Atoms, Molecules & Stoichiometry
A-Level Chemistry Topic 2 19:02 English narration · English + 中文 subtitles burned in
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Here is a problem.
先看一个难题。
A single teaspoon of water holds about two hundred thousand billion billion molecules.
一茶匙水里大约有二十万亿亿个分子。
You could never count them — not in a lifetime, not in a thousand lifetimes.
你永远数不完它们—— 一辈子数不完，一千辈子也数不完。
Yet chemistry is all about counting: how many particles react with how many.
可是化学恰恰就是在数数：多少个粒子和多少个粒子反应。
So chemists invented one idea that makes counting possible. It is called the mole.
于是化学家发明了一个让"数数"变得可行的概念，它叫做摩尔。
Welcome to atoms, molecules and stoichiometry.
欢迎来到原子、分子与化学计量。
We will build the mole from scratch, then use it for masses, gases and solutions.
我们将从头建立摩尔的概念， 然后用它来处理质量、气体和溶液。
Let's begin.
让我们开始吧。
Atoms are far too light to weigh in grams, so we compare every mass to one standard: one twelfth of a carbon-twelve atom.
原子实在太轻，无法用克来称量，所以我们把每一个质量都与同一个标准相比： 碳十二原子质量的十二分之一。
That gives four terms.
由此得到四个术语。
Relative atomic mass is the average mass of an element's atoms on that scale.
相对原子质量是某元素原子在这个标度上的平均质量。
Relative isotopic mass is the mass of one single isotope.
相对同位素质量是单一同位素一个原子的质量。
Relative molecular mass is the sum of the relative atomic masses in one molecule.
相对分子质量是一个分子中各相对原子质量之和。
And relative formula mass is the same sum for a substance with no molecules, like an ionic compound.
而相对式量是同样的求和，用于没有分子的物质，比如离子化合物。
They are all ratios — so none of them carries a unit.
它们都是比值——所以都没有单位。
That standard has a name.
这个标准有名字。
The unified atomic mass unit — spoken as "u" — is defined as exactly one twelfth of the mass of one carbon-twelve atom.
统一原子质量单位——读作"u"——定义为恰好等于一个碳十二原子质量的十二分之一。
Every relative mass on this topic is measured against that single yardstick.
本专题里每一个相对质量都用这把尺子来量。
So when we say relative atomic mass thirty-five point five, we mean the average chlorine atom is thirty-five point five times heavier than one twelfth of carbon-twelve.
所以当我们说相对原子质量三十五点五时， 意思是平均一个氯原子的质量是碳十二原子十二分之一的三十五点五倍。
Memorise the definition: one u equals one twelfth of a carbon-twelve atom.
请记住定义：一个统一原子质量单位等于一个碳十二原子质量的十二分之一。
Exam questions often ask you to state that definition in words.
考题常要求你用文字写出这个定义。
But why an average?
但为什么要取平均？
Because most elements are a mixture of isotopes.
因为大多数元素都是同位素的混合物。
A mass spectrometer separates them and measures how common each one is.
质谱仪把它们分开，并测出每一种各占多少。
Watch: the sample is turned into ions, the ions are sorted by mass, and each isotope lands as its own peak.
看：样品先被电离成离子， 离子再按质量分开，每一种同位素落成自己的一个峰。
The height of a peak tells you the abundance.
峰的高度告诉你丰度。
Chlorine comes out as two peaks — chlorine thirty-five, which is common, and chlorine thirty-seven, which is rarer.
氯出现两个峰——较常见的氯三十五，和较稀少的氯三十七。
So let's average them properly.
那我们就来正确地求平均。
Chlorine is seventy-five percent chlorine thirty-five, and twenty-five percent chlorine thirty-seven.
氯有百分之七十五是氯三十五，百分之二十五是氯三十七。
Multiply each mass by its percentage, add the two, then divide by one hundred.
把每个质量乘以它的百分比，两项相加，再除以一百。
Seventy-five times thirty-five gives two thousand six hundred and twenty-five; twenty-five times thirty-seven gives nine hundred and twenty-five.
七十五乘三十五得二千六百二十五； 二十五乘三十七得九百二十五。
Divide by one hundred, and the relative atomic mass is thirty-five point five.
除以一百，相对原子质量就是三十五点五。
Notice it sits closer to thirty-five, because thirty-five is the more common isotope.
注意它更接近三十五，因为三十五是更常见的同位素。
Try the same idea on copper.
用同样的思路试铜。
A mass spectrometer shows copper is sixty-nine point two percent copper sixty-three, and thirty point eight percent copper sixty-five.
质谱显示铜有百分之六十九点二是铜六十三，百分之三十点八是铜六十五。
Multiply each mass by its percentage.
把每个质量乘以百分比。
Sixty-nine point two times sixty-three gives four thousand three hundred fifty-nine point six.
六十九点二乘六十三得四千三百五十九点六。
Thirty point eight times sixty-five gives two thousand two point zero.
三十点八乘六十五得两千零二点零。
Add those, then divide by one hundred.
相加后再除以一百。
The relative atomic mass of copper is sixty-three point six.
铜的相对原子质量是六十三点六。
Again it sits closer to the more abundant isotope.
同样更接近丰度更高的那种同位素。
Now the big idea.
现在讲核心概念。
Chemists count particles in groups, the way we count eggs in dozens.
化学家把粒子按"份"来数，就像我们用"打"来数鸡蛋。
One mole is the amount that holds as many particles as there are atoms in exactly twelve grams of carbon-twelve.
一摩尔的定义是：所含的粒子数等于恰好十二克碳十二中所含的原子数。
That number is the Avogadro constant: six point zero two times ten to the twenty-three.
这个数就是阿伏伽德罗常量：六点零二乘以十的二十三次方。
Here is the gift. The mass of one mole, in grams, is simply the relative mass.
而好消息是： 一摩尔物质的质量，以克为单位，正好等于它的相对质量。
So one mole of carbon weighs twelve grams.
所以一摩尔碳重十二克。
Which gives the equation you will use most: moles equals mass divided by molar mass.
由此得到你最常用的公式：物质的量等于质量除以摩尔质量。
In the lab you never count particles one by one.
在实验室里你不会一个一个地数粒子。
You weigh them on a balance like this one.
你会像这样用天平称量。
The balance gives you mass in grams.
天平给出以克为单位的质量。
Molar mass turns that mass into moles.
摩尔质量再把质量换算成物质的量。
Molar mass is the mass of one mole, with units grams per mole.
摩尔质量是一摩尔的质量，单位是克每摩尔。
Its number matches the relative atomic or molecular mass — but now the unit is attached.
它的数值等于相对原子质量或相对分子质量—— 但现在带了单位。
Twelve for carbon is relative atomic mass.
碳的十二是相对原子质量。
Twelve grams per mole is the molar mass.
十二克每摩尔才是摩尔质量。
That single link is why weighing works as counting.
正是这一条联系，让称量变成了数数。
Work a simple example.
做一个简单例题。
How many moles are in eight point zero grams of methane, C H four?
八点零克甲烷——碳氢四——是多少摩尔？
Carbon is twelve, hydrogen is one, so four hydrogens add four.
碳是十二，氢是一，四个氢加四。
The molar mass is sixteen grams per mole.
摩尔质量是十六克每摩尔。
Moles equals mass divided by molar mass: eight point zero divided by sixteen.
物质的量等于质量除以摩尔质量：八点零除以十六。
That is zero point five zero moles.
结果是零点五零摩尔。
Always write the unit.
一定要写单位。
And always say what the particles are — here they are methane molecules, not free carbon or hydrogen atoms.
也一定要说清粒子是什么—— 这里是甲烷分子，不是游离的碳原子或氢原子。
One mole of anything holds six point zero two times ten to the twenty-three particles — but the particles may be atoms, molecules, or ions. Always say which.
一摩尔任何东西都含有六点零二乘以十的二十三次方个粒子——但粒子可以是原子、分子或离子。
One mole of sodium atoms is different from one mole of sodium ions, and different again from one mole of sodium chloride formula units.
一定要说清是哪一种。 一摩尔钠原子不同于一摩尔钠离子，也不同于一摩尔氯化钠的化学式单元。
The number is the same. The chemical meaning is not.
数目相同，化学含义却不同。
On exam answers, write "moles of molecules" or "moles of ions" when it matters.
答题时，在需要的地方写"分子的物质的量"或"离子的物质的量"。
Vague "moles of stuff" loses marks when the question asks you to specify.
含糊地说"东西的摩尔"，题目要求指明时就会丢分。
Keep this picture in your head.
把这幅图记在脑子里。
The mole sits at the centre of every calculation, with four roads leading out.
摩尔位于每一个计算的中心，向外通出四条路。
To a mass: divide by the molar mass, or multiply to come back.
通向质量：除以摩尔质量，或反过来相乘。
To a number of particles: multiply by the Avogadro constant.
通向粒子数：乘以阿伏伽德罗常量。
To a gas volume: at room conditions one mole fills twenty-four cubic decimetres.
通向气体体积：在室温常压下，一摩尔气体占二十四立方分米。
To a solution: moles equals concentration times volume.
通向溶液：物质的量等于浓度乘以体积。
Whatever a question hands you, your first move is always the same — get to moles.
无论题目给你什么， 你的第一步永远相同——先换算成摩尔。
Study the map on screen.
仔细看屏幕上的图。
The centre box is moles.
中心方框是物质的量。
One double arrow links mass with n equals m over M.
一条双向箭头连着质量，公式是 n 等于 m 除以 M。
Another links particles with times the Avogadro constant.
另一条连着粒子数，乘以阿伏伽德罗常量。
A third links gas volume with n equals V over twenty-four.
第三条连着气体体积，n 等于 V 除以二十四。
A fourth links solution with n equals c times V.
第四条连着溶液，n 等于 c 乘以 V。
You convert in, then convert out — never jump sideways from mass straight to volume without moles in the middle.
你先换算进去，再换算出来—— 绝不要不经摩尔，从质量直接跳到体积。
Every multi-step stoichiometry question is just walking those roads in order.
每一个多步化学计量题，都只是按顺序走这些路。
Before formulas, one word.
写化学式之前，先弄清一个词。
A compound is a substance made of two or more elements chemically joined.
化合物是由两种或更多元素以化学方式结合而成的物质。
Water is a compound of hydrogen and oxygen.
水是氢和氧的化合物。
Sodium chloride is a compound of sodium and chlorine.
氯化钠是钠和氯的化合物。
A mixture is different — the elements or compounds sit side by side and are not chemically joined.
混合物不同——元素或化合物只是并排放在一起， 并没有化学结合。
In this topic we write formulas for compounds, balance equations for reactions of compounds, and use those formulas to count moles of compounds.
本专题里，我们为化合物写化学式，为化合物的反应配平方程式， 并用这些化学式来计算化合物的物质的量。
Before we calculate, you need formulas.
在计算之前，你得先会写化学式。
In an ionic compound the charges must cancel exactly, so the compound is neutral overall.
在离子化合物中，正负电荷必须完全抵消， 整体呈电中性。
The Periodic Table gives you most of them. Group one gives plus one, group two plus two, group thirteen plus three; group fifteen is minus three, group sixteen minus two, group seventeen minus one.
周期表能告诉你大部分离子的电荷：第一族是正一，第二族正二， 第十三族正三；第十五族是负三，第十六族负二，第十七族负一。
Learn the awkward ones by heart: nitrate, carbonate, sulfate, hydroxide, ammonium.
那些不规则的要背下来：硝酸根、碳酸根、硫酸根、氢氧根、铵根。
And when a metal has more than one charge, a Roman numeral shows the oxidation number.
而当一种金属有不止一种电荷时，罗马数字表示它的氧化数。
Learn four more ions by name and formula: zinc is plus two, silver is plus one, hydrogencarbonate is H C O three minus, and phosphate is P O four three minus.
再背四个离子的名称和化学式：锌是正二，银是正一，碳酸氢根是氢碳氧三负一， 磷酸根是磷氧四负三。
Hydrogen forms H plus, and the group eighteen noble gases do not normally form ions.
氢形成正一价的氢离子，第十八族稀有气体通常不形成离子。
For iron three oxide, balance the charges: two iron three plus ions cancel three oxide two minus ions, so the formula is F e two O three.
对三氧化二铁，要配平电荷：两个三价铁离子抵消三个负二价氧离子， 所以化学式是铁二氧三。
Write the metal first, then the non-metal or polyatomic ion, with the smallest whole-number ratio that cancels charge.
先写金属，再写非金属或多原子离子， 用能抵消电荷的最小整数比。
An equation must be balanced: the same number of every kind of atom on both sides.
化学方程式必须配平：两边每一种原子的个数都相同。
Add state symbols to say what each species is — solid, liquid, gas, or aqueous, which means dissolved in water.
再加上状态符号，说明每种物质的状态——固体、液体、气体，或水溶液，也就是溶解在水中。
Sometimes you write an ionic equation, which shows only the species that actually change.
有时你要写离子方程式，它只写出真正发生变化的物种。
The ions that sit through the reaction unchanged are called spectator ions, and you leave them out completely.
那些自始至终没有变化的离子叫做旁观离子，要把它们完全略去。
Work the classic precipitation.
做经典的沉淀反应。
Silver nitrate aqueous plus sodium chloride aqueous makes solid silver chloride and aqueous sodium nitrate.
硝酸银水溶液加氯化钠水溶液，生成固体氯化银和硝酸钠水溶液。
Expand every aqueous ionic compound into free ions.
把每个水溶液中的离子化合物拆成自由离子。
Cancel the spectator ions — sodium plus and nitrate minus appear on both sides.
删掉旁观离子——钠正离子和硝酸根 两边都有。
What remains is the ionic equation: silver plus plus chloride minus goes to solid silver chloride.
剩下的就是离子方程式：银正离子加氯负离子生成固体氯化银。
Only the ions that form the precipitate stay.
只有形成沉淀的离子留下。
That is how every net ionic equation is built.
每一个净离子方程式都是这样建立的。
Two kinds of formula.
化学式有两种。
The empirical formula is the simplest whole-number ratio of the atoms.
实验式是各原子最简单的整数比。 分子式是一个分子中原子的真实个数。
The molecular formula is how many atoms are really in one molecule.
乙烷的实验式是碳氢三，而实际上是碳二氢六。
Ethane is carbon-hydrogen-three as an empirical formula, but carbon-two-hydrogen-six in reality. To get an empirical formula from percentages, there are three steps. Divide each percentage by the relative atomic mass.
要从百分含量求实验式，有三步： 把每个百分数除以相对原子质量；再把所有结果除以其中最小的那个；然后取整数。
Divide every answer by the smallest one. Round to whole numbers. Forty percent carbon, six point seven hydrogen and fifty-three point three oxygen gives a ratio of one to two to one.
百分之四十的碳、百分之六点七的氢、百分之五十三点三的氧， 得到的比是一比二比一。
Follow the table on screen.
跟着屏幕上的表。
Take one hundred grams of the compound so the percentages become masses in grams.
取一百克化合物，这样百分数就变成以克计的质量。
Carbon forty point zero divided by twelve is three point three three moles.
碳四十点零除以十二是三点三三摩尔。
Hydrogen six point seven divided by one is six point seven moles.
氢六点七除以一是六点七摩尔。
Oxygen fifty-three point three divided by sixteen is three point three three moles.
氧五十三点三除以十六是三点三三摩尔。
Divide every mole value by the smallest, three point three three.
每个摩尔数都除以最小的三点三三。
You get one to two to one.
得到一比二比一。
So the empirical formula is C H two O.
所以实验式是碳氢二氧。
The table is the whole method — fill it left to right.
这张表就是全部方法——从左到右填满。
To get the molecular formula, you also need the relative molecular mass.
要求分子式，还需要相对分子质量。
Find how many times the empirical formula mass fits into the molecular mass, then multiply every subscript by that whole number.
看实验式的式量能整除进分子质量多少次， 再把每一个下标乘以那个整数。
For ethane the empirical formula is C H three, so the empirical mass is twelve plus three equals fifteen.
乙烷的实验式是碳氢三，实验式量为十二加三等于十五。
The real molecular mass is thirty.
真实分子质量是三十。
Thirty divided by fifteen is two, so multiply every subscript by that number: C two H six.
三十除以十五是二，所以每个下标乘二：碳二氢六。
Without Mr you can only stop at the empirical formula.
没有相对分子质量，你只能停在实验式。
Some solids hold water inside their crystals.
有些固体在晶体内部含有水。
That water is called water of crystallisation.
那种水叫做结晶水。
A solid that contains it is hydrated; the same solid with the water removed is anhydrous.
含有结晶水的固体是水合的； 去掉水之后同一种固体是无水的。
For example, hydrated copper two sulfate is C u S O four dot five H two O — five water molecules for every formula unit.
例如，水合硫酸铜是铜硫氧四·五水—— 每一个化学式单元对应五个水分子。
Heating it drives off the water to leave anhydrous copper sulfate, which is pale.
加热会赶走水，留下无水硫酸铜，颜色变浅。
The water of crystallisation is part of the crystal structure, not just wet on the surface.
结晶水是晶体结构的一部分，不是表面随便沾的水。
Now put it to work.
现在来实际运用。
Burn four point eight grams of magnesium in oxygen.
把四点八克镁在氧气中燃烧。
Cross the bridge in three steps.
分三步过这座"桥"。
Mass to moles: four point eight divided by twenty-four is zero point two zero moles.
质量换算成摩尔：四点八除以二十四，等于零点二零摩尔。
Use the ratio from the balancing numbers — one to one here — so you make zero point two zero moles of magnesium oxide.
用配平系数给出的比例——这里是一比一——所以生成零点二零摩尔氧化镁。
Moles back to mass: times forty gives eight point zero grams.
再从摩尔换回质量：乘以四十，得到八点零克。
In a real lab you always get a little less than that, and the percentage yield tells you how much less.
在真实的实验室里， 你得到的总会略少一些，而产率告诉你少了多少。
Read the bridge left to right.
从左到右读这座桥。
Four point eight grams of magnesium divided by relative atomic mass twenty-four gives zero point two zero moles of magnesium.
四点八克镁除以相对原子质量二十四，得到零点二零摩尔镁。
The stoichiometry — the balancing numbers — says magnesium to magnesium oxide is one to one, so you still have zero point two zero moles of product.
化学计量——也就是配平系数——说镁与氧化镁是一比一，所以产物仍是零点二零摩尔。
Multiply by molar mass forty to get eight point zero grams of magnesium oxide.
再乘以摩尔质量四十，得到八点零克氧化镁。
That word stoichiometry just means the mole ratios from the balanced equation.
化学计量这个词， 就是指配平方程式给出的摩尔比。
Never use relative masses as if they were balancing numbers.
绝不要把相对质量当成配平系数来用。
Percentage yield compares the amount you actually made with the maximum possible amount, then multiplies by one hundred percent.
产率把你实际得到的量与最大可能量相比，再乘以百分之一百。
Write it as actual over maximum, times one hundred percent.
写成实际量除以最大量，再乘百分之一百。
You get less for many reasons: side reactions, incomplete reaction, or product lost when you filter or transfer.
你会少得到，原因很多：副反应、反应不完全， 或过滤转移时损失产物。
The maximum is the theoretical yield from the mole bridge.
最大量就是摩尔桥算出的理论产量。
Always base product moles on the limiting reagent, never on a reactant that is still left over.
产物的物质的量一定要以限量试剂为准，绝不能以还剩着的反应物为准。
When you mix two reactants, one of them usually runs out first.
当你把两种反应物混合时，通常有一种会先用完。
That one is the limiting reagent, and it decides how much product you get.
它就是限量试剂， 由它决定生成多少产物。
The other is in excess — there is more than enough of it.
另一种则过量——它绰绰有余。
Look at the picture: four hydrogen molecules meet one oxygen molecule.
看这幅图： 四个氢分子遇到一个氧分子。
The oxygen runs out after making two waters, and two hydrogen molecules are left over.
氧在生成两个水分子后就用完了， 还剩下两个氢分子。
To spot the limiting reagent, find the moles of each, divide by its balancing number, and take the smallest.
要找出限量试剂，先求出各自的物质的量， 再除以它的配平系数，取最小的那个。
Pause on the diagram.
在这张图上停一下。
Four hydrogen molecules and one oxygen molecule go in.
四个氢分子和一个氧分子进去。
Two water molecules come out, and two hydrogen molecules are left unused.
两个水分子出来，还剩两个氢分子没用完。
The oxygen was limiting — it ran out.
氧是限量的——它用完了。
The leftover hydrogen was in excess.
剩下的氢是过量的。
If a question gives you masses of both reactants, convert both to moles, divide each by its coefficient from the equation, and the smaller result is limiting.
如果题目给出两种反应物的质量， 都先换成摩尔，各自除以方程式里的系数，较小的那个就是限量试剂。
Then calculate the product from that limiting amount only.
然后只用限量的量来算产物。
Ignore the excess for the product mass.
算产物质量时，忽略过量的那一方。
Gases are easier than they look.
气体比看上去容易。
At the same temperature and pressure, equal volumes of any gases hold equal numbers of molecules.
在相同温度和压强下，任何气体，相同体积就含有相同数目的分子。
It does not matter whether it is hydrogen or carbon dioxide — same volume, same count.
是氢气还是二氧化碳都没关系——体积相同，个数就相同。
So at room temperature and pressure, one mole of any gas fills twenty-four cubic decimetres.
所以在室温常压下，一摩尔任何气体都占二十四立方分米。
That gives a very simple rule: moles equals volume divided by twenty-four, with the volume in cubic decimetres.
由此得到一条很简单的规则：物质的量等于体积除以二十四，体积以立方分米计。
You use equal-volume thinking when burning hydrocarbons — compounds of only carbon and hydrogen.
燃烧碳氢化合物——只含碳和氢的化合物——时，你会用到等体积思想。
Compare gas volumes of the hydrocarbon and oxygen, or of the carbon dioxide produced.
比较碳氢化合物与氧气的气体体积，或生成的二氧化碳的体积。
At the same temperature and pressure, a two-to-one mole ratio in the equation is also a two-to-one volume ratio.
在相同温度和压强下，方程式里二比一的摩尔比，也是二比一的体积比。
Quote the rule every time: volume equals moles times twenty-four cubic decimetres at room temperature and pressure.
每次都写出规则：在室温常压下，体积等于摩尔数乘以二十四立方分米。
Write the equation you use.
写出你用的方程。
Markers look for it.
阅卷人会找这句话。
Now solutions.
现在讲溶液。
The solute is the substance that dissolves.
溶质是溶解进去的物质。
The solution is the mixture you end up with.
溶液是你最终得到的混合物。
Concentration is the amount of solute in each cubic decimetre of solution, measured in moles per cubic decimetre.
浓度是每立方分米溶液中溶质的物质的量，单位是摩尔每立方分米。
So moles equals concentration times volume, with volume in cubic decimetres.
所以物质的量等于浓度乘以体积，体积用立方分米。
Remember one thousand cubic centimetres make one cubic decimetre.
记住一千立方厘米等于一立方分米。
A burette reading in cubic centimetres must be divided by one thousand before you multiply by concentration.
滴定管以立方厘米读数，乘浓度之前必须先除以一千。
The last road: solutions.
最后一条路：溶液。
Concentration is the moles of solute in each cubic decimetre, so moles equals concentration times volume.
浓度是每立方分米溶液中溶质的物质的量， 所以物质的量等于浓度乘以体积。
The trap is units — a burette reads in cubic centimetres, and a thousand of those make one cubic decimetre.
陷阱在单位上——滴定管读数是立方厘米， 一千立方厘米才等于一立方分米。
Here is a titration. Twenty point zero cubic centimetres of zero point one zero zero molar acid exactly neutralises twenty-five point zero of sodium hydroxide.
来看一个滴定：二十点零立方厘米、 浓度零点一零零摩尔每立方分米的酸，恰好中和二十五点零立方厘米的氢氧化钠。
The acid supplies two times ten to the minus three moles.
酸提供二乘以十的负三次方摩尔。
The ratio is one to one, so the alkali has the same.
比例是一比一，所以碱也是这么多。
Divide by its own volume, and the concentration is zero point zero eight zero zero.
除以它自己的体积，浓度就是零点零八零零。
In a titration a burette adds a solution of known concentration to the unknown in the conical flask, until the indicator changes colour.
滴定时，滴定管把已知浓度的溶液加到锥形瓶里的未知液中，直到指示剂变色。
That colour change is the end point.
那个变色就是终点。
You record the volume delivered from the burette.
你记录滴定管放出的体积。
From known concentration and volume you find moles of the known solution, use the mole ratio from the equation, then divide by the flask volume in cubic decimetres to find the unknown concentration.
用已知浓度和体积求出已知液的物质的量， 再用方程式的摩尔比，最后除以锥形瓶体积（立方分米）得到未知浓度。
Always average concordant titres — readings that agree within zero point one zero cubic centimetres.
一定要平均一致的滴定读数——彼此相差不超过零点一零立方厘米的读数。
Give your answer to a sensible number of significant figures — usually match the data in the question.
答案要用合理的有效数字——通常与题目数据一致。
Three significant figures is common in mole work.
摩尔计算里常见三位有效数字。
Do not write more digits than the data supports.
不要写超过数据支持的位数。
Do not round so early that you lose accuracy in the middle of a multi-step calculation — keep guard digits, then round only at the end.
也不要在多步计算中间过早四舍五入而损失精度—— 中间多留几位，只在最后取整。
And always include the unit: grams, moles, cubic decimetres, or moles per cubic decimetre.
并且一定要写单位：克、摩尔、立方分米， 或摩尔每立方分米。
A naked number rarely scores full marks.
光秃秃的数字很少拿满分。
Three marks students throw away.
三个学生常丢的分。
First, convert volumes to cubic decimetres before you use concentration — the missing divide by a thousand is the most common titration mistake in the whole paper.
第一，在使用浓度之前先把体积换算成立方分米—— 漏掉那个"除以一千"是整张卷子里最常见的滴定错误。
Second, the mole ratio comes from the balancing numbers, never from the relative masses.
第二，摩尔比来自配平系数，绝不是来自相对质量。
Third, give your answer to the same number of significant figures as the data, usually three, and always write the unit.
第三，答案的有效数字要与题目数据一致，通常是三位，并且一定要写单位。
Get these right, and stoichiometry is yours.
把这些做对，化学计量就是你的了。