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化学 1889

离子的电动势作用

瓦尔特·能斯特

浓度之差,悄然就是一份电压。

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In depth · the introduction

取同样的盐水,调成浓淡两份,各插一片金属,电压表的指针就会一动——浓度之差,悄然就是一份电压。

核心想法

电池能发电,是因为化学物质「想」从拥挤的地方挪向稀疏的地方。能斯特的成就,是说清了这份「想」究竟值多少电压。他的方程,把一个电池的电压,与其中离子的浓度联系了起来。

由此落下的经验法则,简洁得漂亮:在室温下,单价离子浓度每差十倍,约值 59 毫伏。一侧浓十倍:59 mV。浓一百倍:约 118 mV。电压随浓度比的对数增长,而非随比值本身。

它是如何诞生的

1880 年代末,全新的物理化学,正在莱比锡奥斯特瓦尔德的实验室里被一砖一瓦地建起来。两个想法刚刚抵达那里:范托夫已表明,溶解的颗粒像气体一样向外施压(渗透压);阿伦尼乌斯则主张,水中的盐早已裂成带电的离子。瓦尔特·能斯特,一位敏锐而雄心勃勃的年轻助手,看出了如何把二者熔在一起。

他推想:如果一个离子像受压的气体,那么一片金属电极就同时感受到两股相反的推力——它自身溶成离子的倾向,与水中已有离子推回来的压强。二者平衡之处,定下电压。在 1889 年的特许任教论文里,他把这幅图景写成了一道方程。(他会在 1920 年拿到诺贝尔奖,但那是为了完全不同的东西——他的热定理,即热力学第三定律。)

它为何重要

在能斯特之前,你能按金属反应的剧烈程度排个序,却无法预言一份电压。在他之后,你能把它算出来。正是这一项本领,支撑着电池的设计、用 pH 计测量酸度、读出血样中钠或钙含量的传感器,以及「金属为何会腐蚀」的科学——还有,惊人地,你体内每一个神经细胞跨膜维持的那一份微小电压。

一个可以想象的画面

想象相邻的两个房间,由一道门相连,一间挤满了人,另一间几乎空着。人们自然会从拥挤的一间往空的一间飘移;若在门口装一道旋转闸,这股飘移就能把它转动、做功。人群差越大,闸转得越费力。一个离子浓度电池正是如此:离子「想」从浓的一侧挪向稀的一侧,而这份「想」,就以电压的形式显现。能斯特方程,正是「拥挤」与「伏特」之间那个精确的兑换率。

两个盛有同种盐、浓度不同的烧杯由盐桥相连,配一只电压表;拖动浓度与温度滑块、选择离子电荷,看电池电压随浓度差增大而上升、在两侧相等时归零。

它的位置

伏打在 1800 年造出第一个电池,法拉第在 1830 年代把电解量化,但二者都说不出,为什么某个电池会给出某个特定的电压。能斯特补上了这一环,并把它架在范托夫与阿伦尼乌斯关于溶液的新想法之上。从这里,一条线径直通向霍奇金与赫胥黎对神经冲动的解释——它建立在同一道方程之上——也通向你此刻读着这段文字的设备里的电池。

The original document
Original source text
Walther Nernst · Zeitschrift für physikalische Chemie 4 (1889): 129–181 · Leipzig
Written as Nernst's habilitation in Wilhelm Ostwald's Leipzig laboratory — the same rooms where van 't Hoff's osmotic theory and Arrhenius's ions were turning physical chemistry into a quantitative science — the memoir asks a deceptively simple question: how large is the electrical force an ion can exert, and on what does it depend?
1 · The osmotic analogy
Nernst takes over van 't Hoff's result that dissolved particles behave like a gas, exerting an osmotic pressure proportional to their concentration, and Arrhenius's claim that in solution a salt is already split into free ions. An ion in solution is therefore like a gas under pressure; differences in that pressure are differences in a tendency to move.
2 · Electrolytic solution pressure (Lösungstension)
To this he adds one new quantity: every metal is supposed to have an “electrolytic solution pressure” P, an intrinsic tendency to shed ions into the solution, leaving electrons behind on the metal. Against it pushes the osmotic pressure p of the ions already dissolved, which tends to drive them back onto the metal. The electrode comes to rest where the two are balanced, and the charge separation built up in reaching that balance is the electrode potential.
3 · The resulting law
Equating the electrical work of moving the ions against the osmotic work of compressing them from one pressure to the other gives a logarithmic law: the potential depends on the logarithm of the concentration (strictly, the ratio of solution pressure to osmotic pressure). In the form used ever since, the electromotive force of a cell is E = E° − (RT/nF) ln Q.
E = (RT / nF) · ln(P / p) → E = E° − (RT / nF) · ln Q ; 2.303 RT/F ≈ 59.2 mV per tenfold concentration ratio at 25 °C.
4 · Concentration cells and consequences
The clearest test is a cell with the same metal in the same salt at two concentrations: the standard term cancels and a voltage appears from the concentration difference alone. From the same law Nernst reads off how cell voltages, solubilities and equilibria depend on concentration — the working equations of electrochemistry.
[ … ]
The literal picture of a “solution pressure” was later dropped in favour of Gibbs's chemical potential, and dilute concentrations were replaced by activities — but the logarithmic law itself, and the 59 mV-per-decade slope, are exactly as Nernst left them.
Leipzig · 1889