bài tập hóa lý có lời giải chi tiết

Chương 1
NGUYÊN LÝ I NHIỆT ĐỘNG HỌC
1.1.1. Nhiệt và công
 

 !  
"# $% &%
"' &% $%
1.1.2. Nguyên lý I nhiệt động học
()*+,-./
∆012
345 678-94:;/
01δ2δ
< =>5?*+@),A/
∫
−=
2
1
V
V
PdVQΔU
1.1.3. Áp dụng nguyên lý I cho một số quá trình.
1.1.3.1. Quá trình đẳng tích: B17#C B1%
∫
==
2
1
V
V
v
0PdVA

DE,@@/
B
1F0
1.1.3.2. Quá trình đẳng áp: G17#C G1%

5
1GHB
I
2B
J
K1G∆B
L7,@/ 
5
1F0MG∆B1∆H0MGBK1∆"
J
1.1.3.3. Quá trình đẳng áp của khí lý tưởng
DE5N=4>O/GB1PD
D@/ 
5
1G∆B1PFD
F0
5
1
5
QPFD
1.1.3.4. Quá trình dãn nở đẳng nhiệt của khí lý tưởng
(A*- RO,SHD17#K>OTU
*/
2
1

1
2
TT
P
P
nRTln
V
V
nRTlnAQ ===
D7,@/
G
J
/45#!O=4,V
G
I
/45#!O=4W
1.1.3.5. Nhiệt chuyển pha
D

5
λ
=
D7,@/
λ
5
/)5H7XYK
λ

12λ
,,

Cλ

12λ
6
Z[/
PU#W>O@44\#/
P1JC]^_`8731^CaJbY`873
P1%C%^I8`873
J1bCJ^YcJ81J%JCaY1IbCI
1.2. Định luật Hess
1.2.1. Nội dung định luật
I
D794,S457X,S>C5de56-7=
4,V=4W856-74=4
(),\'"f##/

B
1F0
5
1F"
D7,@/
∆0/5d,S>
∆"/5d,S45
394gdO,*h@5d*h/∆"
%
I]^
C
∆0
%
I]^


iW494gd@8X4!>H,gf8>OKC
@/
F"1F0MPDF
B∆TA*#W87>94
1.2.2. Các hệ quả của định luật Hess
5d\TU4 !5d'
F"
\
12F"
'
5dTUj#4!=7E,j#
4!85d
F"
5d
1kF"
#
#5
2kF"
#

5dTUj44!85dE,j
44!=7
F"
5d
1kF"


2kF"


#5
Z[/=7*hH∆"
%
I]^C
KC,W4*hH∆"
%
I]^C,
K
,7#l7#j@
1.3. Nhiệt dung
1.3.1. Định nghĩa
a
 ,S45/
PP
p
T
H
dP
δQ
C






∂
∂
=







=

 ,S>/
VV
v
T
U
dT
δQ
C






∂
∂
=







=

mW*/
5
2

1P
,>/
∫
=
2
1
T
T
CdTmQ
7X
∫
=
2
1
T
T
CdTnQ

1.3.2. Ảnh hưởng của nhiệt độ đến nhiệt dung
no56-7,- ,T) pTU4o
8  =48#W/

5
1

%
M
J
DM
I
D
I
"7X 
5
1
%
M
J
DM
2I
D
2I
D7,@/
%
C
J
C
I
C
2I
4#Wo8@)4\[7
#j@
1.2.2. Định luật Kirchhoff
"5d56-7,-,T) pTO,\'
37qq/

p
P
ΔC
T
ΔH
=






∂
∂
"7X
v
V
ΔC
T
ΔU
=






∂
∂
n!>5?,/

∫
+=
T
0
p0T
dTΔCΔHΔH
A!>5?ED
J
,AD
I
,/
b
∫
+=
2
1
12
T
T
pTT
dTΔCΔHΔH
1.4. Bài tập mẫu
B> 6J/D>TA*-8TNJ%OI%
%
!5'N
>OT;9)>;@NOI%
%
TU
IbrJC^IbY`
Zd

V!5,)8@NJ%/
18λ1J%IbrJC^Ib1IbrJ^CIbHYK
#94@N/
1G∆B1GHB

2B

K1GB

 1
1353,332938,314
18
10
nRT =××=
HYK
(A*-/
∆01Q1IaJsrHYK
B> 6I/7br%N6OJ%%
%
 45#!,jJ8@N
O,-TUra]`D>CF094
Zd
;6/
18λ
6
1br%H2ra]K12IbIrr%HK
94/
1G∆B1GHB

2B


K12GB

12PD
 1
18529(cal)3731,987
18
450
−=××
(A*-94/
∆01Q12IIb%IJHK
r
B> 6a/75dgdO45#!,j/
I"
I
Mt1"
a
t"HK
=7*hOI]^3t"
a
t"HKTU2JJ%Cr2I%JCIY`87
 87,S454!8-8,-/

5
H"
I
K1I_CI^MaCIsJ%
2a
D HY`873K


5
HtK1I^CbJMbCJJ%
2a
D HY`873K

5
H"
a
t"K

1JrCI^MJ%rCIJ%
2a
D HY`873K
D>F"
%
5dOI]^r%%3u
Zd
5dOI]^3/
∆"
%
I]^
12I%JCI2H2JJ%CrK12]%C_H3YK
(A* /
∆
5
1
5
H"
a
t"KQ

5
HtKQI
5
H"
I
K
12s_Cs]M]bCr^J%
2a
DHY`3K
5dOr%%3/
∫
+=
500
298
p
0
298
0
500
dTΔCΔHΔH
( )
∫
−
+−+−=
500
298
33
dTT94,58.1067,6990,7.10
12]s_r%CbIHYK
B> 6b/7J%%>t

I
H,gf8>OKO%
%
JC%JaJ%
r
Gv4,\
CCF0F"7494#(A
5
1a_CJY`873
 LRO,S)>%CI8
a

T LR,S45%CI8
a

 i@,S>45#!TUIC%IsJ%
r
G
Zd
s
 LRO,SHD17#K)>%CI8
a

nRT
PV
nRTln
V
V
nRTlnAQ
2

1
2
TT
===

7061
2730,082
44
100
0,2.101
273.ln8,314
44
100
3
=
××
×
××=
HYK
∆Η = ∆01%
T LRO,S45HG17#K%CI8
a

∆"1
5
1
5
HD
I
QD

J
K
 






−=
nR
PV
nR
PV
n.C
12
p

 













××
−××=
1
2730,082
44
100
0,2.101
0,082
37,1
3
= 67469 (Y)
1G∆B1GHB
I
QB
J
K

( )
J15120
0,082
8,314
1
2730,082
44
100
0,2.101
3
=×













××
−×=
∆01Q1s_bs]2JrJI%1rIab]HYK
 i@,S>HB17#K45#!TUIC%IsJ%
r
GHI8K
1%


1
5
2P1a_CJ2^CaJb1I^C_^sHY`873K
∆01

1

HD
I
QD

J
K
D@/
1
1
2
2
T
P
T
P
=

⇒

546K273
1
2
T
P
P
T
1
1
2
2
=×=×=
n/∆01

1J

×
I^C_^sHrbs2I_aK1_^r]HYK
_
∆"1∆0MG∆B1_^r]HYK
B> 6r/m->O7,@@ 87,S>O8.,-@

1ICrPHP
U#W>KD>CC∆0∆"8-87>o494#,?/
 LRO'\,S45O45#!J8EI% 8
a
,Ab% 8
a

T (A,j'\,S>E=4HJ8cb% 8
a
K,AH%Cr8cb% 8
a
K
 w'\,SE%Cr8,AJ8OIr
%

Zd
 LRO'\,S45HG17#K
D>/
( ) ( ) ( )
l.atm2020401.VVPPdVA
2
1
V
V

12
=−=−==
∫

2028
0,082
8,314
20 =×=
HYK
D>/
( )






−=−==
∫
R
VP
R
VP
CTT.CdTCQ
12
p12p
T
T
pp
2

1

( )
702040
R
3,5R
=−=
H8K

7097
0,082
8,314
70 =×=
HYK
(A*-/
∆01Q1r%s]HYK
(A*f5
∆"1
5
1_%]_HYK
T LRO'\,S>HB17#K
⇒
1%
/
^
( )







−=−==
∫
R
VP
R
VP
CTT.CdTCQ
12
v12v
T
T
vv
2
1

( )
5010,540
R
2,5R
−=−×=
H8K
 
5069
0,082
8,314
50 −=×−=
HYK
∆01


12r%s]HYK
 w,SHD17#K
⇒
∆01%
1717
1
5,0
ln298314,81
P
P
nRTlnAQ
2
1
TT
−=××===
HYK
B> 6s/D>=7fTA/


Mt
I
1t
I
∆"
%
I]^
12a]aCr3Y
"
I

MJ`It
I
1"
I
tHK  ∆"
%
I]^
12I^r3Y
I
I
"
s
M_t
I
1bt
I
M"
I
tHK ∆"
%
I]^
12aJJ]Cs3Y
Zd


Mt
I
1t
I
 HJK

"
I
MJ`It
I
1"
I
tHK HIK
I
I
"
s
M_t
I
1bt
I
Ms"
I
tHK HaK
=7
I
"
s
/
IMa"
I
1
I
"
s
HbK

∆"
%
I]^HbK
1b∆"
%
I]^HJK
Ms∆"
%
I]^HIK
2∆"
%
I]^HaK
∆"
%
I]^HbK
1bH2a]aCrKMsH2I^rK2H2aJJ]CsK1JsbCbH3YK
B> 6_D>CC∆094w,SC'\a87>"fEJ8,A
r8Ob%%
%
3
Zd
94/
]
16057(J)
5
1
400ln8,3143
P
P
nRTlnAQ

2
1
TT
−=××===
∆01%
B> 6^75d/J`I
I
MJ`It
I
1t<Ir
%
CJ8@∆"
%
I]^
1]%Ca_Yv4
,\5dOrr^3CTA 87,S45J87
I
Ct
I
tV
I]CJIcI]CasI]C^sY87
2J
3
2J

Zd
"5dOrr^3/
∫
+=
558

298
p
0
298
0
558
dTΔCΔHΔH
D7,@/
∆
5
1I]C^sQJ`IHI]CJIKQJ`IHI]CasK1%CsIHY3
2J
K
∆"
%
rr^
1]%Ca_M%CsIHrr^2I]^KJ%
2a
1]%CraJIH3YK
Chương 2
NGUYÊN LÝ II NHIỆT ĐỘNG HỌC
2.1.1. Định nghĩa entropy
D794'\CTA*f75)E=4J#
=4I,g4,\TU5N/
T
δQ
dS =

∫
=

T
δQ
ΔS
TN
x75,,7TU,N\87
2J
3
2J
Y87
2J
3
2J
2.1.2. Biểu thức toán của nguyên lý II
T
δQ
dS ≥
L!y1z94'\
J%
L!y$z94T!'\
2.1.3. Tiêu chuẩn xét chiều trong hệ cô lập
D7'5H,7=K
A n$% /4ogd
A n1%
I
n&%/4,=?TU
2.1.4. Biến thiên entropy của một số quá trình thuận nghịch
2.1.4.1. Quá trình đẳng áp hoặc đẳng tích
∫
=
2

1
T
T
T
dT
CΔS
A94,S45/
∫
=
2
1
T
T
p
T
dT
CΔS
A94,S>/
∫
=
2
1
T
T
v
T
dT
CΔS
2.1.4.2. Quá trình đẳng nhiệt
D794'\,SC@)45 6/

T
Q
ΔS
T
=
iW94)594@dC94@N{
T
λ
T
ΔH
ΔS
T
==
nc
nc
nc
T
λ
ΔS =

hh
hh
hh
T
λ
ΔS =
iW>O/
1
2
T

V
V
nRTlnQ =
D,/
2
1
1
2T
P
P
nRln
V
V
nRln
T
Q
ΔS ===
(A*f75O,-T!|@)>TU5N/
JJ
∫∫
+⋅++⋅=
nc
chph
2
chph
1
T
T
nc
nc

R
p
chph
chph
T
0
R
pT
T
λ
T
dT
C
T
λ
T
dT
CΔS

∫∫
⋅++⋅+
T
hh
hh
nc
T
k
p
hh
hh

T
T
l
p
T
dT
C
T
λ
T
dT
C
7X
∑ ∑
∫
+=
T
λ
T
dT
CΔS
pT
D7,@/
1
R
p
C
/ O=4}J
2
R

p
C
/ O=4}I
(A*f75*h45d,g4,\TU5N/
∑ ∑
−=
0
298(tc)
0
298(sp)
0
298
SSΔS
2.2. Thế nhiệt động
4A,-T7~8/-Cf5Co 7A,S45
o 7•A,S45Z,,\€TO45N#/
•102Dn
Z1"2Dn
D=8-,-g4,\CTA*A,S45,S>,T) pTU
5N#/
∆•1∆02D∆n
∆Z1∆"2D∆n
B ∆Z1ΣZ
W
2ΣZ
,V
∆•1Σ•
W
2Σ•
,V

DA,S45=7*h4!H∆Z
%
I]^
K@)7#j@

2.2.1. Xét chiều trong hệ đẳng nhiệt, đẳng áp
D7,SC,S45
JI
A Z&% /4ogd
A Z1%
I
Z$% /4,=?TU
2.2.2. Xét chiều trong hệ đẳng nhiệt, đẳng tích
D7,SC,S>
A •&% /4ogd
A •1%
I
•$% /4,=?TU
2.3. Bài tập mẫu
B> 6JD>TA*f75,@'\Jst
I
EI_a3,Aa_a3
74,#/
 iS45
T iS>
vf8t
I
>O 87

1aP`I

Zd
 iW94,S45

5
1

MP1rP`I
( )
cal/K775
273
373
1,987.ln
2
5
32
16.10
T
dT
CnΔS
3
T
T
p
2
1
=××==
∫
T iW94,S>
( )
cal/K465

273
373
1,987.ln
2
3
32
16.10
T
dT
CnΔS
3
T
T
v
2
1
=××==
∫
B> 6Iv4,\,-[?TUTA*f75-J,4O
%
%
J%OJ%%
%
7TA@d,4TUaabCbY` 
*TUbCJ^Y`3
Zd
Z.DH3K,-#-Zd#•'5
Ja
D@5N/
;17

2
;
‚‚1


a
1
J
M
I

⇔
2J%bCJ^HD2a_aK1aabCbMJbCJ^HD2I_aK
⇒
D1arsCsbH3K
(A*f75/
∆n1∆n
J
M∆n
I
M∆n
a
B/
1,225(J/K)
273
334,4
T
λ
ΔS
nc

nc
1
===
1,117(J/K)
T
dT
4,181.ΔS
356,64
273
2
==
∫
1,875(J/K)
T
dT
4,1810.ΔS
356,64
373
3
−==
∫
∆n1%Cbs_HY`3K
B> 6aD>TA*f7594w,SC'\
 J877gEG
J
1%C%%J8,AG
I
1%C%J8
T J878*EG
J

1%CJ8,AG
I
1J8
D7ƒ5*>,gf8O
Zd

K)4,575(cal/11,987.ln0,
P
P
nRlnΔS
2
1
−===
T
K)4,575(cal/11,987.ln0,
P
P
nRlnΔS
2
1
−===
Jb
B> 6bv4,\TA*f7594)I;O%
%
NO
JI%
%
 45#!J8(A@NOJ%%
%
ICIrrHY`KC 

87N
5C
1a%CJaMJJCaJ%
2a
DHY`873K ;
5C
1
_rCa%Y`873
Zd
(A*f7594
∆n1∆n
J
M∆n
I
M∆n
a

B
2,61(J/K)
T
dT
75,3
18
2
ΔS
373
273
1
∫
=⋅=

12,09(J/K)
373
22552
ΔS
2
=
×
=
( )
0,2(J/K)
T
dT
T11,3.1030,13
18
2
ΔS
393
373
3-
1
∫
=+⋅=
∆n1JbC]HY`3K
B> 6rm-T>C!@)>%CJ8
a
7gC@
)>%Cb8
a
N",O:8-,,-J_
%

45#!
JC%JaJ%
r
`8
I
D>TA*f757>A47
Zd
3>A47C)>„5B
I
1%Cr8
a
(A*f75/
∆n1 ∆n
J
M∆n
I

B ∆n
J
/TA*f75>tgA4
∆n
I
/TA*f75>NA4
K)13,32(cal/
V
V
nR.lnΔS
1
2
1

==
Jr
)7,46(cal/K
V
V
nR.lnΔS
'
1
2
2
==
B' ∆n1I%C_^H`3K
B> 6sD>∆0C∆"∆n94)J87"
I
t;OIr
%
J8N
OJ%%
%
CJ87TA 87;_rCIbY`873@
Nb%sI]CsY`87
Zd
V!5
hh
373
298
21p
λ75,24dTQQQ +=+=
∫
)46272,69(J40629,6298)75,24(373Q

p
=+−=
94
( )
J3101,13738,3141nRTVP0AAA
221
=××==∆+=+=
-
∆01Q1baJ_JCrHYK
∆"1
5
1bsI_CsHYK
(A*f7594


a_a
I]^
5IJ
D
…
D
D
FnFnFn +=+=
∫


( )
Y`3JIrC^
a_a
b%sI]Cs

I]^
a_a
_rCIb =+=
B> 6_75d@4#W#/
a•fHKMb"
I
tHK1•f
a
t
b
HKMb"
I
HK

Js
∆"
%
I]^
H3`87K
% 2r_C^ 2Is_ %
n
%
I]^
H`873K
sCb] brCJ aCr aICIJ

5
H•fK1bCJaMsCa^J%
2a
D H`873K


5
H"
I
t

K1IC_MJJ%
2a
D H`873K
 
5
H•f
a
t
b
K1a]C]IMJ^C^sJ%
2a
D H`873K
 
5
H"
I
K1sC]r2%CIJ%
2a
D H`873K
 D>,S45,S>OIr
%
J8u
T D>,S45,S>OJ%%%3u
 vw5dOIr

%
J8u
Zd
Gd/a•fHKMb"
I
tHK1•f
a
t
b
HKMb"
I
HK


 D>∆"
%
I]^
12Is_2bH2r_C^K12arC^3.
D>∆0
%
I]^
1∆"
%
I]^
2∆PD

∆1b2b1%
L7,@∆0
%
I]^

1∆"
%
I]^
12arC^3
T D>∆"
%
J%%%
1∆"
%
I]^
M
∫
1000
298
ΔCp.dT

∆
5
1†b
5
H"
I
KM
5
H•f
a
t
b
K‡Q†b
5

H"
I
tKMa
5
H•fK‡
⇒
∆
5
1bbCra2rC%^J%
2a
D
D@/
∆"
%
J%%%
12ar^%%M
∫
−
−
J%%%
I]^
a
DK DrC%^J%HbbCra

12s^rbCa_HK
∆0
%
J%%%
1∆"
%

J%%%
2

∆PD

∆1b2b1%
⇒
∆0
%
J%%%
1∆"
%
J%%%
12s^rbCa_HK
 vw5dO,E/
∆Z
%
I]^
1∆"
%
I]^
Q

D∆n
%
I]^



J_

D7,@/
∆n
%
I]^
1HbgaICIJMarKQHbgbrCJMagsCb]K
12asC%aHK
∆Z
%
I]^
12ar^%%MI]^gasC%a12Ir%saC%sH)
B/∆Z
%
I]^
&%*5do pTA
Chương 3
CÂN BẰNG HÓA HỌC
3.1. Hằng số cân bằng
3.1.1. Các loại hằng số cân bằng
Gd/HKMT(HK HKM LHK
"U#W?TU>f745#!/
cb
b
B
a
A
d
D
c
C
P

.PP
.PP
K








=
"U#W?TU>f7~,-87`/
cb
b
B
a
A
d
D
c
C
C
.CC
.CC
K









=

"U#W?TU>f75V87/
cb
b
B
a
A
d
D
c
C
x
.xx
.xx
K








=
"U#W?TU>f7#W87/

cb
b
B
a
A
d
D
c
C
n
.nn
.nn
K








=
mW94U#W?TU/
( )
Δn
cb
i
n
Δn
x

Δn
CP
Σn
P
.K.PKRT.KK








===
∆TA*#W87>
∆1HM KQHMTK
A∆1%@3
5
13

13
g
13

J^
3.1.2. Phương trình đẳng nhiệt Van’t Hoff
vw5d/HKMT(HK HKM LHK
D=,-,jC@/
P
0

TT
RTlnπΔGΔG +=
B
P
0
T
RTlnKΔG −=
b
B
a
A
d
D
c
C
p
.PP
.PP
π =

D7,@/G

CG
(
CG

CG
L
45#!*5V=ƒ,)8T!|
⇒


P
P
K
π
T
RTlnΔG
=
Aπ
G
$3
G
/5dgdf7\
Aπ
G
&3
G
/5dgdf7'
Aπ
G
13
G
/5d,=?TU
[/
Δn
i
n
Δn
x
Δn

CP
n
P
π.Pπ(RT)ππ








⋅===
∑
3.2. Cân bằng trong hệ dị thể
3.2.1. Biểu diễn hằng số cân bằng
A45dgd74 \)84!75}7X5
;=7  \T),\€U#W?TU@8X
4!}!;
B> 6/•f
I
t
a
HKMatHK1I•fHKMat
I
HK
"U#W?TU/
3
CO
3

CO
P
P
P
K
2
=
3.2.2. Áp suất phân ly
ˆ5#!N 7#o5?8-!=7,X7!,@O8„
,-,.45#!5?
B> 6/t
a
HK1tHKMt
I
HK
ˆ5#!5?/
PCO
KP
2
=
J]
3.2.3. Độ phân ly
i-5?!,R5?#7!T,V/
o
n
n
α =
/!,R5?

7

/!T,V
3.3. Các yếu tố ảnh hưởng đến hằng số cân bằng
3.3.1. Ảnh hưởng của nhiệt độ đến hằng số cân bằng
DE5N,S45B‰"7qq
I
G
PD
F"
D
3
=
D77d,-;ED
J
,AD
I
Cgf8∆",j

Š!>5?IAC
,/
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( )








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D5
D
J
D
J
P
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3
3
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J
I
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4\3
5
‹C5d \)f7'
A5d;C∆"&%C
⇒
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D

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4\3
5
#Œd8C5d \)f7\.
3.3.2. Ảnh hưởng của áp suất
D=,-,j@/
const.PKK
Δn
xp
==
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∆
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‹C 7,@3
g
d8C?TU#Œ
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A ∆&%/345#!GC4\G
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g
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I%

A∆1%/3
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g 
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?TU5d
3.4. Bài tập mẫu
B> 6J"U#W?TU5d/
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I
tHK t
I
HKM"
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I
tH•WK,A^%%3v4,\
 7#A :J
Zd
Z.g#W87"
I
t85d
tM"
I
t t
I
M"
I


28
250

18
1000
% %
g g g g
H
x
28
250
−
K H
x
18
1000
−
K
g g
B∆1%C@U#W?TU/
4,12
x
18
1000
.x
28
250
x
.nn
.nn

KK
2
OHCO
HCO
nP
2
22
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

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





−
===
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Zd5N,/g1^CrrH87K
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%

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5>/
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a
HK "
a
t"
a
HKM"
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TUsC]IJ%
b
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%
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b
GH3>
!5'„5>?f7,\'>OK
IJ
Zd
Z.#W87T,V"
a
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a
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a
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a
HKM"
I
 % %
g g g
HQgK g g
Dj#W874![?TU/
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i
+=






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=









=
g
G

g
gg
Ž
G
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F
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⇔
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s]IC%
g
%C]_g
II
I
=
−


⇒
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B',-5?/
%C_sb

g
• ==
B> 6ai@bbr
%
8-T>^87+
I
rCa87"
I
=7]Cr87"+
[?TUv4,\"+,g!54E^87+
I
a87"
I

Zd
Z.g#W87"
I
85d/
"
I
M+
I
 I"+
(,V rCa ^ %

Gd g g Ig
?TU HrCaQgK H^QgK Ig
Df7,T/Ig1]Cr
⇒
g1bC_rH87K
"U#W?TU/
II
( )( )
50,49
x8x5,3
4x
.nn
n
K
2
IH
2
HI
n
22
=
−−
==
"„5^87+
I
a87"
I

"
I

M+
I
 I"+
(,V a ^ %
Gd   I
?TU HaQK H^QK I
B,-,j*U#W?TU‹,j/
⇒
( )( )
50,49
y8y3
4y
K
2
n
=
−−
=
⇒
1IC^_
nW87"+=7/
"+
1rC_bH87K
B> 6b"U#W?TU5d/
G
a
HKM
I
HK G
r

HK
Or%%33
G
1a8
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