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## Calculation Method and Application of Multi-Equilibrium Standard Equilibrium Constant

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Received: 2018-05-22   Accepted: 2018-07-10

Abstract

This paper introduces the skillful calculation formula and application scope of multi-equilibrium standard equilibrium constant. It is a simple, fast and accurate approach to solve problems. Moreover, it can also intuitively estimate the directionality and extent of reactions using this formula.

Keywords： Multi-equilibrium ; Standard equilibrium constant ; Skillful ; Calculation formula

LIU Xia. Calculation Method and Application of Multi-Equilibrium Standard Equilibrium Constant. University Chemistry[J], 2019, 34(1): 116-121 doi:10.3866/PKU.DXHX201805033

## 1 多重平衡标准平衡常数的计算公式

(2)反应物或生成物为离子时，且只能是配离子、两性物质HA等时，配离子对应1/$K_{{\rm{f}}}^ \ominus$，HA对应$K_{{\rm{a2}}}^ \ominus$，除此之外的其他离子均不予考虑。

(3)反应物和生成物只有通过解离反应参与了多重平衡时，对应的标准平衡常数才能写入公式中。

### 2.1 沉淀平衡与酸碱平衡

${\rm{Ca}}{{\rm{F}}_2}\left( {\rm{s}} \right) = {\rm{C}}{{\rm{a}}^{2 + }}\left( {{\rm{aq}}} \right) + 2{{\rm{F}}^ - }\left( {{\rm{aq}}} \right)\;\;\;\;\;\;\;\;\;K_{{\rm{sp}}}^ \ominus \left( {{\rm{Ca}}{{\rm{F}}_2}} \right)$

${\rm{HF}}\left( {{\rm{aq}}} \right){\rm{ = }}{{\rm{F}}^ - }\left( {{\rm{aq}}} \right){\rm{ }} + {\rm{ }}{{\rm{H}}^ + }\left( {{\rm{aq}}} \right)\;\;\;\;\;\;\;\;\;\;\;\;\;K_{{\rm{a}}}^ \ominus \left( {{\rm{HF}}} \right)$

${\rm{Ca}}{{\rm{F}}_2}\left( {\rm{s}} \right){\rm{ }} + {\rm{ }}2{{\rm{H}}^ + }\left( {{\rm{aq}}} \right){\rm{ }} = {\rm{C}}{{\rm{a}}^{2 + }}\left( {{\rm{aq}}} \right){\rm{ }} + {\rm{ }}2{\rm{HF}}\left( {{\rm{aq}}} \right)\;\;\;\;\;\;\;\;{K^ \ominus }$

${\rm{MnS}}\left( {\rm{s}} \right){\rm{ }} = {\rm{ M}}{{\rm{n}}^{2 + }}\left( {{\rm{aq}}} \right){\rm{ }} + {{\rm{S}}^{2 - }}\left( {aq} \right)\;\;\;\;\;\;\;\;\;\;\;\;K_{{\rm{sp}}}^ \ominus ({\rm{MnS}})$

${\rm{HAc}}\left( {{\rm{aq}}} \right){\rm{ }} = {\rm{ }}{{\rm{H}}^ + }\left( {{\rm{aq}}} \right){\rm{ }} + {\rm{A}}{{\rm{c}}^ - }\left( {{\rm{aq}}} \right)\;\;\;\;\;\;\;\;\;\;\;\;\;K_{\rm{a}}^ \ominus \left( {{\rm{ HAc}}} \right)$

${{\rm{H}}_{\rm{2}}}{\rm{S}}\left( {{\rm{aq}}} \right){\rm{ }} = {\rm{ }}{{\rm{H}}^{\rm{ + }}}\left( {{\rm{aq}}} \right){\rm{ + H}}{{\rm{S}}^{\rm{ - }}}\left( {{\rm{aq}}} \right)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;K_{{\rm{a1}}}^ \ominus \left( {{{\rm{H}}_{\rm{2}}}{\rm{S}}} \right)$

${\rm{H}}{{\rm{S}}^{\rm{ - }}}\left( {{\rm{aq}}} \right){\rm{ }} = {\rm{ }}{{\rm{H}}^{\rm{ + }}}\left( {{\rm{aq}}} \right){\rm{ + }}{{\rm{S}}^{{\rm{2 - }}}}\left( {{\rm{aq}}} \right)\;\;\;\;\;\;\;\;\;\;\;K_{{\rm{a2}}}^ \ominus \left( {{{\rm{H}}_{\rm{2}}}{\rm{S}}} \right)$

${\rm{MnS}}\left( {\rm{s}} \right){\rm{ }} + {\rm{ }}2{\rm{HAc}}\left( {{\rm{aq}}} \right){\rm{ }} = {\rm{ M}}{{\rm{n}}^{2 + }}\left( {{\rm{aq}}} \right){\rm{ }} + {{\rm{H}}_{\rm{2}}}{\rm{S}}\left( {{\rm{aq}}} \right){\rm{ }} + {\rm{ }}2A{{\rm{c}}^{\rm{ - }}}\left( {{\rm{aq}}} \right)\;\;\;\;\;\;{K^ \ominus }$

${\rm{Fe}}{\left( {{\rm{OH}}} \right)_{\rm{3}}}\left( {\rm{s}} \right){\rm{ = F}}{{\rm{e}}^{3 + }}\left( {{\rm{aq}}} \right){\rm{ + 3O}}{{\rm{H}}^{\rm{ - }}}\left( {{\rm{aq}}} \right)\;\;\;\;\;\;\;K_{{\rm{sp}}}^ \ominus [{\rm{Fe}}{\left( {{\rm{OH}}} \right)_3}]$

$\text{N}{{\text{H}}_{\text{3}}}\left( \text{aq} \right)+{{\text{H}}_{\text{2}}}\text{O}\left( \text{l} \right)\text{=NH}_{4}^{+}\left( \text{aq} \right)\text{+O}{{\text{H}}^{\text{-}}}\left( \text{aq} \right)\ \ \ \ \ \ \ \ \ \ K_{\text{b}}^{\ominus }\left( \text{N}{{\text{H}}_{3}} \right)$

$\text{Fe}{{\left( \text{OH} \right)}_{3}}\left( \text{s} \right)\text{+3NH}_{4}^{+}\left( \text{aq} \right)\text{=F}{{\text{e}}^{\text{3+}}}\left( \text{aq} \right)\text{+3N}{{\text{H}}_{\text{3}}}\left( \text{aq} \right)+\text{3}{{\text{H}}_{\text{2}}}\text{O}\left( \text{l} \right)\ \ \ \ \ {{K}^{\ominus }}$

$\text{Ca}{{\text{C}}_{\text{2}}}{{\text{O}}_{4}}\left( \text{s} \right)=\text{C}{{\text{a}}^{2+}}\left( \text{aq} \right)\text{+}{{\text{C}}_{\text{2}}}\text{O}_{4}^{\text{2}-}\left( \text{aq} \right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ K_{\text{sp}}^{\ominus }(\text{Ca}{{\text{C}}_{\text{2}}}{{\text{O}}_{\text{4}}})$

${\rm{HAc}}\left( {{\rm{aq}}} \right){\rm{ = }}{{\rm{H}}^{\rm{ + }}}\left( {{\rm{aq}}} \right){\rm{ + A}}{{\rm{c}}^{\rm{ - }}}\left( {{\rm{aq}}} \right)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;K_{\rm{a}}^ \ominus \left( {{\rm{HAc}}} \right)$

$\text{H}{{\text{C}}_{\text{2}}}\text{O}_{4}^{-}\left( \text{aq} \right)={{\text{H}}^{+}}\left( \text{aq} \right)+{{\text{C}}_{\text{2}}}\text{O}_{4}^{\text{2}-}\left( \text{aq} \right)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ K_{\text{a}2}^{\ominus }({{\text{H}}_{\text{2}}}{{\text{C}}_{\text{2}}}{{\text{O}}_{4}})$

${\rm{Ca}}{{\rm{C}}_{\rm{2}}}{{\rm{O}}_4}\left( {\rm{s}} \right){\rm{ }} + {\rm{ HAc}}\left( {{\rm{aq}}} \right){\rm{ }} = {\rm{ C}}{{\rm{a}}^{2 + }}\left( {{\rm{aq}}} \right){\rm{ }} + {\rm{H}}{{\rm{C}}_{\rm{2}}}{\rm{O}}_4^ - \left( {{\rm{aq}}} \right){\rm{ }} + {\rm{ }}2{\rm{A}}{{\rm{c}}^ - }\left( {{\rm{aq}}} \right)\;\;\;\;\;\;\;\;\;{K^ \ominus }$

CaC2O4溶于HAc的反应式为：

### 2.2 沉淀之间相互转化

${\rm{Ca}}{{\rm{C}}_{\rm{2}}}{{\rm{O}}_{\rm{4}}}\left( {\rm{s}} \right){\rm{ = C}}{{\rm{a}}^{{\rm{2 + }}}}\left( {{\rm{aq}}} \right){\rm{ + }}{{\rm{C}}_{\rm{2}}}{\rm{O}}_{\rm{4}}^{{\rm{2 - }}}\left( {{\rm{aq}}} \right)\;\;\;\;\;\;\;\;\;\;\;\;K_{{\rm{sp}}}^ \ominus \left( {{\rm{Ca}}{{\rm{C}}_{\rm{2}}}{{\rm{O}}_{\rm{4}}}} \right)$

${\rm{CaC}}{{\rm{O}}_{\rm{3}}}\left( {\rm{s}} \right){\rm{ = C}}{{\rm{a}}^{{\rm{2 + }}}}\left( {{\rm{aq}}} \right){\rm{ + CO}}_{\rm{3}}^{{\rm{2 - }}}\left( {{\rm{aq}}} \right)\;\;\;\;\;\;\;\;\;\;\;K_{{\rm{sp}}}^ \ominus \left( {{\rm{CaC}}{{\rm{O}}_{\rm{3}}}} \right)$

${\rm{Ca}}{{\rm{C}}_{\rm{2}}}{{\rm{O}}_4}\left( {\rm{s}} \right){\rm{ }} + {\rm{CO}}_3^{{\rm{2}} - }\left( {{\rm{aq}}} \right){\rm{ }} = {\rm{ CaC}}{{\rm{O}}_{\rm{3}}}\left( {\rm{s}} \right){\rm{ + }}{{\rm{C}}_{\rm{2}}}{\rm{O}}_4^{{\rm{2}} - }\left( {{\rm{aq}}} \right)\;\;\;\;\;\;{K^ \ominus }$

### 2.6 氧化还原反应参与的多重平衡

$3{\rm{CuS }} + {\rm{ 8HN}}{{\rm{O}}_3} = {\rm{ }}3{\rm{Cu}}{\left( {{\rm{N}}{{\rm{O}}_{\rm{3}}}} \right)_{\rm{2}}}{\rm{ + 3S}} \downarrow {\rm{ }} + {\rm{ 4}}{{\rm{H}}_{\rm{2}}}{\rm{O + 2NO}} \uparrow \;\;\;\;\;\;\;K_5^ \ominus$

${\rm{CuS}}\left( {\rm{s}} \right){\rm{ }} = {\rm{ C}}{{\rm{u}}^{2 + }}\left( {{\rm{aq}}} \right){\rm{ }} + {\rm{ }}{{\rm{S}}^{2 - }}\left( {{\rm{aq}}} \right)\;\;\;\;\;\;\;\;\;\;K_{{\rm{sp}}}^ \ominus ({\rm{CuS}})$

${{\rm{H}}_{\rm{2}}}{\rm{S}}\left( {{\rm{aq}}} \right){\rm{ = }}{{\rm{H}}^{\rm{ + }}}\left( {{\rm{aq}}} \right){\rm{ + H}}{{\rm{S}}^{\rm{ - }}}\left( {{\rm{aq}}} \right)\;\;\;\;\;\;\;\;\;\;\;\;\;K_{{\rm{a}}1}^ \ominus \left( {{{\rm{H}}_{\rm{2}}}{\rm{S}}} \right)$

${\rm{H}}{{\rm{S}}^{\rm{ - }}}\left( {{\rm{aq}}} \right){\rm{ = }}{{\rm{H}}^{\rm{ + }}}\left( {{\rm{aq}}} \right){\rm{ + }}{{\rm{S}}^{\rm{2}}}^{\rm{ - }}\left( {{\rm{aq}}} \right)\;\;\;\;\;\;\;\;\;\;\;\;\;\;\;K_{{\rm{a2}}}^ \ominus \left( {{{\rm{H}}_{\rm{2}}}{\rm{S}}} \right)$

$3{{\rm{H}}_{\rm{2}}}{\rm{S }} + {\rm{ }}2{\rm{HN}}{{\rm{O}}_3} = {\rm{ }}3{\rm{S}} \downarrow {\rm{ }} + {\rm{ }}2{\rm{NO}} \uparrow + 4{{\rm{H}}_{\rm{2}}}{\rm{O}}\;\;\;\;\;\;K_4^ \ominus$

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