א‬‫א‬FFEE

٤

56. ‫א‬١٦٧‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬FE
-٣٨-
‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
 
‫א‬‫א‬W 
 J‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K 
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
K 
 J‫א‬‫א‬‫א‬‫א‬‫א‬K 
 
‫א‬‫א‬‫א‬W١٢ 
 
‫א‬‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
 

57. ‫א‬١٦٧‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬FE
-٣٩-
١٧K‫א‬‫א‬‫א‬ 
F‫א‬‫א‬‫א‬E 
‫א‬W 
 ‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬W 
١K‫א‬‫א‬K
٢K‫א‬‫א‬K
٣K‫א‬‫א‬K
٤K‫א‬‫א‬K
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
Dissociation or Association
‫א‬  mkT b=∆
‫א‬  mkT f=∆−
T∆‫א‬‫א‬K 
 m‫א‬F‫א‬‫א‬‫א‬‫א‬KE 
 kb‫א‬‫א‬‫א‬K 
 kf‫א‬‫א‬‫א‬K 
‫א‬mW 
solutesolvent
solute
MWW
1000W
m
×
×
= 
‫א‬‫א‬W 
 
b
solvent
solute
solute k
WT
1000W
MW ×
×∆
×
= 
 
    f
solvent
solute
solute k
WT
1000W
MW ×
×∆
×
= 

58. ‫א‬١٦٧‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬FE
-٤٠-
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 
‫א‬‫א‬‫א‬W 
١KK
٢KK
٣KK
٤K‫א‬K
٥K‫א‬‫א‬K
‫א‬‫א‬‫א‬W 
١K‫א‬‫א‬١٠٠K
٢KF‫א‬KE
٣K‫א‬K
٤KK
٥KK
‫א‬‫א‬W 
١ J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
٢ J‫א‬‫א‬‫א‬‫א‬٥٪K
٣ J‫א‬‫א‬F١KE 
kb‫א‬‫א‬‫א‬soluteMW‫א‬‫א‬
T∆‫א‬‫א‬‫א‬‫א‬K
 

59. ‫א‬١٦٧‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬FE
-٤١-
 J‫א‬‫א‬‫א‬‫א‬ 
 
‫א‬‫א‬‫א‬W 
١KNaphthalene.
٢KPhenolK 
‫א‬‫א‬‫א‬W 
١K‫א‬F١٥٠KE 
٢K‫א‬K
٣KK
‫א‬‫א‬W 
١K‫א‬١٠‫א‬‫א‬‫א‬‫א‬F70 ºCE‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬K
٢K‫א‬٢‫א‬‫א‬‫א‬‫א‬K
٣Kkf‫א‬‫א‬‫א‬F‫א‬EsoluteMW‫א‬‫א‬
T∆‫א‬‫א‬‫א‬F‫א‬E‫א‬F‫א‬H‫א‬KE
٤K‫א‬kbkf‫א‬‫א‬‫א‬K 
 

60. ‫א‬١٦٧‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬FE
-٤٢-
١٨K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 
‫א‬W 
 ‫א‬F‫א‬‫א‬‫א‬E‫א‬‫א‬FPE‫א‬FCE
‫א‬W 
      F = C - P +1
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
FE‫א‬FKE 
 ‫א‬‫א‬FC = 2E‫א‬F‫א‬E
FP = 1EFP = 2EK 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬Phase diagram‫א‬‫א‬‫א‬
K 
‫א‬‫א‬‫א‬W 
١KK
٢KK
‫א‬‫א‬‫א‬W 
١K‫א‬F٥٠KE
٢K‫א‬K 
٣K‫א‬K 
٤KK 
٥KK
‫א‬‫א‬W 
 J‫א‬٣{٠٠‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
F٦٠E٪‫א‬‫א‬W
OHphenol
phenol
2
WW
W
%
+
=×

61. ‫א‬١٦٧‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬FE
-٤٣-
%×‫א‬‫א‬،W‫א‬‫א‬‫א‬٢٥
١{٠٠LK 
 J‫א‬‫א‬‫א‬‫א‬F٧٠E‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬K
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬FTKE
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬FW٥٠،٤٠،٣٠،٢٠،١٥،١٠KE٪‫א‬
W
‫א‬٪٦٠٥٠٤٠٣٠٢٠١٥١٠
T/ºC
 
٤K‫א‬‫א‬٪‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬maxFTCE‫א‬‫א‬K 
 
 
 
 
 
 
 
 
 
 
 
 
 

62. ‫א‬١٦٧‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬FE
-٤٤-
 
١٩K‫א‬‫א‬‫א‬‫א‬‫א‬ 
‫א‬W 
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬F‫א‬‫א‬E‫א‬
‫א‬‫א‬K‫א‬
‫א‬‫א‬W 
     F = C - P 
F‫א‬‫א‬‫א‬،P‫א‬‫א‬،C‫א‬K 
‫א‬‫א‬‫א‬‫א‬‫א‬F١٠E
‫א‬‫א‬‫א‬١٠٠٪‫א‬
‫א‬‫א‬FPE 
     Pa +Pb +Pc=100% 
Pa‫א‬،Pb‫א‬،Pc‫א‬K‫א‬F٦٠٪،٣٠٪،
١٠٪E‫א‬‫א‬٦٠٪FPcE
‫א‬‫א‬٣٠٪FPbE،‫א‬‫א‬FPaE‫א‬‫א‬
١٠٪،‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬K 
‫א‬‫א‬‫א‬W 
K‫א‬KK
 
‫א‬‫א‬‫א‬W 
٥‫א‬F١٠٠KE١٠KK
‫א‬‫א‬W 
١ J‫א‬‫א‬‫א‬‫א‬‫א‬FWE
‫א‬١٢٣٤٥
‫א‬ml ١٠٩٨٧٦

63. ‫א‬١٦٧‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬FE
-٤٥-
‫א‬ml٢٣٤٥٦
٢ J‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬K
٣ J‫א‬‫א‬‫א‬‫א‬‫א‬FW/WEW
‫א‬FFZ٪‫א‬EDF‫א‬EEC١٠٠ 
‫א‬١٢٣٤٥
٪
٪
٪
  
‫א‬‫א‬Z٠{٩٩٦LK 
 ‫א‬Z٠{٨٩٤LK 
 ‫א‬Z٠{٧٨٩LK 
٤ J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
F‫א‬‫א‬‫א‬KE

64. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٤٦-
 
‫א‬‫א‬‫א‬ 
‫א‬‫א‬‫א‬
‫א‬ m/s8
10998.2 ×=c
FE‫א‬‫א‬m/s2
806.9=g
‫א‬ c/mol485,96=F
‫א‬‫א‬
molKatmlR
molKcalR
molKJR
./.082.0
./987.1
./314.8
=
=
=
 
BoltzmanKJk /1038.1 23−
×=
‫א‬Avogadro123
10022.6 −
×= molN
‫א‬F‫א‬E
esue
Ce
10
19
10803.4
10602.1
−
−
×=
×=
PlancksJh .10626.6 34−
×=
‫א‬‫א‬ kgu 27
1066.1 −
×=
‫א‬kgme
31
10109.9 −
×=
‫א‬kgmp
27
10673.1 −
×=
‫א‬kgmn
27
10675.1 −
×=
‫א‬F‫א‬‫א‬EeE=2.71828182846 
‫א‬‫א‬‫א‬π 91415926535.3=π 

65. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٤٧-
 
‫א‬‫א‬1K=1ºC+273.16
‫א‬ 
1 atm = 760 mm Hg
= 760 Torr
= 101.325 kPa
1 bar = 105
Pa 
‫א‬ 1 l =103
cm3
= 1000 ml
‫א‬1 N = 105
dyne
‫א‬ 1 J = 107
erg
1 cal = 4.184 J
‫א‬ 1 year = 365.25 days(d)
1 day = 24 hours (h)
1 hour = 60 minutes (min)
1 minute = 60 second(s)
‫א‬‫א‬109
esu×1 C = 3 

66. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٤٨-
‫א‬‫א‬ 
‫א‬‫א‬‫א‬
‫א‬‫א‬SI
‫א‬meterm
‫א‬ ‫א‬kilogramKg
‫א‬secondS
‫א‬NewtonN
‫א‬JouleJ
‫א‬‫א‬WattW
‫א‬mol
‫א‬Candlecd
‫א‬AmpereA
‫א‬PascalPa
‫א‬‫א‬cgs
‫א‬Centimetercm
‫א‬‫א‬gramg
‫א‬seconds
‫א‬‫א‬dynedyne
‫א‬‫א‬ergerg
‫א‬
‫א‬‫א‬VoltVolt
‫א‬‫א‬OhmΩ
‫א‬‫א‬ColomC
‫א‬literL
‫א‬atmosphereatm
‫א‬‫א‬Kelvink

67. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٤٩-
‫א‬‫א‬‫א‬‫א‬ 
 
‫א‬‫א‬‫א‬‫א‬‫א‬K 
‫א‬‫א‬‫א‬‫א‬‫א‬
femtof10-15
picop10-12
nanon10-9
microµ10-6
millim10-3
centic10-2
decid10-1
kilok103
megaM106
gigaJ109
‫א‬tetraT1012
‫א‬W 
1 m = 10 dm = 100 cm =106
µm

68. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٥٠-
 
 
‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬
Α
α
Bβ
Γγ
∆δ
‫א‬Ηη
Σσ 
Ππ
Φφ
Ψψ
Ωω
Θθ
Rρ
Κκ
‫א‬Εε
Μµ
Νυ
‫א‬Λλ
 Ττ
 χ
 Ξξ

69. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٥١-
 
‫א‬‫א‬‫א‬٢٥
‫א‬‫א‬
‫א‬ka
‫א‬ H2CO2
11
2
7
1 106.5,103.4 −−
×=×= kk
‫א‬HCN10
108.4 −
×
‫א‬F‫א‬ECH3COOH5
108.1 −
×
‫א‬F‫א‬EHCOOH4
108.1 −
×
‫א‬C6H5COOH5
103.6 −
×
‫א‬H3BO3
10
102.7 −
×
‫א‬HCl7
10
‫א‬HBr9
10
‫א‬‫א‬HI11
10
‫א‬H3PO4
13
3
8
2
3
1
108.4
,102.6,109.6
−
−−
×=
×=×=
k
kk
‫א‬H3BO39
109.5 −
×
‫א‬H2S13
2
8
1 102.1,109.8 −−
×=×= kk
‫א‬kb
‫א‬NH4OH5
107.1 −
×
C6H5NH2
10
101.4 −
×
‫א‬CH3NH2
4
105 −
×
C5H5N9
107.1 −
×
 

70. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٥٢-
‫א‬‫א‬‫א‬‫א‬ 
 
‫א‬
kb
°C/molal
kf
°C/molal
‫א‬H2O0.511.86
‫א‬CH3CH2OH1.22-
‫א‬CH3OH0.83-
‫א‬C6H62.535.12
‫א‬C6H5CH333.3-
‫א‬‫א‬(C2H5)2O2.021.79
C Cl3H3.63-
‫א‬‫א‬C Cl45.0229.8
‫א‬5.6137.7
‫א‬CH3COOH3.073.9
‫א‬‫א‬C6H122.7920
C6H5Br3.8714.4
C10H85.806.9
C6H5OH3.607.4

71. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٥٣-
‫א‬‫א‬٢٥K 
‫א‬‫א‬‫א‬‫א‬±
λ∞
‫א‬H+
349.8
‫א‬Li+
38.69
‫א‬Na+
50.11
‫א‬K+
73.52
‫א‬NH4
+
73.4
‫א‬Ca+
2
159.5
‫א‬Ba+
2
163.6
‫א‬Pb+
2
171
‫א‬Zn+
2
152.8
‫א‬‫־‬OH198.0
‫א‬‫־‬Cl75.23
‫א‬‫־‬Br78.1
‫א‬‫־‬I76.80
‫א‬‫־‬CH3COO40.9
‫א‬‫־‬SO4
2
2
179.8
‫א‬ ‫־‬CO3
2
2
169.3

72. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٥٤-
‫א‬‫א‬‫א‬‫א‬‫א‬٢٥F‫א‬‫א‬EK 
‫א‬‫א‬‫א‬
Li+
+ e = Li-3.045
K+
+ e = K-2.925
Na+
+ e = Na-2.714
Al3+
+ 3e = Al-1.662
Zn2+
+ 2e = Zn-0.763
Fe2+
+ 2e = Fe-0.440
PbSO4 + 2e = Pb + SO4
2-
-0.36
Ni2+
+ 2e = Ni-0.250
Sn2+
+ 2e = Sn-0.136
Pb2+
+ 2e = Pb-0.126
H+
+ e = ½H20.00
Sn4+
+ 2e = Sn2+
0.15
Cu2+
+ e = Cu+
0.153
AgCl + e = Ag + Cl-
0.222
Hg2Cl2 + 2e =2Hg +2Cl-
0.268
Cu2+
+ 2e = Cu0.337
Cu+
+ e = Cu0.521
I2 + 2e = 2I-
0.536
O2 + 2H+
= H2O20.68
Fe3+
+ e = Fe2+
0.771
Ag+
+ e = Ag0.799
O2 + 4H+
+ 4e = 2H2O1.229
PbO2 + 4H+
+ 2e = Pb2+
+ 2H2O1.455

73. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٥٥-
‫א‬‫א‬‫א‬‫א‬٢٥ 
 
‫א‬‫א‬‫א‬ks
‫א‬Al(OH)3
15
107.3 −
×
‫א‬Ca(OH)25.5× 10-6
‫א‬Mg(OH)2
11
102.1 −
×
‫א‬Ba(OH)25× 10-3
‫א‬Cu(OH)22.2× 10-20
‫א‬AgCl10
100.1 −
×
‫א‬AgI16
105.1 −
×
‫א‬AgBr13
107.7 −
×
‫א‬Ag2CrO4
12
100.9 −
×
‫א‬CuS45
105.8 −
×
‫א‬Hg2S10-47
‫א‬PbS29
107 −
×
‫א‬Bi2S310-97
‫א‬Ag2S6.3× 10-50
‫א‬BaSO4
10
101.1 −
×
‫א‬CaSO49.1× 10-6
‫א‬ CaCO32.8× 10-6
‫א‬BaCO35.1×10-6
‫א‬ZnCO3
10
102 −
×
 

74. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٥٦-
‫א‬‫א‬F‫א‬E 
‫א‬‫א‬‫א‬
‫א‬ph.ph ‫א‬FE
FE
‫א‬‫א‬M.OFE
FE
‫א‬Litmus‫א‬‫א‬FE
FE
‫א‬‫א‬‫א‬‫א‬ 
‫א‬‫א‬
‫א‬

‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬
Mohr
‫א‬‫א‬
‫א‬
‫א‬Fluorescein‫א‬‫א‬‫א‬
Fajan
‫א‬‫א‬‫א‬
‫א‬
‫א‬MurexideEDTA‫א‬‫א‬‫א‬
EBTEDTA ‫א‬‫א‬
‫א‬EDTA ‫א‬‫א‬

‫א‬PVC
EDTA‫א‬‫א‬


75. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٥٧-
‫א‬‫א‬F/kcal mol-1
∆Ho
E٢٥K 
‫א‬‫א‬∆Ho
‫א‬ ∆Ho

‫א‬‫א‬CO -26.42‫א‬C6H6
11.72
‫א‬CO2
-94.05‫א‬CH4
-57.08
‫א‬CH4
-17.89‫א‬C2H3
-66.41
‫א‬C2H2
54.19‫א‬‫א‬CCl4
-33.25
‫א‬CH3CH3
-20.24‫א‬H2O-68.32
‫א‬C3H8
-24.82‫א‬‫א‬NaCl-98.35
‫א‬C6H6
19.82‫א‬‫א‬NaCO3
-270.53
‫א‬CH3OH-48.08‫א‬‫א‬SiO2
-217.92
‫א‬C2H5OH-56.63‫א‬‫א‬
CuCO3
-288.73
‫א‬H2O-57.80‫א‬‫א‬PbO-51.20
‫א‬NH3
-11.04‫א‬‫א‬AgCl-30.38
‫א‬HCl-22.06‫א‬‫א‬AgBr-23.80
‫א‬HBr-8.66‫א‬‫א‬AgI-14.93
‫א‬HI6.2‫א‬‫א‬PbS-23.52
‫א‬SO2
-70.96
‫א‬SO3
-94.45
‫א‬C2H4
12.50
HCOH-116
 J‫א‬‫א‬F2,Br2,Cl2,O2,N2,H2‫א‬K 
 J‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬K

76. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٥٨-
‫א‬‫א‬‫א‬FEK 
 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬ 
H-H432H─Si323
O-O146C─N305
N-N160C─O358
F-F154C─S259
-ClCl239C─F485
Br-Br193C─Cl339
C-C347C─Br276
C═C614C─I240
C≡C839N─F272
N═N418N─Cl200
O═O495N─Br243
H─C413C═O799
H─Cl427C≡O1072
H─O467N═O607
H─N391C≡N887
H─Br363N≡N941
H─S347

77. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٥٩-
 
‫א‬‫א‬W 
FbaseEFpowerE‫א‬‫א‬،
‫א‬W 
١K‫א‬10‫א‬‫א‬‫א‬logK
٢K‫א‬e = 2.71828‫א‬‫א‬‫א‬lnK
١W‫א‬‫א‬‫א‬‫א‬34.67K 
1.540=log 34.67
ln 34.67 = 3.5459
٢W‫א‬‫א‬‫א‬1.67–‫א‬‫א‬‫א‬3.76K 
Anti log (3.76) =5754.3393
Anti ln (-1.76) = 0.1720
‫اﻟﻌﻤﻠﻴ‬‫ﺔ‬‫اﻟﻠﻮﻏﺎرﻳﺘﻤﺎت‬ ‫ﻓﻲ‬ ‫اﻟﻤﻘﺎﺑﻞ‬
‫اﻟﺠﻤﻊ‬*
log A + log B ≠ log (A+B)
‫اﻟﻄﺮح‬*
log A - log B ≠ log (A-B)
‫اﻟﻀﺮب‬*
log A + log B = log (AB)
‫اﻟﻘﺴﻤ‬‫ﺔ‬*
log A - log B = log (A/B)
‫اﻷس‬*
B log A = log (AB
)
‫اﻟﻤﻘﻠﻮب‬*
)
A
1
- log A = log (
log 10 =1 ; ln e = 1
log 0 = ln 0 = -∞
log 1 = ln 1 = 0
‫ﺗﺤﻮﻳﻞ‬ln A = 2.303 log A
G
lnlog‫א‬K 

78. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٦٠-
‫א‬‫א‬‫א‬W 
‫א‬‫א‬‫א‬‫א‬‫א‬W 
ax2
+ bx+ c = 0
c,b,a‫א‬‫א‬x‫א‬W 
 
aacbbx 2)4( 2
−±−=
 
‫א‬‫א‬x‫א‬K 
 
W‫א‬x‫א‬‫א‬‫א‬W 
422
=+ xx
‫א‬W‫א‬‫א‬‫א‬W 
ax2
+ bx + c = 0 
 
x2
+ 2x - 4 = 0 
x‫א‬W 
 
aacbbx 2)4( 2
−±−= 
( ) 12)41442( ×−×−±−= 
   x = 1.236x = -3.236 
 
‫א‬W 
 ‫א‬‫א‬‫א‬Scientific notation‫א‬‫א‬‫א‬‫א‬K
‫א‬W‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬FE‫א‬‫א‬‫א‬،‫א‬‫א‬
‫א‬‫א‬‫א‬K‫א‬
‫א‬‫א‬‫א‬K 

79. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٦١-
١W‫א‬3570000000‫א‬‫א‬8
107.35 ×
K 
٢W‫א‬0.000000000357‫א‬10
1057.3 −
×9
107.35 −
×
8
10357 −
×‫א‬‫א‬‫א‬K 

80. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٦٢-
‫א‬‫א‬W 
١K‫א‬A10a
+B10a
= (A+B)10a
٢K‫א‬A10a
-B10a
= (A-B)10a
٣K‫א‬    10a
10b
= 10(a+b)
٤K‫א‬10a
/10b
= 10(a-b)
٥K‫א‬1/10a
= 10-a
100
= 1
10∞
= ∞
0a
= 0
١W‫א‬0.0037 ,0.00081K 
‫א‬W‫א‬‫א‬‫א‬W 
( ) 00451.0101.45101.837
101.81037
44
44
=×=+=
×+×
−−
−−
 
٢W‫א‬35
101.7,108 −
××K 
‫א‬W 
6580108.65101.78101.7108 23535
=×=××=××× −−

81. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٦٣-
‫א‬‫א‬W 
 ‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
١K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬FxEa, n‫א‬W
‫א‬‫א‬‫א‬
adxax
1−n
nxn
x
x
dxxln
dxexn
e
0a
2
x
dx−
x
1
( )2
xa
dx
−
 
xa −
1
 
٢K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬F(xW
‫א‬‫א‬‫א‬‫א‬
2
2
1 xx
1
1
1 +
+
n
x
n
n
x
x
ex
e
axa
xln
x
1
( )xa −− ln
xa −
1
 

82. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٦٤-
‫א‬ 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
‫א‬‫א‬‫א‬‫א‬‫א‬F‫א‬E‫א‬‫א‬‫א‬
FNEFMEK 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬FPEK
‫א‬‫א‬‫א‬‫א‬‫א‬K 
‫א‬‫א‬‫א‬W 
FVE‫א‬FMWEFME‫א‬‫א‬W 
1000
WMVM
W
××
= 
V‫א‬،W‫א‬‫א‬K 
‫א‬W‫א‬‫א‬‫א‬V،‫א‬‫א‬‫א‬‫א‬MK 
V‫א‬EWN‫א‬‫א‬W
W
W
M
EVN
W
××
= 
 
‫א‬‫א‬‫א‬W 
V‫א‬MWM
‫א‬W
W
C
M
dP
M
××
=
10
 
 d‫א‬‫א‬،P‫א‬‫א‬‫א‬،MC‫א‬
‫א‬‫א‬KMC‫א‬‫א‬VC‫א‬V‫א‬
M‫א‬ 
     VMVM CC ×=× 
‫א‬     ‫א‬‫א‬  ‫א‬  ‫א‬ ‫א‬ 
‫א‬K 

83. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٦٥-
     
dP
MVM
M
VM
V W
C
C
××
××
=
×
=
10
 
‫א‬VC‫א‬‫א‬‫א‬MC‫א‬V
‫א‬MK 
V‫א‬EWN‫א‬W
    
dP
EVN
N
VN
V W
C
C
××
××
=
×
=
10
 
NC‫א‬‫א‬،VC‫א‬‫א‬‫א‬‫א‬‫א‬NC
‫א‬V‫א‬NK 
 
١W‫א‬‫א‬‫א‬‫א‬200 mlNaCl0.1 MK 
‫א‬W 
       
( )
g71.23
1000
5.35232001.0
M
dP10
M
W
C
=
+××
=
××
=
 
٢W‫א‬‫א‬‫א‬‫א‬‫א‬80%
1.325 g/cm3
500 mlH2SO40.05 N 
‫א‬W‫א‬0.05 N500 ml،‫א‬‫א‬‫א‬K 
‫א‬‫א‬‫א‬FZE‫א‬‫א‬÷٢ 
‫א‬ 
    ml
dP
EVN
V W
C 16.1
325.18010
4950005.0
10
=
××
××
=
××
××
= 
W 
‫א‬‫א‬‫א‬‫א‬‫א‬K
‫א‬‫א‬‫א‬‫א‬
‫א‬K
‫א‬‫א‬‫א‬‫א‬K
 

84. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٦٦-
‫א‬FmWE 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K 
     
SW WM
W
m
×
×
=
1000
 
WS‫א‬‫א‬K‫א‬‫א‬‫א‬m‫א‬‫א‬W 
      
W
tW
Mm
WMm
W
×+
××
=
1000
 
W‫א‬‫א‬Wt‫א‬‫א‬‫א‬K 
W3.5 g0.5 molal NaCl‫א‬K 
‫א‬W‫א‬ 
( )
( )
gW
W
Mm
WMm
W
W
tW
1.0
5.585.01000
5.35.585.0
1000
=
×+
××
=
×+
××
=
 
 
‫א‬     
gW
WW
S
S
9.3499
3500
=
−=
 
 
 
 
 
 
 
 

85. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٦٧-
‫א‬ 
 ‫א‬‫א‬‫א‬
K‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
0.1 ml‫א‬‫א‬‫א‬،13.0 ml
13 ml13.00 mlK‫א‬‫א‬‫א‬‫א‬‫א‬K 
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬N = 0.01
‫א‬‫א‬‫א‬‫א‬‫א‬KN= 0.390.39990.4K
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬
0.1 ml‫א‬F10.2 ,10.0 ,10.1E‫א‬10.1‫א‬F11.0 ,10.5
,10.0E‫א‬± 0.1K‫א‬
‫א‬K 

86. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٦٨-
‫א‬‫א‬W 
 ‫א‬‫א‬‫א‬‫א‬K‫א‬
‫א‬‫א‬K‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K‫א‬‫א‬
‫א‬F‫א‬‫א‬E‫א‬‫א‬
‫א‬least squareK‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K‫א‬‫א‬‫א‬‫א‬،‫א‬‫א‬‫א‬correlation factor
‫א‬‫א‬‫א‬‫א‬‫א‬K 
  ‫א‬      ‫א‬ ‫א‬   ‫א‬
‫א‬K‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬٤٥‫א‬K‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬‫א‬K 
 ‫א‬‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬‫א‬‫א‬K 
 ‫א‬‫א‬‫א‬‫א‬
‫א‬‫א‬K 

87. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
-٦٩-
W‫א‬‫א‬‫א‬‫א‬‫א‬K 
ln xTime
1.255
0.7510
0.015
-0.4620
-1.2625
١K‫א‬١٢‫א‬‫א‬y ,xK 
٢K‫א‬x‫א‬٢٥
‫א‬xK
٣K‫א‬ y‫א‬  -1.5F‫א‬    
‫א‬E٢0.5K‫א‬K
‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬K
٤K‫א‬‫א‬‫א‬x‫א‬‫א‬
‫א‬y‫א‬‫א‬‫א‬
‫א‬Z
12
12
xx
yy
−
−
٥K‫א‬‫א‬x =0‫א‬‫א‬‫א‬yK 

88. ‫א‬ ١٦٧ ‫א‬ 
‫א‬‫א‬‫א‬FE  
‫א‬ 
1.‫א‬............................................................................................................................................-٢-
2.‫א‬‫א‬‫א‬‫א‬‫א‬Viscometer.................................................-٤-
٣K‫א‬‫א‬...................................................................................................-٦-
٤K‫א‬‫א‬‫א‬......................................................................................................................-٨-
٥K‫א‬‫א‬‫א‬‫א‬.....................................................................................-١٠-
٦K‫א‬‫א‬‫א‬................................................................................................-١٣-
٧K‫א‬‫א‬.....................................................................................................-١٥-
٨K‫א‬‫א‬‫א‬..........................................................................................-١٨-
٩K‫א‬.........................................................................................................-٢٠-
١٠K................................................................................................-٢٢-
١١K‫א‬‫א‬.......................................................................................................................-٢٥-
١٢K‫א‬‫א‬.................................................................................................................................-٢٧-
١٣K‫א‬‫א‬‫א‬‫א‬......................................................................................-٣٠-
١٤K‫א‬‫א‬‫א‬........................................................................................................................-٣٢-
١٥K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬.........................................................................................-٣٤-
١٦K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬.........................-٣٦-
١٧K‫א‬‫א‬‫א‬......................................................................................................٣٩
١٨K‫א‬‫א‬‫א‬‫א‬‫א‬‫א‬..............................................................٤٢
١٩K‫א‬‫א‬‫א‬‫א‬‫א‬........................................................................٤٤

89.  
 

90.  
 
 
 
 
 
 
 
 
 