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假设我们有一种弱酸

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记作HA

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A是一个代表

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代表能够写在这儿的全部元素

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它可以是氟 也可以是氨

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如果你加氢氨就变成了铵根

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所以我们这儿讨论的不是任何特定的元素

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这只是酸的一种通式

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假设它处于电离平衡生成… 当然

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你已经见过很多次了 生成一个质子

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这个反应在水溶液中进行

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质子与这个分离

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还有它的共轭碱

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我们也可以写出碱水解平衡

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我们说共轭碱可以水解

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或者说它可以从水分子中抓来一个氢

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并产生氢氧根

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我们已经讲过很多次了

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但这不是这集的重点

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那么我们就来想一下

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如果我们向某一边推动反应

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平衡会如何变化

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你应该想到了

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我马上要谈到勒夏特列原理了

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这个原理说的是

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如果你改变影响平衡的一个条件

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平衡将会移动

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来减弱这种改变

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假设我改变的条件是

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我换个颜色

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我要加入一些强碱

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颜色太深了

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我加入一些氢氧化钠(NaOH)

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我们知道这是一种强碱

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如果你往溶液中加氢氧化钠

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钠的部分只会电离成为钠离子

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但更重要的是

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溶液中现在有了氢氧根

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它们会拐带氢离子

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所以溶液中加了氢氧根的时候

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你每加入1mol

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不用1mol

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你加入溶液的每一个氢氧根

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它就会消耗一个氢离子

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对吧？

46
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例如 如果溶液中有

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1mol氢离子

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然后往溶液中加1mol氢氧化钠

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所有的氢氧根会和全部这个反应

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氢氧根将会和氢离子反应

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并生成水

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这样它们就像

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双双从溶液中消失了

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它们不是真的消失了 而是都变水了

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因此所有的氢离子都会不复存在

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至少起初的氢离子会消失

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开始的1mol氢离子会消失

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那么这个反应会怎样变化？

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呐 我们知道这是个可逆反应

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那么这些氢消失以后

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因为这是个可逆反应

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而HA是个弱酸

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更多的HA将转化为

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这两种产物

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来补偿氢离子的损失

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你甚至可以算出结果

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开始时氢离子浓度降低了

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但它很快达到新的平衡

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而HA浓度将降低

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这个浓度会上升

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然后氢离子的浓度会降得少一些

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因为当然了 一开始加氢氧化钠的时候

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它消耗了所有的氢离子

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但之后你还有这个

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你可以把它看作

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氢离子的一种储备 可以提供氢离子

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当这些消失以后

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HA的电离程度增加

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平衡将向右移动

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所以 氢氧根很快地消耗了氢离子

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但是当平衡向右移动的时候

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很多的氢离子重新出现

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如果再回想一下这个过程

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如果我直接往水里加这些氢氧化钠

85
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如果我只是把NaOH溶解在水中

86
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也就是直接把它扔水中

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它将完全电离成

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钠离子和氢氧根离子

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因此就瞬间

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通过加入一定物质的量的

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氢氧化钠 来本质上增加了

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氢氧根浓度

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你立马就提升了溶液的pH 对吧？

94
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记住 当你增加溶液中氢氧根时

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你就降低了pOH 对吗？

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那是因为pOH是氢氧根离子浓度的负对数

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因此增加氢氧根 就是在降低pOH

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也就是增加pH

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想想氢氧根 它使溶液的碱性更强

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高pH也意味着碱性强

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如果加入1mol/L的NaOH 溶液的pH值就会是14

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如果这是一种强酸 而不是强碱

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溶液的pH值将会是0

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希望你现在已经比较

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熟悉这个概念了

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如果有点儿转不过来

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只要多去熟悉一下对数的性质

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你一定会懂的

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回到正题

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如果你把这个加到水中

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你立马就能得到超高的pH

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因为氢氧根浓度已经突破天际了

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但如果你加到这里

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你把氢氧化钠加入到这个溶液中

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溶液中有

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一种弱酸和它的共轭碱

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弱酸和它的共轭碱

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会怎么样？

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当然 它会马上反应掉溶液中全部这个

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把它吃光光

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但你会在这里得到补给

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它在电离出越来越多的氢离子

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它将弥补很大一部分的损失

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因此到最后 改变并不会那么大

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而这边 直接加在水里的话

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pH值就剧烈上升了

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这里 pH值的增长量小多了

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在以后的视频中 我们会计算

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少增加了多少pH值

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你可以把这个溶液看作

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一种pH变化的缓冲器

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虽然你往溶液中加入了

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强碱

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溶液pH的增长量

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并不会像你预期那么大

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你也可以从另一方面考虑

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如果我把同样的反应写成

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共轭碱的水解

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记住啦 这是一样的东西

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那么我们可以写成A-

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我刚写出了它的共轭碱

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它跟周围的溶液的水发生反应

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并达到平衡状态

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我们目前讨论的东西

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都在水溶液中

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当然跟它反应的水

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不会是氢氧根

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记住 它们是等价的反应

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这里我写的是酸的电离

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而这里我写的是碱的水解

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不过它们是等价的

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现在

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如果你要往溶液中加入强酸

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会怎么样？

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如果我们加入盐酸(HCl)

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呐 盐酸呢 如果你直接扔它进

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没有溶质的水中

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它会完全电离成

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一些氢离子和一些氯离子

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这会立即使酸性变得十分强

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会得到很低的pH

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如果你有1mol的这个

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如果浓度是1mol/L

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溶液的pH会降到0

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但如果你把盐酸加到

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这个溶液中呢？

167
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这个含有弱碱

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和它的共轭酸的溶液

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嗯… 所有这些由盐酸

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电离而来的质子

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将和原有的氢氧根反应

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它们彼此中和了

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两者结合 并且转化成水

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成为溶液的一部分

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所以啊 开始时氢氧根浓度下降

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但是这儿有弱碱的储备

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而勒夏特列原理告诉我们

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呐 如果我们的改变是

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降低我们的氢氧根总浓度

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那么平衡将向着

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减弱这种改变的方向移动

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因此反应会向右移

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因此会有更多的弱碱

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转化成弱酸并产生更多的氢氧根

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因此pH值不会像把它加入水中那样

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下降那么多

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氢离子的加入使pH值下降

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但接着这家伙会从水里抓来更多更多的氢

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就会有更多的氢氧根产生

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因此我们可以把它看作

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对强酸或强碱的影响的

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一个软垫或者一个弹簧

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这就是为什么它被称为缓冲剂

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因为它对溶液的酸性提供了一种缓冲

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如果你往水中加入强碱

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水的pH值会立即上升

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酸性显著下降

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但如果向缓冲剂中加入强碱

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根据勒夏特列原理

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本质上 不会对pH值有那么大的影响

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00:08:56,440 --> 00:08:57,470
同样道理

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00:08:57,490 --> 00:08:59,720
如果你向同样的缓冲剂中加入酸

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00:08:59,730 --> 00:09:01,810
它对pH值的影响

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不会像

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你把同样的酸加入水中的大

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因为这个可逆反应总是可以

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00:09:08,000 --> 00:09:11,510
当你加入酸时 补充失去的

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00:09:11,530 --> 00:09:13,000
氢氧根离子

209
00:09:13,020 --> 00:09:16,010
或者在你加入碱时 补充所失去的

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00:09:16,030 --> 00:09:17,860
氢离子

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00:09:17,880 --> 00:09:20,140
这就是为什么它被称为缓冲剂 它提供了一种缓冲

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00:09:20,150 --> 00:09:23,320
所以它让溶液的pH有一定的稳定性

213
00:09:23,340 --> 00:09:30,630
缓冲剂的定义就是

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00:09:30,650 --> 00:09:34,450
一种溶液含有弱酸和它的共轭碱

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00:09:34,470 --> 00:09:36,370
并达到平衡

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00:09:36,400 --> 00:09:38,450
这就是缓冲剂 它被称为缓冲剂是

217
00:09:38,480 --> 00:09:40,920
因为它可以缓冲pH值的变化

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这是一种

219
00:09:43,320 --> 00:09:46,560
酸性变化的缓冲器

220
00:09:46,590 --> 00:09:48,540
那么 接下来

221
00:09:48,570 --> 00:09:51,390
我们来讨论缓冲剂的计算

222
00:09:51,400 --> 00:09:54,390
实际上也就是弱酸的计算

223
00:09:54,410 --> 00:09:57,780
那么我们重新写一下这个方程

224
00:09:57,800 --> 00:10:01,780
HA在平衡状态中

225
00:10:01,800 --> 00:10:04,790
所有东西都在水溶液中

226
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有氢离子和它的共轭碱

227
00:10:10,180 --> 00:10:15,020
我们知道这有个平衡常数

228
00:10:15,040 --> 00:10:17,420
我们在这上做过很多集

229
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这里的平衡常数等于

230
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氢离子的浓度

231
00:10:23,660 --> 00:10:26,730
乘以共轭碱的浓度

232
00:10:26,750 --> 00:10:29,890
我说的浓度指的是物质的量浓度

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单位是mol/L 除以

234
00:10:32,900 --> 00:10:34,530
弱酸的浓度

235
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现在

236
00:10:36,530 --> 00:10:43,950
现在我们来解一下氢离子的浓度

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因为我的目标是

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推导出一个公式

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我们称其为Hendersen-Hasselbalch方程

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很多书都要求你去记这个公式

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但我认为你不需要背

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我想你应该掌握

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从基本条件得出这个公式的方法

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让我们先解出氢离子浓度

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那么就能够得到

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pH值和公式中其它量的关系

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那么 如果我们想得到氢离子浓度

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我们可以给方程两边

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同时乘上这个的倒数

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你就得到了氢离子的浓度…

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Ka乘以

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我在方程两边乘上它的倒数

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那么 乘上弱酸浓度

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除以共轭碱的浓度

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等于亲爱的氢离子的浓度

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好咧

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现在

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我们对方程两边取负对数

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那么这块东西的负对数

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这个反应的平衡常数

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乘以HA浓度 除以共轭碱浓度

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等于氢离子浓度的

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负对数

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也就是pH 对吧？

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氢离子浓度的负对数

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就是pH值的定义

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我用不同的颜色写p和H

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p只是代表负对数

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负对数 就是这样 底数是10

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我们看看能否再简化一下

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根据对数的性质

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我们知道如果你取两个数的乘积的

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对数

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那就相当于是这个的对数

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加上那个的对数

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因此这个可以化简成 -lgKa减去

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弱酸浓度除以共轭碱浓度

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这比值的对数

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等于pH

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这就是我们弱酸的pKa

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也就是我们平衡常数的

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负对数

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这就是pKa

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HA的负对数比上A

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我们可以把这个变成加号

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把这里变成-1次方 对吧？

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这是另一条对数性质

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如果你转不过来

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可以回顾一下对数的视频

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这个的-1次方就是它的倒数

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因此我们可以说

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加上共轭碱浓度除以弱酸的浓度

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的对数

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等于pH值

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这里这个

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就叫Hendersen-Hasselbalch方程

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我真的不鼓励你死记硬背

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因为如果你企图强记它

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几个小时内你就会忘掉

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这个是不是加号

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你可能会忘记这个

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你还可能忘记

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A-和HA

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哪个在分母上哪个在分子上

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如果你忘了 后果很严重

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更好的做法是从

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基本条件入手 相信我

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我刚才花了几分钟推导

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但如果你在纸上写快些的话

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你不需要像我一样一步一步来

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推出这个方程几乎不花任何时间

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比硬背要好多了

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而且到30岁你都不会忘记

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那么这个方程有什么用呢？

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这个方程建立了pH和pKa之间的联系

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而这是反应平衡的一个常数 对吧？

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加上酸和共轭碱的比值的

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对数

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所以我的共轭碱浓度越高

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而酸的浓度越小

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pH就越高 对吧？

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如果这个增多而这个减少

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我的pH就会变大 这很合理

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因为溶液里的碱增多了

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如果我求它的倒数

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可能就是…