Богатиков А.Н., Красицкий В.А., Лапков К.Н. и др. Сборник задач, вопросов и упражнений по общей неорганической химии
Подождите немного. Документ загружается.
11
Fheyjguch[t_fwd\b\Ze_glZ]ZaZOk\yaZgkfheyjgufh[t_fhf
]ZaZOkhhlghr_gb_f
V
m
∗
)
(
1
X
z
=
∗
z
X
V
m
)(
.
<lh`_\j_fyfheyjguch[t_fwd\b\Ze_glZ]ZaZOqbke_gghjZ
\_ghlghr_gbxh[t_fZ]ZaZOdkhhl\_lkl\mxs_fmobfbq_kdhfmdh
ebq_kl\m\_s_kl\Z
V
∗
)
(
1
X
z
=
∗
)
(
1
)
(
X
z
n
XV
.
Ijbf_j
Hij_^_eblv qbkeh wd\b\Ze_glghklb nZdlhj wd\b\Z
e_glghklbwd\b\Ze_glbfheyjgmxfZkkmwd\b\Ze_glZnhknhjghcdb
kehlu\j_Zdpbb
Ca(OH)
2
+ H
3
PO
4
:&D+32
4
+ 2H
2
O.
J_r_gb_
GZoh^bfqbkehwd\b\Ze_glghklbz
*
<^Zgghcj_Zdpbbhlh^ghc
fhe_dmeuG
3
PO
4
hls_ieyxlkybhgZG
+
beb^jm]bfbkeh\Zfbh^ghc
fhe_dme_ dbkehlu wd\b\Ze_glguobfbq_kdb khhl\_lkl\mxl bhgZ
G
+
Ihwlhfmqbkehwd\b\Ze_glghklbz
*
\^Zgghcj_ZdpbbjZ\gh
GZoh^bf nZdlhj wd\b\Ze_glghklb b hij_^_ey_f wd\b\Ze_gl
dbkehluIhhij_^_e_gbx
2
1
1
*
==
z
f .
WlhagZqblqlhh^ghfmbhgmG
+
\^Zgghcj_Zdpbbkhhl\_lkl\m_l
qZklviheh\bgZfhe_dmeudbkehludhlhjZyby\ey_lky\^Zgghc
j_Zdpbb__obfbq_kdbfwd\b\Ze_glhf
GZoh^bffheyjgmxfZkkmwd\b\Ze_glZdbkehlu
M
∗
)
PO
H(
1
4
3
z
=
]fhev
49
2
98
2
)
PO
H
(
4
3
==
M
.
Ijbf_j
Hij_^_eblvwd\b\Ze_glbjZkkqblZlvfheyjgmxfZkkm
wd\b\Ze_glZ]b^jhdkb^ZojhfZ,,,\j_Zdpbb
2Cr(OH)
3
+ 3H
2
SO
4
= Cr
2
(SO
4
)
3
+ 6H
2
O.
J_r_gb_
GZoh^bfqbkehwd\b\Ze_glghklbKUHG
3
:
qZklbpZfKUHG
3
khhl\_lkl\mxlbhgh\G
+
,
qZklbp_
- " -
x bhgh\
12
hldm^Z o AgZqbl qbkeh wd\b\Ze_glghklb ]b^jhdkb^Z ojhfZ z
*
\
^Zgghcj_ZdpbbjZ\gh
GZoh^bf nZdlhj wd\b\Ze_glghklb KUHG
3
b hij_^_ey_f _]h
obfbq_kdbcwd\b\Ze_gl
bhgZfG
+
wd\b\Ze_glgZ qZklbpZKUHG
3
,
bhgmH
+
- " - yqZklbphldm^Zy = 1/3.
WlhagZqblqlh\^Zgghcj_Zdpbbwd\b\Ze_glhf]b^jhdkb^ZojhfZ
,,,y\ey_lkymkeh\gZyqZklbpZ–qZklv_]hnhjfmevghc_^bgbpu
JZkkqblZ_fagZq_gb_fheyjghcfZkkuwd\b\Ze_glZKUHG
3
:
M
)
)
OH
(
Cr(
3
1
3
=
3
)
)
OH
(Cr(
3
M
]fhev
Ijbf_j
Hij_^_eblvwd\b\Ze_glbjZkkqblZlvfheyjgmxfZkkm
wd\b\Ze_glZ]b^jhdkb^ZfZj]ZgpZII\j_Zdpbb
2Mn(OH)
2
+ 12KOH + 5Cl
2
:.0Q2
4
+ 10KCl + 8H
2
O.
J_r_gb_
GZoh^bfqbkehwd\b\Ze_glghklb^eyFQHG
2
:
Ihkdhevdm \ nhjfmevghc_^bgbp_ wlh]h ]b^jhdkb^Z kh^_j`blky
Zlhf fZj]ZgpZ \ kl_i_gb hdbke_gbyZ \ nhjfmevghc _^bgbp_
D0Q2
4
–
\ kl_i_gb hdbke_gby^_eZ_f \u\h^ qlhqZklbp_
FQHG
2
khhl\_lkl\mxlwe_dljhgh\AgZqblqbkehwd\b\Ze_glghklb
]b^jhdkb^ZjZ\gh
GZoh^bf nZdlhj wd\b\Ze_glghklb ]b^jhdkb^Z b hij_^_ey_f
_]hobfbq_kdbcwd\b\Ze_gl
5
1
*
1
==
z
f
.
WlhagZqblqlh\^Zgghcj_Zdpbbwd\b\Ze_glhf]b^jhdkb^ZfZj
]ZgpZ,,y\ey_lkymkeh\gZyqZklbpZ
–
qZklv_]hnhjfmevghc_^b
gbpu
JZkkqblZ_fagZq_gb_fheyjghcfZkkuwd\b\Ze_glZ]b^jhdkb^Z
M
)
)
OH
(
Mn
(
5
1
2
=
5
)
)
OH
(
Mn(
2
M
=
5
]fhev
89
]fhev
Ijbf_j
Hij_^_eblvwd\b\Ze_glbjZkkqblZlvagZq_gb_fheyj
ghcfZkkuwd\b\Ze_glZkmevnZlZZexfbgby\j_Zdpbb
Al
2
(SO
4
)
3
+ 3Pb(NO
3
)
2
= 2Al(NO
3
)
3
+ 3PbSO
4
.
J_r_gb_
GZoh^bfqbkehwd\b\Ze_glghklb$O
2
(SO
4
)
3
.
<^Zgghcj_Zdpbbh[f_gZg_ijbgbfZxlmqZklbybhguG
+
<wlhf
kemqZ_ijbgbfZxlky\h\gbfZgb_^jm]b_bhgukihklhyggufaZjy^hf
13
jZ\gufbeb–<gZr_fijbf_j_wlhbhguNO
−
3
BamjZ\g_gbyj_
Zdpbb\b^ghqlhh^ghcqZklbp_$O
2
(SO
4
)
3
wd\b\Ze_glgubhgh\12
−
3
,
l_qbkehwd\b\Ze_glghklbz
*
^eykmevnZlZZexfbgbyjZ\ghr_klb
GZoh^bfnZdlhjwd\b\Ze_glghklbbhij_^_ey_fwd\b\Ze_gl
bhgZf12
−
3
khhl\_lkl\m_lqZklbpZ$O
2
(SO
4
)
3
,
bhgm - " - xqZklbphldm^Zx = 1/6.
WlhagZqblqlh\^Zgghcj_Zdpbbh[f_gZobfbq_kdbfwd\b\Ze_g
lhf kmevnZlZ Zexfbgby y\ey_lky mkeh\gZy qZklbpZ –qZklv _]h
nhjfmevghc_^bgbpu
JZkkqblZ_fagZq_gb_fheyjghcfZkkuwd\b\Ze_glZ
M
)
)
SO
(
Al
(
6
1
3
4
2
=
6
)
)
SO
(
Al(
3
4
2
M
]fhev
Ijbf_j
Hij_^_eblvwd\b\Ze_glbjZkkqblZlvagZq_gb_fheyj
gh]hh[t_fZwd\b\Ze_glZk_jh\h^hjh^Z\j_Zdpbb
H
2
S
–2
+ 8HNO
3
:+
2
S
+6
O
4
+ 8NO
2
+ 4H
2
O.
J_r_gb_
GZoh^bf qbkeh wd\b\Ze_glghklb G
2
S Ihkdhevdm \ fhe_dme_
k_jh\h^hjh^Zkl_i_gvhdbke_gbyk_jujZ\gZ–Z\fhe_dme_k_jghc
dbkehlu hgZ jZ\gZ^_eZ_f \u\h^ qlhfhe_dme_H
2
Skhhl\_lkl
\mxlwe_dljhgh\WlhagZqblqlhqbkehwd\b\Ze_glghklbz
*
k_jh
\h^hjh^Z\^Zgghcj_ZdpbbjZ\gh
GZoh^bfnZdlhjwd\b\Ze_glghklbk_jh\h^hjh^Zbhij_^_ey_f
_]hwd\b\Ze_gl
we_dljhgZfkhhl\_lkl\m_l fhe_dmeZG
2
S,
we_dljhgm - " - xfhe_dmehldm^Zx = 1/8.
Wlh agZqbl qlh obfbq_kdbf wd\b\Ze_glhf k_jh\h^hjh^Z \ ^Zg
ghcj_Zdpbby\ey_lkymkeh\gZyqZklbpZ–\hkvfZyqZklv_]hfhe_dmeu
GZoh^bfagZq_gb_fheyjgh]hh[t_fZwd\b\Ze_glZk_jh\h^hjh^Z
V
m
)
S
H(
8
1
2
=
8
m
V
=
8
efhev
4,22
efhev
Ijbf_j
G_ba\_klgucf_lZeefZkkhc]kh`]eb\dbkehjh^_
bihemqbebhdkb^f_lZeeZfZkkhc]Hij_^_eblvf_lZee
J_r_gb_
AZibr_fh[smxko_fmj_ZdpbbF_
0
H
0
2
:F_
x
+
2
H
2
−
x
.
14
< khhl\_lkl\bb k aZdhghf wd\b\Ze_glh\ obfbq_kdh_ dhebq_kl\h
wd\b\Ze_glZ f_lZeeZ jZ\gh obfbq_kdhfm dhebq_kl\m wd\b\Ze_glZ
dbkehjh^Z
n
)
Me(
1
*
z
=
)
O(
1
2
*
z
n
=>
=
)
O
(
1
)
O
(
)
Me
(
1
)
Me
(
2
*
2
*
z
M
m
z
M
m
.
A^_kv m(Me) –fZkkZf_lZeeZ\klmib\r_]h\j_Zdpbx
m(O
2
) –fZkkZdbkehjh^Z\klmib\r_]h\j_Zdpbx
)
Me
(
1
*
z
M
–fheyjgZyfZkkZwd\b\Ze_glZf_lZeeZ
)
O
(
1
2
*
z
M
–fheyjgZyfZkkZwd\b\Ze_glZdbkehjh^Z
GZc^_ffZkkmdbkehjh^Z\klmib\r_]h\j_Zdpbx
m(O
2
) = mhdkb^Z– mf_lZeeZ ]–] ]
GZc^_ffheyjgmxfZkkmwd\b\Ze_glZfhe_dmeyjgh]hdbkehjh
^ZIjbh[jZah\Zgbbhdkb^ZdZ`^Zyfhe_dmeZdbkehjh^Zijbkh_^bgy_l
we_dljhgZbij_\jZsZ_lky\hdkb^-bhgZO
0
2
:O
–2
.
Lh]^Z we_dljhgZfkhhl\_lkl\m_lfhe_dmeZH
2
,
we_dljhgm - " - xfhe_dmehldm^Zx = 1/4.
Wlh agZqbl qlh obfbq_kdbf wd\b\Ze_glhf dbkehjh^Z \ ^Zgghc
j_Zdpbby\ey_lkymkeh\gZyqZklbpZ–q_l\_jlZyqZklvfhe_dmeuGZc
^_fagZq_gb_fheyjghcfZkkuwd\b\Ze_glZdbkehjh^Z
M
)
O(
4
1
2
= ]fhev
8
4
32
4
)
O
(
2
==
M
.
Ih^klZ\bf qbkeh\u_ agZq_gby \_ebqbg \ \ujZ`_gb_ aZdhgZ
wd\b\Ze_glh\
M
)
Me(
1
*
z
=
89
,
8
8
10
)
O
(
)
O
(
1
)
Me
(
2
2
*
⋅
=
⋅
m
z
Mm
]fhev
>eyf_lZeeZqbkehwd\b\Ze_glghklbz
*
jZ\ghkl_i_gb_]hhdbk
e_gby\kh_^bg_gbbIhkdhevdmM
(Me) =
M
)
Me(
1
*
z
·
z
*
lhijb
z
*
= 1
FF_ ]fhev
z
*
= 2
FF_ ]fhev
z
*
= 3
FF_ ]fhev
15
H^gh\Ze_glgh]h f_lZeeZ k fheyjghc fZkkhc]fhev b ^\mo\Z
e_glgh]hf_lZeeZkfheyjghcfZkkhc]fhevg_kms_kl\m_lLj_o
\Ze_glgucf_lZeekfheyjghcfZkkhc–ZexfbgbcAl).
Ijbf_j
IjbjZkl\hj_gbb\dbkehl_f_lZeeZfZkkhc]\u
^_ebeky\h^hjh^h[t_fhfegmHij_^_eblvf_lZee
J_r_gb_
AZibr_fh[smxko_fmj_ZdpbbF_
0
+ nH
+
:Me
n+
+
2
n
H
0
2
.
<khhl\_lkl\bbkaZdhghfwd\b\Ze_glh\dhebq_kl\h\_s_kl\Zwd
\b\Ze_glZf_lZeeZjZ\ghdhebq_kl\m\_s_kl\Zwd\b\Ze_glZ\h^hjh^Z
Ke_^h\Zl_evgh
=
)
H
(
1
)
H
(
)
Me
(
1
)
Me
(
2
*
2
*
z
V
V
z
M
m
m
.
A^_kv m(Me) –fZkkZf_lZeeZ
V(H
2
) –h[t_f\h^hjh^Z
M
)
Me(
1
*
z
–fheyjgZyfZkkZwd\b\Ze_glZf_lZeeZ
)
H
(
1
2
*
z
V
m
–fheyjguch[t_fwd\b\Ze_glZ\h^hjh^Z
JZkkqblZ_fagZq_gb_fheyjgh]hh[t_fZwd\b\Ze_glZ\h^hjh^Z
Ihkdhevdmfhe_dmeZ\h^hjh^Zh[jZam_lkyihko_f_H
+
:H
0
2
lh
jZkkm`^Z_flZd
we_dljhgZfkhhl\_lkl\m_lfhe_dmeZG
2
,
we_dljhgmkhhl\_lkl\m_lxfhe_dmehldm^Zx =
2
1
.
LZdbfh[jZahfwd\b\Ze_glhf\h^hjh^Z\^Zgghcj_Zdpbby\ey_l
ky mkeh\gZy qZklbpZ – iheh\bgZ _]h fhe_dmeu Ihwlhfm fheyjguc
h[t_fwd\b\Ze_glZ\h^hjh^Z[m^_ljZ\_g
V
m
)
H(
2
1
2
= efhev
2
,
11
2
4
,
22
2
==
m
V
.
Ih^klZ\bfagZq_gby\_ebqbg\\ujZ`_gb_aZdhgZwd\b\Ze_glh\
gZc^_ffheyjgmxfZkkmwd\b\Ze_glZf_lZeeZbhij_^_ebff_lZee
M
)
Me(
1
*
z
=
72
,
6
2
,
11
58
,
9
)
H
(
)
H
(
1
)
Me
(
2
2
*
⋅
=
⋅
V
z
Vm
m
]fhev
16
IhkdhevdmF
)
Me(
1
*
z
=
*
)
Me(
z
M
lhfheyjgZyfZkkZf_lZeeZ[m
^_l\ujZ`ZlvkyM(Me) = M
)
Me(
1
*
z
·z
*
,
=^_z
*
bebKfijbf_j
Ijbz
*
= 1
FF_ ]fhev
ijbz
*
= 2
FF_ ]fhev
ijbz
*
= 3
FF_ ]fhev
H^gh
-
b^\mo\Ze_glgh]hf_lZeeh\kgZc^_ggufbagZq_gbyfbfh
eyjguofZkkg_kms_kl\m_llj_o\Ze_glgucf_lZeekfheyjghcfZkkhc
]fhev
–
lblZg7L
Ijbf_j
Baoehjb^Zg_ba\_klgh]hf_lZeeZfZkkhc]ihem
q_ggbljZlwlh]h`_f_lZeeZfZkkhc]Hij_^_eblvf_lZee
J_r_gb_
Ihkdhevdm obfbq_kdh_ dhebq_kl\h wd\b\Ze_glZ oehjb^Z f_
lZeeZjZ\ghobfbq_kdhfmdhebq_kl\mwd\b\Ze_glZ_]hgbljZlZlh
=
+−+
)
)
NO
(
Me
(
1
)
)
NO
(
Me
(
)
MeCl
(
1
)
Cl
Me
(
3
*
3
*
x
x
x
x
x
x
z
M
m
z
M
m
.
Ijbj_r_gbbih^h[guoaZ^Zqg_h[oh^bfhihfgblvqlhfheyjgZy
fZkkZwd\b\Ze_glZkeh`gh]h\_s_kl\ZjZ\gZkmff_fheyjguofZkkwd
\b\Ze_glh\ _]h khklZ\guo qZkl_c >himklbf qlh fheyjgZy fZkkZwd
\b\Ze_glZg_ba\_klgh]hf_lZeeZjZ\gZx]fhevMqblu\Zyqlhfheyj
gZy fZkkZ wd\b\Ze_glZ oehjb^-ZgbhgZ Cl
–
]fhev Z fheyjgZy
fZkkZ wd\b\Ze_glZ gbljZl-ZgbhgZ NO
−
3
jZ\gZ ]fhev b ih^klZ\b\
agZq_gby\_ebqbg\\ujZ`_gb_aZdhgZwd\b\Ze_glh\ihemqbf
62
64
,
23
5
,
35
34
,
18
+
=
+
xx
hlkx^Zx ]fhev
Hij_^_ebff_lZee
IhkdhevdmM(Me) = M
)
Me(
1
*
z
· z
*
,
]^_ z
*
– kl_i_gv hdbke_gby f_lZeeZ \ kh_^bg_gbb lh ijb
z
*
= 1 Ü FF_ = ]fhevÜ ]fhev–f_lZeeg_kms_kl\m_l
ijbz
*
= 2 · FF_ ]fhevÜ ]fhev–f_lZeedZ^fbc&G
17
AZdhg:\h]Z^jh
<jZ\guoh[t_fZojZaebqguo]Zah\ijbh^bgZdh\uo\g_rgbomkeh
\byo^Z\e_gbbbl_fi_jZlmj_kh^_j`blkyh^bgZdh\h_qbkehfhe_dme
Ijbj_r_gbbaZ^Zqbkihevamxlkyke_^kl\bybawlh]haZdhgZ
IjbghjfZevguomkeh\byo–^Z\e_gbbdIZbl_fi_jZ
lmj_
K beb Dfhev ex[h]h ]ZaZ aZgbfZ_l h[t_f ijbf_jgh
jZ\guc e Hg gZau\Z_lky fheyjguf h[t_fhf ]ZaZ ijb ghjfZev
guo mkeh\byo b h[hagZqZ_lky V
o
m
. ?^bgbpu baf_j_gby – efhev beb
f
3
fhev
Fheyjguch[t_f]ZaZqbke_gghjZ\_ghlghr_gbxh[t_fZ]ZaZd
khhl\_lkl\mxs_fmobfbq_kdhfmdhebq_kl\mwlh]h\_s_kl\Z
)
(
)
(
Xn
XV
V
m
=
.
Hlghkbl_evgZy iehlghklv ]ZaZ O ih ]ZamY – D
y
(X) – [_ajZa
f_jgZy\_ebqbgZjZ\gZyhlghr_gbxfheyjguofZkk^Zgguo]Zah\
)
(
)
(
)
(
YM
XM
X
D
Y
=
.
HgZihdZau\Z_l\hkdhevdhjZa]ZaOe_]q_bebly`_e__]ZaZY_k-
ebboh[t_fuh^bgZdh\uGZijbf_jhlghkbl_evgZyiehlghklvZffbZ-
dZih\h^hjh^m
)
NH(
3
H
2
D
=
]fhev
2
]fhev
17
)
H
(
)
NH
(
2
3
=
M
M
= 8,5.
?keblj_[m_lkygZclbagZq_gb_hlghkbl_evghciehlghklb]ZaZO)
ih \ha^mom lh fheyjgmx fZkkm ]ZaZ O ^_eyl gZ kj_^gxx fheyjgmx
fZkkm\ha^moZF
kjjZ\gmx]fhevGZijbf_jhlghkbl_evgZy
iehlghklvoehjh\h^hjh^Zih\ha^mom
D
(HCl) =
]fhev
29
]fhev
5
,
36
)
.
(
)
HCl
(
=
kjM
M
= 1,259.
Kj_^g_cfheyjghcfZkkhc]Zah\hckf_kbF
gZau\ZxlfZkkmkf_
kb h[t_f dhlhjhc ijb g m jZ\_g e HgZ k\yaZgZ k fheyjgufb
fZkkZfb]Zah\khhlghr_gb_f
F
kf_kb 3(O) · F(O) + 3(Y) · M(Y).
A^_kv3Xb3Y) –h[t_fgu_^heb]Zah\\kf_kbF(XbM(Y) –fh
eyjgu_fZkku]Zah\H[t_fgZy^hey]ZaZ3\kf_kb–\_ebqbgZjZ\
18
gZyhlghr_gbxh[t_fZ]ZaZ O d h[t_fm kf_kbDZdb fZkkh\Zy ^hey
hgZfh`_l\ujZ`Zlvky\^heyo_^bgbpubeb\ijhp_glZo
Iehlghklv]ZaZ!–\_ebqbgZqbke_gghjZ\gZhlghr_gbx_]h
fheyjghcfZkkudfheyjghfmh[t_fm
!(X) =
m
V
XM
)(
.
GZijbf_jiehlghklv\ha^moZijbgmjZ\gZ
! \ha^
efhev
4
,
22
]fhev
29
.)
kj
(
.
=
m
V
M
]e
AZdhg;hcey
–
FZjbhllZ
Ijbihklhygghcl_fi_jZlmj_h[t_f^Zgghcihjpbb]ZaZh[jZl-
ghijhihjpbhgZe_g_]h^Z\e_gbx
Wlh agZqbl qlh ijb m\_ebq_gbb ^Z\e_gby ]ZaZ \ hij_^_e_ggh_
qbkehjZa_]hh[t_fmf_gvrZ_lky\hklhevdh`_jZaIhwlhfmijhba
\_^_gb_^Z\e_gby]ZaZgZ_]hh[t_fijbihklhygghcl_fi_jZlmj_y\ey
_lky\_ebqbghcihklhygghc
p
1
V
1
= p
2
V
2
= const.
Ijbf_j
Ijb ^Z\e_gbb dIZ h[t_f ]ZaZ jZ\_ge <u
qbkeblvagZq_gb_h[t_fZ^Zgghcihjpbb]ZaZijb^Z\e_gbbdIZ
J_r_gb_
BamjZ\g_gby;hcey-FZjbhllZ\ujZabfV
2
bgZc^_f_]hagZq_gb_
e
3
,
6
6
,
162
4
,
10
5
,
98
2
1
1
2
=
⋅
==
p
Vp
V
.
AZdhg=_c
-
ExkkZdZ
Ijb ihklhygghf ^Z\e_gbb h[t_f ^Zgghc ihjpbb ]ZaZ ijyfh
ijhihjpbhgZe_g_]hZ[khexlghcl_fi_jZlmj_
WlhagZqblqlhijbm\_ebq_gbbZ[khexlghcl_fi_jZlmju]ZaZ\
hij_^_e_ggh_qbkeh jZa _]h h[t_f m\_ebqb\Z_lky \h klhevdh `_jZa
Ihwlhfm hlghr_gb_ h[t_fZ ]ZaZ d _]h Z[khexlghc l_fi_jZlmj_ ijb
ihklhygghf^Z\e_gbby\ey_lkyihklhygghc\_ebqbghc
const
2
2
1
1
==
T
V
T
V
.
19
Ijbf_j
Ijbl_fi_jZlmj_
Kh[t_f]ZaZjZ\_ge<u
qbkeblvagZq_gb_h[t_fZ^Zggh]h]ZaZijbl_fi_jZlmj_18
K
J_r_gb_
JZkkqblZ_fZ[khexlgu_agZq_gbyl_fi_jZlmju
ZT
1
= t
1
+ 273 = 18 + 273 = 291 K;
[) T
2
= t
2
+ 273 = 118 + 273 = 391 K.
Ba mjZ\g_gby=_c-ExkkZdZ \ujZabf V
2
b jZkkqblZ_f_]h agZ
q_gb_
e
03
,
9
291
391
72
,
6
1
2
1
2
=
⋅
==
T
TV
V
.
H[t_^bg_gguc]Zah\ucaZdhg
Ijhba\_^_gb_\_ebqbgu^Z\e_gby^Zgghcihjpbb]ZaZgZ\_ebqbgm
_]hh[t_fZhlg_k_ggh_dagZq_gbxZ[khexlghcl_fi_jZlmju_klv
\_ebqbgZihklhyggZy
const
1
1
1
0
0
0
==
T
Vp
T
Vp
.
WlhmjZ\g_gb_gZau\Z_lkymjZ\g_gb_fDeZi_cjhgZ?]hqZklhbk
ihevamxl^eyjZkq_lZh[t_fZ]ZaZijbghjfZevguomkeh\byo_kebba
\_klgh_]hagZq_gb_ijb^jm]bomkeh\byo
Ijbf_j
Ijbl_fi_jZlmj_
Kb^Z\e_gbbdIZh[t_f]Z
aZjZ\_ge<uqbkeblvagZq_gb_h[t_fZ]ZaZijbghjfZevguomk
eh\byo
J_r_gb_
Ba mjZ\g_gby h[t_^bg_ggh]h]Zah\h]haZdhgZ \ujZabf V
0
b jZk
kqblZ_f_]hagZq_gb_
e
2
,
70
318
3
,
101
4
,
120
8
,
68
273
1
0
1
1
0
0
=
⋅
⋅⋅
==
Tp
VpT
V
.
?kebobfbq_kdh_dhebq_kl\h]ZaZjZ\ghfhevlhagZq_gb_^jh
[b
T
p
V
y\ey_lky ihklhygghc \_ebqbghc b gZau\Z_lkymgb\_jkZevghc
]Zah\hcihklhygghcR <kemqZ_dh]^Z^Z\e_gb_]ZaZ\ujZ`Z_lky\
dIZ Z h[t_f – \ ebljZo lh R ijbgbfZ_l agZq_gb_ jZ\gh_
8,314 >`fhev · KKmq_lhfwlh]h^eyfhev]ZaZfh`ghaZibkZlv
R
T
pV
=
bebpV = RT.
20
?keb`_obfbq_kdh_dhebq_kl\h]Zahh[jZagh]h\_s_kl\ZjZ\ghn
fhevlh
pV = nRT.
WlhmjZ\g_gb_gZau\Z_lkymjZ\g_gb_fDeZi_cjhgZ – F_g^_e__\Z.
Mqblu\Zyqlh
M
m
n
=
^Zggh_mjZ\g_gb_fh`ghaZibkZlv\\b^_
.
R
T
M
m
pV
=
Hghk\yau\Z_lfZl_fZlbq_kdb^Z\e_gb_]ZaZ_]hh[t_ffZkkmb
l_fi_jZlmjm >Zggh_mjZ\g_gb_iha\hey_l\uqbkeblv ex[mxba\oh
^ysbo\g_]h\_ebqbg_kebba\_klguhklZevgu_\_ebqbgu
Ijbf_j
<uqbkeblvagZq_gb_fheyjghcfZkku\_s_kl\Z_keb
_]hiZjufZkkhc]ijbl_fi_jZlmj_
o
Kb^Z\e_gbbdIZaZ
gbfZxlh[t_fjZ\gucfe
J_r_gb_
Ba mjZ\g_gby DeZi_cjhgZ-F_g^_e__\Z \ujZabf M b jZkkqblZ_f
__agZq_gb_
]fhev
78
2
,
1
2
,
83
360
314
,
8
6
,
2
=
⋅
⋅⋅
==
pV
mRT
M
AZdhgiZjpbZevguo^Z\e_gbc]Zah\
H[s__^Z\e_gb_ kf_kb]Zah\g_ \klmiZxsbo\obfbq_kdh_\aZb
fh^_ckl\b_ jZ\ghkmff_iZjpbZevguo^Z\e_gbcdZ`^h]hbagbo
P
j
(1)
j
(2)
+ …
j
(n)
.
IZjpbZevgh_ ^Z\e_gb_ ]ZaZj
–^Z\e_gb_dhlhjh_ijhba\h^be
[uwlhl]Za_keb[uhgh^bgijbl_o`_mkeh\byoaZgbfZe\_kvh[t_f
]Zah\hckf_kb
IZjpbZevgh_^Z\e_gb_]ZaZ\kf_kbijhihjpbhgZevgh_]hh[t_f
ghc^he_
j
(1)
=
J
3
(1)
.
Ijbf_j
H[s__ ^Z\e_gb_ kf_kb khklhys_c ba ZahlZ fZkkhc
14 ]bdbkehjh^ZfZkkhc]jZ\ghdIZ<uqbkeblvagZq_gbyiZj
pbZevguo^Z\e_gbc]Zah\\kf_kb
J_r_gb_
Ihkdhevdm \ kf_kb h[t_fgu_ ^heb ]Zah\ qbke_ggh jZ\gu bo
fhevguf^heyflh\^ZgghfkemqZ_iZjpbZevgu_^Z\e_gby]Zah\[m
^mlijhihjpbhgZevgubofhevguf^heyf