封闭体系中碳酸盐的平衡

封闭体系中碳酸盐的平衡

求算封闭体系：c T=常数=3×10-3mol/L时，CaCO3的溶解度？解：在封闭体系，c T=常数，本题以c T =3×10-3mol/L为例。

查表可知碳酸钙的溶度积：Ksp=[Ca2+][CO32-]=10-8.32

∵在碳酸钙溶液中存在如下平衡：

CaCO3 ⇌Ca2+ + CO32-K sp = [Ca2+][CO32-] = 10-8.23 (1)

∴[Ca2+] =

K sp

[CO32-]= K sp/( c T a2) (2)

∴lg[Ca2+] = lgK sp - lgc T - lgα2 (3)

lg[CO32-] = lgK sp - lg[Ca2+]= lgc T + lgα2 (4)

又∵α2与H+浓度的关系为：α2 = (1 + [H+]2

K1K2+

[H+]

K2)

-1 (5)

将（5）代入（3）、（4）得到lg[Ca2+]和lg[CO32-]关于[H+]的关系式。

在Excel中求不同pH下的lg[Ca2+]和lg[CO32-]列表如表1：

表1 ：不同pH下碳酸钙溶液中各种离子的浓度

pH c T K SP K1 K2 [H+] lga2 lg[Ca2+] lg[CO32+] 4.0 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.0000E-04 -8.6819 2.8848 -11.2048 4.2 0.003 4.7863E-09 4.4668E-07 4.6774E-11 6.3096E-05 -8.2831 2.4859 -10.8059 4.4 0.003 4.7863E-09 4.4668E-07 4.6774E-11 3.9811E-05 -7.8848 2.0877 -10.4077 4.6 0.003 4.7863E-09 4.4668E-07 4.6774E-11 2.5119E-05 -7.4877 1.6905 -10.0105

4.8 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.5849E-05 -7.0921 1.2949 -9.6149

5.0 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.0000E-05 -

6.6990 0.9019 -9.2219 5.2 0.003 4.7863E-09 4.4668E-07 4.6774E-11 6.3096E-06 -6.3097 0.5126 -8.8326 5.4 0.003 4.7863E-09 4.4668E-07 4.6774E-11 3.9811E-06 -5.9262 0.1291 -8.4491 5.6 0.003 4.7863E-09 4.4668E-07 4.6774E-11 2.5119E-06 -5.5511 -0.2460 -8.0740

5.8 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.5849E-06 -5.1878 -0.6093 -7.7107

6.0 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.0000E-06 -4.8404 -0.9567 -

7.3633 6.2 0.003 4.7863E-09 4.4668E-07 4.6774E-11 6.3096E-07 -4.5125 -1.2846 -7.0354 6.4 0.003 4.7863E-09 4.4668E-07 4.6774E-11 3.9811E-07 -4.2068 -1.5903 -6.7297 6.6 0.003 4.7863E-09 4.4668E-07 4.6774E-11 2.5119E-07 -3.9238 -1.8733 -6.4467

6.8 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.5849E-07 -3.6620 -2.1351 -6.1849

7.0 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.0000E-07 -3.4179 -2.3792 -5.9408 7.2 0.003 4.7863E-09 4.4668E-07 4.6774E-11 6.3096E-08 -3.1877 -2.6095 -5.7105 7.4 0.003 4.7863E-09 4.4668E-07 4.6774E-11 3.9811E-08 -2.9675 -2.8296 -5.4904 7.6 0.003 4.7863E-09 4.4668E-07 4.6774E-11 2.5119E-08 -2.7545 -3.0426 -5.2774

7.8 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.5849E-08 -2.5464 -3.2507 -5.0693

8.0 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.0000E-08 -2.3416 -3.4555 -4.8645 8.2 0.003 4.7863E-09 4.4668E-07 4.6774E-11 6.3096E-09 -2.1393 -3.6579 -4.6621 8.4 0.003 4.7863E-09 4.4668E-07 4.6774E-11 3.9811E-09 -1.9389 -3.8582 -4.4618 8.6 0.003 4.7863E-09 4.4668E-07 4.6774E-11 2.5119E-09 -1.7404 -4.0567 -4.2633

8.8 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.5849E-09 -1.5441 -4.2530 -4.0670

9.0 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.0000E-09 -1.3508 -4.4463 -3.8737 9.2 0.003 4.7863E-09 4.4668E-07 4.6774E-11 6.3096E-10 -1.1616 -4.6355 -3.6845 9.4 0.003 4.7863E-09 4.4668E-07 4.6774E-11 3.9811E-10 -0.9786 -4.8185 -3.5015 9.6 0.003 4.7863E-09 4.4668E-07 4.6774E-11 2.5119E-10 -0.8044 -4.9928 -3.3272

9.8 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.5849E-10 -0.6424 -5.1547 -3.1653

10.0 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.0000E-10 -0.4967 -5.3004 -3.0196 10.2 0.003 4.7863E-09 4.4668E-07 4.6774E-11 6.3096E-11 -0.3709 -5.4262 -2.8938 10.4 0.003 4.7863E-09 4.4668E-07 4.6774E-11 3.9811E-11 -0.2675 -5.5297 -2.7903 10.6 0.003 4.7863E-09 4.4668E-07 4.6774E-11 2.5119E-11 -0.1867 -5.6104 -2.7096

10.8 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.5849E-11 -0.1267 -5.6704 -2.6496

11.0 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.0000E-11 -0.0841 -5.7130 -2.6070 11.2 0.003 4.7863E-09 4.4668E-07 4.6774E-11 6.3096E-12 -0.0550 -5.7422 -2.5778 11.4 0.003 4.7863E-09 4.4668E-07 4.6774E-11 3.9811E-12 -0.0355 -5.7616 -2.5584 11.6 0.003 4.7863E-09 4.4668E-07 4.6774E-11 2.5119E-12 -0.0227 -5.7744 -2.5456

11.8 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.5849E-12 -0.0145 -5.7826 -2.5374

12.0 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.0000E-12 -0.0092 -5.7879 -2.5321 12.2 0.003 4.7863E-09 4.4668E-07 4.6774E-11 6.3096E-13 -0.0058 -5.7913 -2.5287 12.4 0.003 4.7863E-09 4.4668E-07 4.6774E-11 3.9811E-13 -0.0037 -5.7934 -2.5266 12.6 0.003 4.7863E-09 4.4668E-07 4.6774E-11 2.5119E-13 -0.0023 -5.7948 -2.5252

12.8 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.5849E-13 -0.0015 -5.7957 -2.5243

13.0 0.003 4.7863E-09 4.4668E-07 4.6774E-11 1.0000E-13 -0.0009 -5.7962 -2.5238 13.2 0.003 4.7863E-09 4.4668E-07 4.6774E-11 6.3096E-14 -0.0006 -5.7965 -2.5235 13.4 0.003 4.7863E-09 4.4668E-07 4.6774E-11 3.9811E-14 -0.0004 -5.7968 -2.5232 13.6 0.003 4.7863E-09 4.4668E-07 4.6774E-11 2.5119E-14 -0.0002 -5.7969 -2.5231