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Файл:Расчет констант кислотно-основных свойств наночастиц оксидных суспензий с помощью программ Mathcad. Учебное пособие
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Ɍɢɬɪɨɜɚɧɢɟ ɨɤɫɢɞɧɵɯ ɫɭɫɩɟɧɡɢɣ
¨©·
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¹
R ʟ= 8.314 ɭɧɢɜɟɪɫɚɥɶɧɚɹ ɝɚɡɨɜɚɹ ɩɨɫɬɨɹɧɧɚɹ (
T ʟ= 303 ɬɟɦɩɟɪɚɬɭɪɚ (Ʉ)
F ʟ= 96485 ɩɨɫɬɨɹɧɧɚɹ Ɏɚɪɚɞɟɹ (
C ʟ= 0. 1 ɤɨɧɰɟɧɬɪɚɰɢɹ ɮɨɧɨɜɨɝɨ ɷɥɟɤɬɪɨɥɢɬɚ (ɦɨɥɶ/ɥ)
pH0 ʟ= 7.4 pH ɬɨɱɤɢ ɧɭɥɟɜɨɝɨ ɡɚɪɹɞɚ
m ʟ= 100 ɦɚɫɫɚ ɧɚɜɟɫɤɢ ɜ ɩɟɪɟɫɱɟɬɟ ɧɚ ɥɢɬɪ (ɝ/ɥ)
S ʟ= 10 × 10
k01 ʟ= 160 × 10
4
ɩɥɨɳɚɞɶ ɩɨɜɟɪɯɧɨɫɬɢ ɧɚɜɟɫɤɢ (ɫɦ2/ɝ)
–6
ɟɦɤɨɫɬɶ ɜɧɭɬɪɟɧɧɟɣ ɱɚɫɬɢ Ⱦɗɋ (Ɏ/ɫɦ2)
Ȗ ʟ= 1 ɤɨɷɮɮɢɰɢɟɧɬ ɚɤɬɢɜɧɨɫɬɢ H
i ORIGIN rows pH
ɞɢɚɩɚɡɨɧ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɯ ɬɨɱɟɤ
end
Ȼɥɨɤ ɪɚɫɱɟɬɚ ɜɟɥɢɱɢɧɵ ɚɞɫɨɪɛɰɢɢ ɜ ɤɚɠɞɨɣ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɬɨɱɤɟ
pH
ori
10
G
pH
i
end
10
i
Ȼɥɨɤ ɪɚɫɱɟɬɚ ɡɚɪɹɞɚ q
F
q0G
ɪɚɫɱɟɬ q
mS
ɜ ɤɚɠɞɨɣ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɬɨɱɤɟ
0
(Ʉɥ/ɫɦ2) ɜ ɤɚɠɞɨɣ ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɨɣ ɬɨɱɤɟ
0
Ȼɥɨɤ ɜɜɨɞɚ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɡɚɪɹɞɚ (q
) ɨɬ ɪɚɡɥɢɱɧɵɯ ɩɚɪɚɦɟɬɪɨɜ
0
ɬɟɨɪɟɬɢɱɟɫɤɚɹ ɡɚɜɢɫɢɦɨɫɬɶ ɩɨɬɟɧɰɢɚɥɚ ij (ȼ) ɨɬ pH
ph
§
I ph() J
RT
ln
10
F
10
pH0
ȽɅȺȼȺ 4.
Ⱦɠ
)
ɦɨɥɶ·Ʉ
Ʉɥ
)
ɦɨɥɶ
+
ɩɨɞɛɨɪ ɡɧɚɱɟɧɢɣ ɨɬɧɨɲɟɧɢɣ ɤɨɧɫɬɚɧɬ (ɫɜɟɪɯɭ ɜɧɢɡ – B
6
§
710
B
¨
©
50
700
¸
, B2, B3)
1
ɮɭɧɤɰɢɹ (ɩɪɟɨɛɪɚɡɨɜɚɧɧɨɟ ɭɪɚɜɧɟɧɢɟ) ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɡɚɜɢɫɢɦɨɫɬɢ ɡɚɪɹɞɚ
ɨɬ ɪɚɡɥɢɱɧɵɯ ɩɚɪɚɦɟɬɪɨɜ
q
0
pH0
B
C sinh ln
1B2
f1 B ph qx
q
©
x
§
C cosh ln
cosh I ph()
B
2
10
sinh I ph()
§
§
ph
10
©
©
pH0
·
10
ph
10
¹
qxF
k01 R T
qxF
k01 R T
F
©
ln
ln
RT
F
RT
¹
·
§
pH0
10
§
ph
10
©
10
10
¹
¹
pH0
¹
·
·
·
ph
B3
51
ɂ. Ƚ. ȽɈɊɂɑȿȼ, Ɍ. Ʉ. ȺɌȺɇȺɋəɇ, ɉ. ɂ. ɆɂɊɁɈəɇ. Ɋɚɫɱɟɬ ɤɨɧɫɬɚɧɬ ɤɢɫɥɨɬɧɨ-ɨɫɧɨɜɧɵɯ ɫɜɨɣɫɬɜ
p
¨
·
¸
¹
¨
·
¸
¹
2
ɧɚɧɨɱɚɫɬɢɰ ɨɤɫɢɞɧɵɯ ɫɭɫɩɟɧɡɢɣ ɫ ɩɨɦɨɳɶɸ ɩɪɨɝɪɚɦɦ Mathcad
qx 0
ɭɫɬɚɧɨɜɤɚ ɧɚɱɚɥɶɧɨɝɨ ɩɪɢɛɥɢɠɟɧɢɹ
q0 ( ph ) ʟ
root f1 B ph qx()qx()
ɬɟɨɪɟɬɢɱɟɫɤɚɹ ɡɚɜɢɫɢɦɨɫɬɶ q(pH)
=
Ȼɥɨɤ ɩɨɞɛɨɪɚ ɨɬɧɨɲɟɧɢɣ ɤɨɧɫɬɚɧɬ (B
ɂɡɦɟɧɟɧɢɟ ɡɧɚɱɟɧɢɣ B
, B2, B3 ɜ ɩɪɟɞɵɞɭɳɟɦ ɛɥɨɤɟ ɞɨ ɫɨɨɬɜɟɬɫɬɜɢɹ ɬɟɨ-
1
, B2, B3)
1
ɪɟɬɢɱɟɫɤɨɣ ɡɚɜɢɫɢɦɨɫɬɢ q(pH) ɷɤɫɩɟɪɢɦɟɧɬɚɥɶɧɵɦ ɞɚɧɧɵɦ
ɝɪɚɮɢɤ ɫɨɨɬɜɟɬɫɬɜɢɹ ɬɟɨɪɟɬɢɱɟɫɤɨɣ ɡɚɜɢɫɢɦɨɫɬɢ q(pH) ɷɤɫɩɟɪɢɦɟɧ-
Ʉɥ/ɫɦ
ɬɚɥɶɧɵɦ ɞɚɧɧɵɦ
q
0
q0 ph()
Ȼɥɨɤ ɪɚɫɱɟɬɚ ɤɨɧɫɬɚɧɬ
K1B32 10
pK1log K
K
3
pK3log K
pK
2
K210
pK4pH0 2 pK3
K410
H0
ɧɚɯɨɠɞɟɧɢɟ K
ɧɚɯɨɠɞɟɧɢɟ pK
1
K
1
ɧɚɯɨɠɞɟɧɢɟ K
B
2
ɧɚɯɨɠɞɟɧɢɟ pK
3
pH0 2 pK1
pK2
ɧɚɯɨɠɞɟɧɢɟ pK
ɧɚɯɨɠɞɟɧɢɟ K
ɧɚɯɨɠɞɟɧɢɟ pK
pK4
ɧɚɯɨɠɞɟɧɢɟ K
K
5106u
5 106u
§
5.574 10
¨
2.844 10
¨
1.115 10
¨
1.422 10
©
0
4 6 8 10
pH
ph
end
ɧɚɯɨɠɞɟɧɢɟ ɦɚɫɫɢɜɨɜ ɡɧɚɱɟɧɢɣ K ɢ pK:
ɩɪɟɞɫɬɚɜɥɟɧɢɟ ɪɟɡɭɥɶɬɚɬɚ ɜ ɭɞɨɛɧɨɣ ɮɨɪɦɟ
5
u
¸
11
u
¸
6
u
u
¸
9
pK
4.254
§
10.546
¨
¨
5.953
8.847
©
¸
¸
1
1
3
3
2
2
4
4
52
Ɂɚɜɢɫɢɦɨɫɬɶ pK ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɮɨɧɨɜɨɝɨ ɷɥɟɤɬɪɨɥɢɬɚ
ට
ɢɫɯɨɞɧɵɟ ɬɨɱɤɢ – ɬɟɤɭɳɢɟ ɡɧɚɱɟɧɢɹ pK
Ɍɢɬɪɨɜɚɧɢɟ ɨɤɫɢɞɧɵɯ ɫɭɫɩɟɧɡɢɣ
ȽɅȺȼȺ 4.
x01()
y1 pK1pK
y2 pK
T
T
2pK4
3
T
ɩɨɥɭɱɟɧɢɟ ɤɨɷɮɮɢɰɢɟɧɬɨɜ ɞɥɹ ɩɨɫɬɪɨɟɧɢɹ ɡɚɜɢɫɢɦɨɫɬɢ
reg1 regress x y1 1()
reg2 regress x y2 1()
ɡɚɜɢɫɢɦɨɫɬɢ pK ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɮɨɧɨɜɨɝɨ ɷɥɟɤɬɪɨɥɢɬɚ
pk1 c( ) interp reg1 x y1 c()
pk2 c( ) interp reg2 x y2 c()
C ʟ= 0 .. 3 ɞɢɚɩɚɡɨɧ ɡɧɚɱɟɧɢɣ ɤɨɧɰɟɧɬɪɚɰɢɢ ɮɨɧɚ ɞɥɹ ɝɪɚɮɢɤɚ
ɝɪɚɮɢɤ ɡɚɜɢɫɢɦɨɫɬɢ pK ɨɬ ɤɨɧɰɟɧɬɪɚɰɢɢ ɮɨɧɨɜɨɝɨ ɷɥɟɤɬɪɨɥɢɬɚ
12
pK
2
10
pK
pK
4
pH
0
3
y1
pk1 C()
y2
pk2 C()
8
6
pK
1
4
0 1 2
xC x C
ɦɨɥɶ
ɥ
53
ɁȺɄɅɘɑȿɇɂȿ
Ɋɚɡɪɚɛɨɬɚɧɵ ɱɟɬɵɪɟ ɦɟɬɨɞɢɤɢ ɨɩɪɟɞɟɥɟɧɢɹ ɤɨɧɫɬɚɧɬ ɤɢɫɥɨɬɧɨɨɫɧɨɜɧɵɯ ɫɜɨɣɫɬɜ ɧɚɧɨɱɚɫɬɢɰ ɨɤɫɢɞɧɵɯ ɫɭɫɩɟɧɡɢɣ. ɉɪɢɦɟɧɹɟɦɵɟ ɫɩɨɫɨɛɵ
ɪɚɫɱɟɬɚ ɤɨɧɫɬɚɧɬ ɨɫɧɨɜɚɧɵ ɧɚ ɢɫɩɨɥɶɡɨɜɚɧɢɢ ɨɫɧɨɜɧɵɯ ɩɚɪɚɦɟɬɪɨɜ ɞɜɨɣɧɨɝɨ
ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɫɥɨɹ, ɜɨɡɧɢɤɚɸɳɟɝɨ ɧɚ ɝɪɚɧɢɰɟ ɨɤɫɢɞ/ɷɥɟɤɬɪɨɥɢɬ. ȼ ɨɫɧɨɜɭ
ɩɪɟɞɥɚɝɚɟɦɵɯ ɦɟɬɨɞɨɜ ɩɨɥɨɠɟɧɚ ɢɞɟɹ ɨ ɬɨɦ, ɱɬɨ ɤɢɫɥɨɬɧɨ-ɨɫɧɨɜɧɵɟ ɫɜɨɣɫɬɜɚ
ɨɩɪɟɞɟɥɹɸɬɫɹ ɜɟɥɢɱɢɧɨɣ ɩɨɬɟɧɰɢɚɥɚ ɢ ɩɨɜɟɪɯɧɨɫɬɧɨɝɨ ɡɚɪɹɞɚ.
ɉɪɢ ɪɚɫɱɟɬɚɯ ɩɪɢɦɟɧɹɟɬɫɹ
ɦɨɞɟɥɶ ɬɪɟɯɫɥɨɣɧɨɝɨ ɫɬɪɨɟɧɢɹ ɞɜɨɣɧɨɝɨ
ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɫɥɨɹ, ɫɨɨɬɜɟɬɫɬɜɭɸɳɚɹ ɦɨɞɟɥɢ Ƚɪɷɦɚ-ɉɚɪɫɨɧɫɚ, ɤɨɬɨɪɚɹ ɬɪɟɛɭɟɬ ɭɱɟɬɚ ɫɟɦɢ ɩɚɪɚɦɟɬɪɨɜ: pH, ɤɨɧɰɟɧɬɪɚɰɢɢ ɮɨɧɨɜɨɝɨ ɷɥɟɤɬɪɨɥɢɬɚ, ɜɧɭɬɪɟɧɧɟɣ ɢ ɜɧɟɲɧɟɣ ɟɦɤɨɫɬɢ Ⱦɗɋ, ɨɛɳɟɝɨ ɤɨɥɢɱɟɫɬɜɚ ɚɤɬɢɜɧɵɯ ɰɟɧɬɪɨɜ, pH
ɬɨɱɤɢ ɧɭɥɟɜɨɝɨ ɡɚɪɹɞɚ, ɜɟɥɢɱɢɧɵ ɩɨɬɟɧɰɢɚɥɚ, ɚ ɬɚɤɠɟ ɞɪɭɝɢɯ ɩɚɪɚɦɟɬɪɨɜ. ȿɫɥɢ ɧɟ ɭɱɢɬɵɜɚɬɶ ɜɟɥɢɱɢɧɭ ɩɨɬɟɧɰɢɚɥɚ, ɬɨ ɩɨɥɭɱɚɸɬɫɹ ɧɟɩɪɚɜɢɥɶɧɵɟ ɪɚɫɩɪɟɞɟɥɟɧɢɹ ɢɨɧɨɜ ɨɬ
pH. ɍɱɟɬ ɩɨ ɤɪɚɣɧɟɣ ɦɟɪɟ ɬɪɟɯ ɩɚɪɚɦɟɬɪɨɜ (ɡɚɪɹɞɚ, ɩɨɬɟɧɰɢɚɥɚ ɢ ɟɦɤɨɫɬɢ) ɩɪɢɜɨɞɢɬ ɤ ɩɪɚɜɢɥɶɧɨɦɭ ɪɚɫɱɟɬɧɨɦɭ ɪɚɫɩɪɟɞɟɥɟɧɢɸ ɢɨɧɨɜ
ɜ ɪɚɫɬɜɨɪɟ.
ȼɫɟ ɩɪɨɝɪɚɦɦɵ ɧɚɩɢɫɚɧɵ ɞɥɹ ɪɚɫɬɜɨɪɨɜ ɫɢɦɦɟɬɪɢɱɧɵɯ (1:1) ɷɥɟɤɬɪɨɥɢɬɨɜ. ɉɪɟɞɫɬɚɜɥɹɟɬ ɢɧɬɟɪɟɫ ɪɚɡɪɚɛɨɬɤɚ ɩɪɨɝɪɚɦɦ, ɭɱɢɬɵɜɚɸɳɢɯ ɧɟɫɢɦɦɟɬɪɢɱɧɵɟ (1:2) ɷɥɟɤɬɪɨɥɢɬɵ. Ɇɟɬɨɞɢɱɟɫɤɢ ɧɟ ɪɚɡɪɚɛɨɬɚɧɨ ɜɪɟɦɹ ɜɵɞɟɪɠɤɢ ɫɭɫɩɟɧɡɢɣ, ɩɨɬɨɦɭ ɱɬɨ ɩɪɨɢɫɯɨɞɢɬ ɞɥɢɬɟɥɶɧɚɹ ɝɢɞɪɚɬɚɰɢɹ ɩɨɜɟɪɯɧɨɫɬɢ ɨɤɫɢɞɨɜ,
ɢɡɦɟɧɹɸɳɚɹ
ɬɨɱɤɭ ɧɭɥɟɜɨɝɨ ɡɚɪɹɞɚ, ɱɬɨ ɜɥɟɱɟɬ ɢɡɦɟɧɟɧɢɟ ɤɢɫɥɨɬɧɨ-
ɨɫɧɨɜɧɵɯ ɫɜɨɣɫɬɜ.
Ʌɸɛɨɣ ɨɤɫɢɞ ɢɡɦɟɧɹɟɬ ɫɜɨɸ ɫɬɟɯɢɨɦɟɬɪɢɸ ɜ ɩɪɨɰɟɫɫɟ ɜɡɚɢɦɨɞɟɣɫɬɜɢɹ
ɫ ɷɥɟɤɬɪɨɥɢɬɨɦ. ɉɪɟɞɫɬɚɜɥɹɟɬ ɢɧɬɟɪɟɫ ɜɜɟɫɬɢ ɩɨɩɪɚɜɤɢ ɧɚ ɷɬɢ ɢɡɦɟɧɟɧɢɹ.
ɉɪɟɞɫɬɚɜɥɟɧɧɵɟ ɦɟɬɨɞɵ ɞɚɸɬ ɫɨɝɥɚɫɨɜɚɧɧɨɟ ɡɧɚɱɟɧɢɟ ɤɨɧɫɬɚɧɬ, ɱɬɨ
ɩɨɡɜɨɥɹɟɬ ɞɨɛɢɜɚɬɶɫɹ ɛɨɥɟɟ ɜɵɫɨɤɨɣ ɬɨɱɧɨɫɬɢ ɩɨɤɚɡɚɬɟɥɟɣ pK.
Ʉɚɠɞɵɣ ɦɟɬɨɞ ɩɪɟɞɫɬɚɜɥɟɧ ɜ ɜɢɞɟ ɩɨɞɪɨɛɧɨ ɩɪɨɤɨɦɦɟɧɬɢɪɨɜɚɧɧɨɣ
ɩɪɨɝɪɚɦɦɧɨɣ ɡɚɝɨɬɨɜɤɢ ɞɥɹ ɫɪɟɞɵ Mathcad, ɱɬɨ
ɞɟɥɚɟɬ ɜɨɡɦɨɠɧɵɦ ɢɯ ɢɫɩɨɥɶɡɨɜɚɧɢɟ ɛɟɡ ɝɥɭɛɨɤɢɯ ɡɧɚɧɢɣ ɜɵɫɲɟɣ ɦɚɬɟɦɚɬɢɤɢ ɢ ɧɚɜɵɤɨɜ ɩɪɨɝɪɚɦɦɢɪɨɜɚɧɢɹ. ɇɨ ɩɨɫɤɨɥɶɤɭ ɩɪɟɞɥɨɠɟɧɧɵɟ ɩɪɨɝɪɚɦɦɵ ɜ ɛɨɥɶɲɢɧɫɬɜɟ ɫɥɭɱɚɟɜ ɞɚɸɬ
ɦɧɨɠɟɫɬɜɟɧɧɵɟ ɪɟɲɟɧɢɹ, ɧɟɨɛɯɨɞɢɦɨ ɢɡɵɫɤɢɜɚɬɶ ɧɨɜɵɟ ɦɚɬɟɦɚɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ, ɤɨɬɨɪɵɟ ɦɨɝɥɢ ɛɵ ɞɚɜɚɬɶ ɟɞɢɧɫɬɜɟɧɧɨɟ ɪɟɲɟɧɢɟ ɢɥɢ ɡɧɚɱɢɬɟɥɶɧɨ ɫɨɤɪɚɬɢɬɶ ɢɯ ɤɨɥɢɱɟɫɬɜɨ. Ɍɚɤɠɟ ɩɪɟɞɫɬɚɜɥɹɟɬ ɢɧɬɟɪɟɫ ɪɚɡɪɚɛɨɬɚɬɶ ɚɜɬɨɦɚɬɢɱɟɫɤɢɟ ɦɟɬɨɞɵ ɨɩɪɟɞɟɥɟɧɢɹ
ɡɧɚɱɟɧɢɣ ɫɨɨɬɧɨɲɟɧɢɣ ɤɨɧɫɬɚɧɬ (B1, B2, B3) ɩɪɢ ɢɫ-
ɫɥɟɞɨɜɚɧɢɢ ɡɚɜɢɫɢɦɨɫɬɟɣ ɡɚɪɹɞɚ ɨɬ pH.
54
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ɧɚ ɝɪɚɧɢɰɟ ɨɤɫɢɞ/ɷɥɟɤɬɪɨɥɢɬ // ɗɥɟɤɬɪɨɯɢɦɢɹ. – 1992. – Ɍ. 28. – ȼɵɩ. 1.
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ɪɚɫɱɟɬɚ ɤɨɧɫɬɚɧɬ ɤɢɫɥɨɬɧɨ-ɨɫɧɨɜɧɵɯ ɪɚɜɧɨɜɟɫɢɣ ɧɚ ɝɪɚɧɢɰɟ ɨɤɫɢɞ/ɷɥɟɤɬɪɨɥɢɬ // ɗɥɟɤɬɪɨɯɢɦɢɹ. – 1993. – Ɍ. 29. – ʋ 3. – ɋ. 304–309.
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ɷɥɟɤɬɪɢɱɟɫɤɨɝɨ ɫɥɨɹ ɢ ɤɨɧɫɬɚɧɬ ɤɢɫɥɨɬɧɨ-ɨɫɧɨɜɧɵɯ ɪɚɜɧɨɜɟɫɢɣ ɞɥɹ ɝɪɚɧɢɰɵ
ɨɤɫɢɞ/ɷɥɟɤɬɪɨɥɢɬ ɢɡ ɡɧɚɱɟɧɢɣ ɷɥɟɤɬɪɨɤɢɧɟɬɢɱɟɫɤɨɝɨ ɩɨɬɟɧɰɢɚɥɚ // ɗɥɟɤɬɪɨɯɢɦɢɹ. – 1994. – Ɍ. 30. – ʋ 1. – ɋ. 119–123.
5. Ƚɨɪɢɱɟɜ ɂ. Ƚ., Ⱦɨɪɨɮɟɟɜ Ɇ. ȼ., ɒɚɩɥɵɝɢɧ ɂ. ɋ., Ȼɚɬɪɚɤɨɜ ȼ. ȼ., ɏɨɪɨɲɢɥɨɜ
Ⱥ. ȼ. Ɋɚɫɱɟɬ ɤɨɧɫɬɚɧɬ ɤɢɫɥɨɬɧɨ-ɨɫɧɨɜɧɵɯ ɪɚɜɧɨɜɟɫɢɣ ɧɚ ɝɪɚɧɢɰɟ ɨɤɫɢɞɷɥɟɤɬɪɨɥɢɬ ɩɨ ɡɚɜɢɫɢɦɨɫɬɢ ɡɚɪɹɞɚ ɩɨɜɟɪɯɧɨɫɬɢ ɨɤɫɢɞɚ ɨɬ pH ɷɥɟɤɬɪɨɥɢɬɚ
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Горичев
Игорь Георгиевич
Атанасян Татьяна Климентьевна
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