氧化还原反应方程式配平2

2022-01-29 12:26 作者:匆匆-cc 0人读过 | 我要投稿

氧化还原专题2

先吐槽一句了。。。

码字实在不易。

上篇可见链接。

例7.（A Little Trick）配平

$%5Cce%7BMnO4-%7D%2B%5Cce%7BH%2B%7D%2B%5Cce%7BH2O2%7D%5Cxlongequal%7B%5Cquad%7D%20%5Cce%7BMn%5E2%2B%7D%2B%5Cce%7BO2%20%5E%7D%2B%5Cce%7BH2O%7D$

解：

$%5Cce%7B%5Coverset%7Bv%205%7D%7BMn%7DO4-%7D%2B%5Cce%7BH%2B%7D%2B%5Cce%7BH2%5Coverset%7B%5E%201%5Ctimes%202%7D%7BO%7D%7B%7D_2%7D%5Cxlongequal%7B%5Cquad%7D%20%5Cce%7BMn%5E2%2B%7D%2B%5Cce%7BO2%20%5E%7D%2B%5Cce%7BH2O%7D$

$%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B2%7D%7D%5Cce%7B%5Coverset%7Bv%205%5Ctimes%202%7D%7BMn%7DO4-%7D%2B%5Cce%7BH%2B%7D%2B%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B5%7D%7D%5Cce%7BH2%5Coverset%7B%5E%20(1%5Ctimes%202)%5Ctimes%205%7D%7BO%7D%7B%7D_2%7D%5Cxlongequal%7B%5Cquad%7D%20%5Cce%7BMn%5E2%2B%7D%2B%5Cce%7BO2%20%5E%7D%2B%5Cce%7BH2O%7D$

$%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B2%7D%7D%5Cce%7B%5Coverset%7Bv%205%5Ctimes%202%7D%7BMn%7DO4-%7D%2B%5Cce%7BH%2B%7D%2B%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B5%7D%7D%5Cce%7BH2%5Coverset%7B%5E%20(1%5Ctimes%202)%5Ctimes%205%7D%7BO%7D%7B%7D_2%7D%5Cxlongequal%7B%5Cquad%7D%20%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B2%7D%7D%5Cce%7BMn%5E2%2B%7D%2B%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B5%7D%7D%5Cce%7BO2%20%5E%7D%2B%5Cce%7BH2O%7D$

$%5Cunderbrace%7B%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B2%7D%7D%5Cce%7B%5Coverset%7Bv%205%5Ctimes%202%7D%7BMn%7DO4-%7D%2B%5Ccolor%7Bskyblue%7D%7B%5Ctextbf%7B6%7D%7D%5Cce%7BH%2B%7D%2B%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B5%7D%7D%5Cce%7BH2%5Coverset%7B%5E%20(1%5Ctimes%202)%5Ctimes%205%7D%7BO%7D%7B%7D_2%7D%7D_%7B-4e%5E-%7D%5Cxlongequal%7B%5Cquad%7D%20%5Cunderbrace%7B%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B2%7D%7D%5Cce%7BMn%5E2%2B%7D%2B%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B5%7D%7D%5Cce%7BO2%20%5E%7D%2B%5Cce%7BH2O%7D%7D_%7B-4e%5E-%7D$

$2%5Cce%7BMnO4-%7D%2B6%5Cce%7BH%2B%7D%2B5%5Cce%7BH2O2%7D%5Cxlongequal%7B%5Cquad%7D%202%5Cce%7BMn%5E2%2B%7D%2B5%5Cce%7BO2%20%5E%7D%2B8%5Cce%7BH2O%7D$

貌似一切顺利，无甚问题。

但不妨看一下几个方程式，诸位请品鉴。

$2%5Cce%7BMnO4-%7D%2B6%5Cce%7BH%2B%7D%2B3%5Cce%7BH2O2%7D%5Cxlongequal%7B%5Cquad%7D%202%5Cce%7BMn%5E2%2B%7D%2B4%5Cce%7BO2%20%5E%7D%2B6%5Cce%7BH2O%7D$

$2%5Cce%7BMnO4-%7D%2B6%5Cce%7BH%2B%7D%2B%5Cce%7BH2O2%7D%5Cxlongequal%7B%5Cquad%7D%202%5Cce%7BMn%5E2%2B%7D%2B3%5Cce%7BO2%20%5E%7D%2B4%5Cce%7BH2O%7D$

Q：配平了吗？

乍一看，配平了。

实际上，违背了得失电子守恒。

在这里，重新提出真正配平的定义。

满足元素守恒、电荷守恒、得失电子守恒三大基本规律。

从某种意义上，后两条是初中化学所忽视的，所以说高中化学才是化学真正的滥觞。

笔者初学配平时曾对此题无能为力，原因正在于：

$2%5Cce%7BMnO4-%7D%2B6%5Cce%7BH%2B%7D%2B5%5Cce%7BH2O2%7D%5Cxlongequal%7B%5Cquad%7D%202%5Cce%7BMn%5E2%2B%7D%2B5%5Cce%7BO2%20%5E%7D%2B8%5Cce%7BH2O%7D%5Ctag%7B1%7D$

$2%5Cce%7BH2O2%7D%5Cxlongequal%7B%5Cquad%7D2%5Cce%7BH2O%7D%2B%5Cce%7BO2%20%5E%7D%20%5Ctag%7B2%7D$

两式可任意比叠加不影响元素守恒。

说到这里，不妨提一笔针对元素守恒的奇妙（fei wu）方法。

例8.（元素守恒法）配平

$%5Cce%7BKNO3%7D%2B%5Cce%7BC%7D%2B%5Cce%7BS%7D%20%5Cxlongequal%7B%E7%82%B9%E7%87%83%7D%5Cce%7BK2S%7D%2B%5Cce%7BNO2%7B%7D%5E%7D%2B%5Cce%7BCO2%7B%7D%5E%7D$

解：

定 $%5Cce%7BKNO3%7D$ 的系数为 $1$ ，剩余项的系数为 $a%2Cb%2Cc%2Cd%2Ce$

根据元素守恒，我们有

$%5Cbegin%7Bcases%7D%0A1%3D2c%0A%5C%5C1%3Dd%0A%5C%5C3%3D2d%2B2e%0A%5C%5Ca%3De%0A%5C%5Cb%3Dc%0A%5Cend%7Bcases%7D$

解得

$%5Cbegin%7Bcases%7D%0Aa%3Db%3Dc%3De%3D%5Cfrac%7B1%7D%7B2%7D%0A%5C%5Cd%3D1%0A%5Cend%7Bcases%7D$

化作整系数，得

$%5Cbegin%7Bcases%7D%0Aa%3Db%3Dc%3De%3D1%0A%5C%5Cd%3D2%0A%5Cend%7Bcases%7D$

故

$2%5Cce%7BKNO3%7D%2B%5Cce%7BS%7D%2B%5Cce%7BC%7D%5Cxlongequal%7B%E7%82%B9%E7%87%83%7D%5Cce%7BK2S%7D%2B2%5Cce%7BNO2%7B%7D%5E%7D%2B%5Cce%7BCO2%7B%7D%5E%7D$

笔者曾用此方法计算过例4，大约需要比较强的数学计算功底与30分钟。

如果方程更复杂，除了代入消元法和加减消元法，采用行列式计算也是可行的（虽然计算量爆炸）。

## 后面是练习

例9.配平

$%5Cce%7BNO2%7D%2B%5Cce%7BH2O%7D%5Cxlongequal%7B%5Cquad%7D%5Cce%7BNO%7D%2B%5Cce%7BHNO3%7D$

解：

$%5Cce%7BNO2%7D%2B%5Cce%7BH2O%7D%5Cxlongequal%7B%5Cquad%7D%5Cce%7B%5Coverset%7Bv%202%7D%7BN%7DO%7D%2B%5Cce%7BH%5Coverset%7B%5E%201%7D%7BN%7DO3%7D$

$%5Cce%7BNO2%7D%2B%5Cce%7BH2O%7D%5Cxlongequal%7B%5Cquad%7D%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B1%7D%7D%5Cce%7B%5Coverset%7Bv%202%5Ctimes%201%7D%7BN%7DO%7D%2B%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B2%7D%7D%5Cce%7BH%5Coverset%7B%5E%201%5Ctimes%202%7D%7BN%7DO3%7D$

$%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B3%7D%7D%5Cce%7BNO2%7D%2B%5Cce%7BH2O%7D%5Cxlongequal%7B%5Cquad%7D%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B1%7D%7D%5Cce%7B%5Coverset%7Bv%202%5Ctimes%201%7D%7BN%7DO%7D%2B%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B2%7D%7D%5Cce%7BH%5Coverset%7B%5E%201%5Ctimes%202%7D%7BN%7DO3%7D$

$%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B3%7D%7D%5Cce%7BNO2%7D%2B%5Ccolor%7Bgreen%7D%7B%5Ctextbf%7B1%7D%7D%5Cce%7BH2O%7D%5Cxlongequal%7B%5Cquad%7D%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B1%7D%7D%5Cce%7B%5Coverset%7Bv%202%5Ctimes%201%7D%7BN%7DO%7D%2B%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B2%7D%7D%5Cce%7BH%5Coverset%7B%5E%201%5Ctimes%202%7D%7BN%7DO3%7D$

$3%5Cce%7BNO2%7D%2B%5Cce%7BH2O%7D%5Cxlongequal%7B%5Cquad%7D%5Cce%7BNO%7D%2B2%5Cce%7BHNO3%7D$

例10.配平

$%5Cce%7BFeS2%7D%2B%5Cce%7BO2%7D%5Cxlongequal%7B%5Cquad%7D%5Cce%7BFe2O3%7D%2B%5Cce%7BSO2%7D$

解：

$%5Ccolor%7Bred%7D%7B%5Ctextbf%7B2%7D%7D%5Cce%7B%5Coverset%7B-8%7D%7BFe%7D%5Coverset%7B%2B4%7D%7BS2%7D%7D%2B%5Cce%7BO2%7D%5Cxlongequal%7B%5Cquad%7D%5Ccolor%7Bred%7D%7B%5Cce%7BFe2O3%7D%7D%2B%5Cce%7BSO2%7D$

$%5Ccolor%7Bred%7D%7B%5Ctextbf%7B2%7D%7D%5Cce%7B%5Coverset%7B%5E%2011%5Ctimes%202%7D%7BFe%7DS2%7D%2B%5Cce%7B%5Coverset%7Bv%204%7D%7BO2%7D%7D%5Cxlongequal%7B%5Cquad%7D%5Cce%7BFe2O3%7D%2B%5Cce%7BSO2%7D$

$%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B4%7D%7D%5Cce%7B%5Coverset%7B%5E%2022%5Ctimes%202%7D%7BFe%7DS2%7D%2B%5Ccolor%7Bblue%7D%7B%5Ctextbf%7B11%7D%7D%5Cce%7B%5Coverset%7Bv%204%5Ctimes%2011%7D%7BO2%7D%7D%5Cxlongequal%7B%5Cquad%7D%5Cce%7BFe2O3%7D%2B%5Cce%7BSO2%7D$

$%5Cce%7BFeS2%7D%2B%5Cce%7BO2%7D%5Cxlongequal%7B%5Cquad%7D%5Cce%7BFe2O3%7D%2B%5Cce%7BSO2%7D$

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