Thermodynamics and Electrochemistry
AP Chemistry Topic 9 8:16 English narration · English + 中文 subtitles burned in
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Transcript
Two puzzles.
两个谜题。
Hold an ice cube: it melts in your hand, even though melting takes energy in.
把一块冰握在手里：它会融化，尽管融化要吸收能量。
Now look at a diamond.
再看一颗钻石。
Every diamond should slowly turn into graphite — pencil lead.
每一颗钻石都应该慢慢变成石墨，也就是铅笔芯。
And yet nothing happens.
可是什么都没有发生。
One change goes by itself; the other never goes.
一种变化自己就会发生，另一种永远不会。
So what really decides?
究竟是什么在决定？
One number decides it, and it is built from two ideas.
决定它的是一个数，而这个数由两个想法组成。
The first is entropy: how spread out matter and energy are.
第一个是熵：物质和能量分散的程度。
In the solid, particles sit in a neat pattern.
在固体里，粒子排成整齐的图案。
Melt it and they slide past each other.
熔化以后，它们互相滑动。
Boil it and they fly apart and fill the container.
沸腾以后，它们四散开来，充满整个容器。
More ways to arrange them means higher entropy.
排列方式越多，熵就越高。
So when does entropy increase?
那么熵在什么时候升高？
Entropy increases solid to liquid to gas.
固体变液体，液体变气体。
A solid dissolving.
固体溶解。
And the one the exam loves: making more moles of gas than you use.
还有考试最爱考的一点：生成的气体摩尔数比消耗的多。
Heating raises it too.
加热也会提高熵。
To calculate it, add the standard entropies of the products and subtract the reactants.
要计算熵变，把产物的标准熵加起来，再减去反应物的。
One equation decides.
一个公式就能决定。
Gibbs free energy change equals the enthalpy change, minus the temperature times the entropy change.
自由能变等于焓变，减去温度乘以熵变。
It is a tug of war.
这是一场拔河。
The energy term pulls toward yes when a reaction gives out heat.
反应放热时，能量项拉向行。
The entropy term pulls toward yes when things spread out.
东西变得分散时，熵项拉向行。
When the two disagree, temperature is the referee.
两者相反时，温度就是裁判。
Watch what happens as we heat it.
看看加热时会发生什么。
The entropy term grows, and the free energy falls.
熵项变大，自由能下降。
Once the free energy crosses zero, the reaction is favored.
自由能一旦越过零，反应就变得有利。
All four cases, one table.
四种情况都在这张表里。
Gives out heat and entropy rises: favored at every temperature.
放热而且熵升高：任何温度下都有利。
Takes in heat and entropy falls: never favored.
吸热而且熵降低：任何温度下都不利。
In the other two boxes the terms disagree, so temperature decides — and they also decide whether a salt dissolves.
另外两格里两项相反，所以由温度决定—— 同样这两项也决定一种盐能不能溶解。
Note the wording too: the exam says thermodynamically favourable — thermodynamically favored — not spontaneous.
还要注意用词： 考试说的是热力学有利，而不是自发。
Let's use it.
我们来用一用。
A reaction takes in forty kilojoules per mole; its entropy change is plus one hundred and twenty joules per mole per kelvin.
某个反应吸收四十千焦每摩尔；熵变是正的一百二十焦耳每摩尔每开尔文。
Above what temperature is it favored?
在高于多少温度时它才有利？
Pause and try it.
先暂停，自己试一试。
We want the free energy below zero, so the temperature must be bigger than the enthalpy change divided by the entropy change.
我们希望自由能小于零，所以温度必须大于焓变除以熵变。
Watch the units — one hundred and twenty joules is nought point one two zero kilojoules.
注意单位——一百二十焦耳等于零点一二零千焦。
Forty divided by that is three hundred and thirty-three kelvin — about sixty degrees Celsius.
四十除以它，得到三百三十三开尔文——大约六十摄氏度。
Now the second puzzle.
现在回到第二个谜题。
Every diamond is thermodynamically favored to become graphite: the free energy really does fall.
每一颗钻石在热力学上都倾向于变成石墨：自由能确实在下降。
But look at the hill.
但看那座山。
The barrier is enormous, so it takes longer than the age of the Earth.
能垒极高，所需的时间比地球的年龄还长。
We say the reaction is kinetically controlled — under kinetic control.
我们说这个反应受动力学控制。
And stuck is not the same as at equilibrium.
而卡住并不等于处于平衡。
Thermodynamics gives the direction, kinetics gives the speed.
热力学给出方向，动力学给出速率。
Free energy also says where a reaction stops.
自由能还能告诉你反应停在哪里。
The standard free energy change equals minus R T times the natural log of K.
标准自由能变等于负的 R T 乘以 K 的自然对数。
Negative means K is bigger than one: products win. Positive: reactants win.
为负时 K 大于一，产物占优；为正时反应物占优。
At equilibrium it is zero.
在平衡时它等于零。
Now the second box: an unfavorable step can still be driven.
再看第二个框：不利的一步仍然可以被推动。
Couple it to a favorable one that shares an intermediate, and take the sum of the free energies — plus twenty with minus fifty gives minus thirty.
把它与一个共享中间体的有利反应偶联， 把自由能相加——正二十加上负五十，得到负三十。
In your cells that partner is ATP.
在你的细胞里，那个搭档就是三磷酸腺苷。
Same idea, different coat.
同样的想法，换一件外衣。
Take a favorable redox reaction and split it in two.
取一个有利的氧化还原反应，把它一分为二。
Zinc gives up electrons on the left; copper ions take them on the right.
左边锌放出电子，右边铜离子接受电子。
Join them with a wire and the electrons must travel through it: that is a current.
用导线连起来，电子就只能从导线里通过：这就是电流。
The salt bridge lets ions cross so both solutions stay neutral.
盐桥让离子来回移动，使两边溶液保持电中性。
This is a galvanic cell, also called a voltaic cell — a battery.
这就是原电池，也就是电池。
Two kinds of cell, one rule for both.
两类电池，一条共同的规则。
A galvanic cell runs a favorable reaction and gives you electricity.
原电池让一个有利的反应进行，给你电。
An electrolytic cell does the opposite: you supply electricity to force an unfavorable reaction.
电解池正好相反：你提供电，去迫使一个不利的反应发生。
In both, oxidation happens at the anode and reduction at the cathode.
在这两种电池里，氧化都发生在阳极，还原都发生在阴极。
How strong is the push?
这股推力有多大？
The cell potential, in volts.
就是电池电势，单位是伏特。
Take the standard reduction potential of the cathode and subtract the one for the anode.
用阴极的标准还原电势，减去阳极的标准还原电势。
It links straight back to thermodynamics: the standard free energy change equals minus n, times the Faraday constant, times the cell potential.
它直接连回热力学：标准自由能变等于负的 n，乘以法拉第常数，再乘以电池电势。
So a positive voltage means a negative free energy — a favorable cell.
所以正的电压意味着负的自由能——这是一个有利的电池。
A negative voltage means it needs an outside push.
负的电压则意味着它需要外界推一把。
So that voltmeter is measuring free energy.
所以那个电压表量的就是自由能。
These come from a table like this, and every value is written as a reduction.
这些电势来自像这样的一张表，每一个数值都写成还原的形式。
High up, the substance takes electrons easily — a strong oxidising agent, so it is the cathode.
在上方，物质容易得到电子，是强氧化剂，所以它是阴极。
Low down, the metal gives electrons away — a strong reducing agent, so it is the anode.
在下方，金属容易失去电子，是强还原剂，所以它是阳极。
Pick the higher one as the cathode.
把位置高的当作阴极。
Let's work one.
我们来做一道。
Two half-reactions, with their standard reduction potentials.
这里是两个半反应和它们的标准还原电势。
Pause and try it.
先暂停，自己试一试。
Copper is higher up the table, so copper is the cathode and zinc the anode.
铜在表中的位置更高，所以铜是阴极，锌是阳极。
Now subtract: nought point three four, minus minus nought point seven six.
现在做减法：零点三四，减去负零点七六。
Two minus signs make a plus, giving plus one point one zero volts.
两个负号变成正号，得到正一点一零伏。
Positive, so this cell is favorable.
是正的，所以这个电池是有利的。
And the free energy is minus two, times the Faraday constant, times one point one zero: about minus two hundred and twelve kilojoules per mole.
而自由能等于负二，乘以法拉第常数，再乘以一点一零， 大约是负二百一十二千焦每摩尔。
Negative, exactly as the positive voltage promised.
是负的，正如那个正电压所预示的。
A battery does not hold that voltage.
但电池不会一直保持那个电压。
As the reaction runs, reactants are used up and products build up, so the reaction quotient rises and the voltage falls.
随着反应进行，反应物被消耗，产物不断积累， 所以反应商升高，电压下降。
At equilibrium the quotient equals K and the voltage is zero: a flat battery.
达到平衡时，反应商等于 K，电压降到零， 也就是一节没电的电池。
That concentration dependence is the Nernst equation.
所以电池离平衡越远，电压就越大。
So the further a cell is from equilibrium, the bigger its voltage. And a working cell is never at equilibrium, so think about Q, not Le Chatelier.
而工作中的电池从来不处于平衡，所以要想反应商，不要搬勒夏特列原理。
Now push the other way — electrolysis.
现在往反方向推。
Connect a power supply and you can force an unfavorable reaction to run.
接上电源，你就能迫使一个不利的反应进行。
Positive ions travel to the negative cathode and pick up electrons; negative ions travel to the positive anode and give electrons away.
正离子跑向负的阴极并得到电子；负离子跑向正的阳极并失去电子。
Metal plates out on one electrode, a gas often bubbles off the other.
金属在一个电极上析出，另一个电极上常常有气体冒出。
One last calculation — pure bookkeeping.
最后一道计算——就是记账。
Two point zero amps flow for thirty minutes through copper sulfate.
二点零安的电流通过硫酸铜溶液三十分钟。
What mass of copper forms?
析出多少克铜？
Pause and try it.
先暂停，自己试一试。
First the charge: current times time gives three thousand six hundred coulombs.
先求电荷量：电流乘时间，得到三千六百库仑。
Divide by the Faraday constant: nought point zero three seven three moles of electrons.
除以法拉第常数：零点零三七三摩尔电子。
Each copper ion needs two, so halve that.
每个铜离子需要两个电子，所以取一半。
Multiply by sixty-three point five grams per mole and you get one point two grams of copper.
再乘以六十三点五克每摩尔，就得到一点二克铜。
That is Faraday's law in three lines.
这就是三行之内的法拉第定律。
Three marks students lose every year.
有三个分，学生年年都丢。
First, match your units: the enthalpy change is in kilojoules, the entropy change in joules — convert before you subtract.
第一，统一单位：焓变的单位是千焦，熵变的单位是焦耳， 相减之前先换算。
Second, favorable does not mean fast; if a favorable reaction is not happening, say high activation energy.
第二，有利不等于快；如果一个有利的反应没有发生， 答案就是活化能很高。
Third, cathode minus anode, and keep the signs.
第三，阴极减阳极，并且注意符号。
Four things to take away.
有四点要记住。
Entropy is the spread of matter and energy, and gases raise it most.
熵是物质和能量的分散程度，气体让它升得最多。
Free energy is enthalpy minus temperature times entropy; below zero means favorable.
自由能等于焓减去温度乘以熵，小于零就是有利。
Free energy fixes the equilibrium constant, and coupling drives an uphill step.
自由能决定平衡常数，偶联可以推动上坡的一步。
And in a cell, the anode oxidises and the voltage is free energy in disguise.
而在电池里，阳极发生氧化，电压就是换了模样的自由能。