📚 Accurate Relative Atomic Masses | 准确相对原子质量
Accurate relative atomic masses are the foundation of quantitative chemistry. They allow chemists to convert between mass and amount in moles, and they are determined experimentally by mass spectrometry, not by simply reading the periodic table. In this revision guide we look at how the relative atomic mass is defined, why the values we use are never whole numbers, how a mass spectrometer produces data accurate to four or five significant figures, and how to use those data correctly in calculations and exam questions.
准确的相对原子质量是定量化学的基础。它们使化学家能够在质量和摩尔数之间进行换算，并且是通过质谱法实验测定的，而不仅仅是从周期表中读取。在本篇复习指南中，我们将讨论相对原子质量是如何定义的、为什么我们使用的数值从来不是整数、质谱仪如何给出准确到四到五位有效数字的数据，以及如何在计算和考试题目中正确使用这些数据。
1. Relative Atomic Mass and Relative Isotopic Mass | 相对原子质量与相对同位素质量
The relative atomic mass, symbol Aᵣ, of an element is the weighted mean mass of all atoms of the element compared with 1/12 of the mass of one atom of carbon-12. It is a dimensionless quantity: it is a ratio of two masses, so it has no units.
一种元素的相对原子质量（符号 Aᵣ）是该元素所有原子的加权平均质量与一个碳-12 原子质量的 1/12 之比。它是一个无量纲的量：它是两个质量之比，因此没有单位。
The relative isotopic mass is the mass of one specific isotope of an element on the same carbon-12 scale. For example, chlorine-35 has a relative isotopic mass of 34.969, not exactly 35, because the mass of a ³⁵Cl atom is not exactly 35 times 1/12 of the mass of a ¹²C atom.
相对同位素质量是某一特定同位素在相同碳-12 标度下的质量。例如，氯-35 的相对同位素质量为 34.969，而不是正好 35，因为一个 ³⁵Cl 原子的质量并不正好是一个 ¹²C 原子质量 1/12 的 35 倍。
The key difference is averaging. A relative isotopic mass describes a single isotope; a relative atomic mass describes the natural mixture of all the isotopes of that element, weighted according to their abundances. This is why Aᵣ is often called a weighted mean mass rather than simply an average mass.
关键区别在于"平均"。相对同位素质量描述的是单一同位素；相对原子质量描述的则是该元素所有同位素的天然混合物，并按各自的丰度加权。这就是为什么 Aᵣ 常被称为加权平均质量，而不仅仅是平均质量。
Both quantities are dimensionless, but they allow chemists to compare the masses of different atoms on a consistent scale.
这两个量都是无量纲的，但它们使化学家能够在一致的标度上比较不同原子的质量。
2. The Carbon-12 Standard and the Atomic Mass Unit | 碳-12 标度与原子质量单位
Since 1961 the international standard has been carbon-12. One unified atomic mass unit, symbol u (also called the dalton, Da), is defined as exactly 1/12 of the mass of one atom of carbon-12.
自 1961 年以来，国际标准一直是碳-12。一个统一原子质量单位（符号 u，也称道尔顿 Da）被定义为正好等于一个碳-12 原子质量的 1/12。
1 u = 1/12 × m(¹²C) = 1.66054 × 10⁻²⁷ kg
Because of this definition, the relative isotopic mass of carbon-12 is exactly 12.000000, with no experimental uncertainty at all. Every other isotope has a value that is slightly above or below a whole number, and those values must be measured.
由于这一约定，碳-12 的相对同位素质量正好是 12.000000，完全不存在实验不确定度。其他所有同位素的数值都略高于或略低于某个整数，而这些数值必须通过实验测定。
ng its relative isotopic mass by 1.66054 × 10⁻²⁷ kg, which is the same as dividing its molar mass by the Avogadro constant.
这一定义的一个有用推论是原子质量单位与克之间的换算。把某一原子的相对同位素质量乘以 1.66054 × 10⁻²⁷ kg，就得到单个原子以千克计的质量，这与用其摩尔质量除以阿伏加德罗常数得到的结果相同。
3. Why Relative Atomic Masses Are Not Whole Numbers | 为什么相对原子质量不是整数
Most elements exist as mixtures of isotopes, so the weighted average is rarely a whole number. Chlorine has two stable isotopes, ³⁵Cl and ³⁷Cl, with relative isotopic masses of 34.969 and 36.966 and natural abundances of about 75.76% and 24.24% respectively.
大多数元素以同位素混合物的形式存在，因此加权平均值很少是整数。氯有两种稳定同位素 ³⁵Cl 和 ³⁷Cl，相对同位素质量分别为 34.969 和 36.966，天然丰度约为 75.76% 和 24.24%。
48, while using the accurate relative isotopic masses gives 35.45. The difference is small, but in an exam question that asks for an accurate value, the accurate masses must be used.
用质量数快速估算可得 (35 × 0.7576) + (37 × 0.2424) = 35.48，而使用准确的相对同位素质量则得到 35.45。差别不大，但在要求"准确数值"的考试题中，必须使用准确的同位素质量。
| Isotope | 同位素 | Relative isotopic mass | 相对同位素质量 | Abundance | 丰度 |
| ³⁵Cl | 34.969 | 75.76% |
| ³⁷Cl | 36.966 | 24.24% |
| ⁶³Cu | 62.930 | 69.15% |
| ⁶⁵Cu | 64.928 | 30.85% |
Many elements have more than two isotopes, so the calculation simply contains more terms. Magnesium, for example, has three stable isotopes, and neon has three as well, one of which is present in only 0.27% abundance.
许多元素有两种以上的同位素，因此计算式中只是多了几项而已。例如镁有三种稳定同位素，氖也有三种，其中一种的丰度仅为 0.27%。
4. Mass Spectrometry: How Accurate Values Are Measured | 质谱法：准确数值的测定方式
A mass spectrometer measures the mass-to-charge ratio (m/z) of ions formed from a sample. Because the charge is normally +1, the m/z value is effectively the mass of the ion, and the size of each peak tells us the relative abundance of that isotope.
质谱仪测定由样品生成的离子的质荷比（m/z）。由于电荷通常为 +1，m/z 值实际上就是离子的质量，而每个峰的大小告诉我们该同位素的相对丰度。
The stages of a modern instrument are worth knowing in order, because exam questions frequently ask for them.
现代仪器的各个阶段值得按顺序掌握，因为考试题经常要求写出这些步骤。
- Vaporisation: the sample is heated and turned into a gas. | 汽化：样品被加热并转化为气体。
- Ionisation: an electron gun knocks out electrons to form positive ions, mostly with a single positive charge. | 电离：电子枪打出电子，形成正离子，多数带一个正电荷。
- Acceleration: an electric field accelerates the ions, so all ions enter the analyser with the same kinetic energy. | 加速：电场加速离子，使所有离子以相同的动能进入分析器。
- Separation: a magnetic field (or a time-of-flight drift tube) separates the ions according to their m/z value. | 分离：磁场（或飞行时间漂移管）按 m/z 值将离子分离。
- Detection: ions hitting the detector produce a current, which is amplified and recorded as a peak. | 检测：离子打到检测器上产生电流，经放大后记录为一个峰。
The whole system is kept under a high vacuum, because collisions with air molecules would scatter the ions and broaden the peaks, destroying the accuracy of the measurement.
整个系统保持高真空状态，因为与空气分子碰撞会散射离子、使峰变宽，从而破坏测量的准确性。
5. Reading a Mass Spectrum and Finding Abundances | 解读质谱图与求取丰度
The number of peaks in the spectrum of an element tells you how many isotopes are present, and the relative heights of the peaks give the relative abundances.
元素质谱图中峰的数目告诉你有多少种同位素存在，而峰的相对高度则给出相对丰度。
Chlorine gives two peaks in an approximately 3:1 ratio, because ³⁵Cl is roughly three times as abundant as ³⁷Cl. Bromine also gives two peaks, but in an approximately 1:1 ratio, because ⁷⁹Br and ⁸¹Br have nearly equal abundances. These ratios are the fingerprint of halogen-containing molecules.
氯给出两个峰，比例约为 3:1，因为 ³⁵Cl 的丰度大约是 ³⁷Cl 的三倍。溴同样给出两个峰，但比例约为 1:1，因为 ⁷⁹Br 和 ⁸¹Br 的丰度几乎相等。这些比例是含卤素分子的"指纹"。
In the mass spectrum of a molecule, the peak with the highest m/z value is the molecular ion peak, labelled M⁺. It is formed when a molecule is ionised but not fragmented, and its m/z value equals the relative molecular mass of the molecule.
在分子的质谱图中，m/z 值最大的峰是分子离子峰，标记为 M⁺。它由一个分子被电离但未发生碎片化而生成，其 m/z 值等于该分子的相对分子质量。
nt, and a peak at m/z = 29 suggests CHO⁺ or C₂H₅⁺. The M and M+2 peaks in a 3:1 ratio indicate one chlorine atom, while a 1:1 M and M+2 pattern indicates one bromine atom.
碎片峰出现在较小的 m/z 值处，可用于推断结构特征。例如，m/z = 15 的峰提示 CH₃⁺ 碎片，m/z = 29 的峰提示 CHO⁺ 或 C₂H₅⁺。比例为 3:1 的 M 和 M+2 峰表明存在一个氯原子，而比例为 1:1 的 M 和 M+2 峰则表明存在一个溴原子。
6. Calculating Weighted Mean Relative Atomic Mass | 计算加权平均相对原子质量
The weighted mean is calculated by multiplying each relative isotopic mass by its fractional abundance and adding the results. If abundances are given as percentages, divide each one by 100 first, or equivalently divide the final total by 100.
加权平均值通过将每个相对同位素质量乘以它的分数丰度然后相加得到。如果给出的丰度是百分数，要先把每个除以 100，或者等价地把最终总和除以 100。
Aᵣ = Σ (fractional abundance × relative isotopic mass)
Aᵣ = (Σ percentage abundance × relative isotopic mass) ÷ 100
The two forms are mathematically identical, so choose whichever your exam board uses. What matters is that you never simply average the isotope masses, because that would ignore the abundances and give the wrong answer.
这两种形式在数学上完全相同，选择你所在考试局使用的那种即可。重要的是绝不能简单地对同位素质量取平均，因为那会忽略丰度，得出错误答案。
Take care to convert each percentage correctly. It is easy to type 75.76 as 0.757 (a common slip) or to enter 24.24 when the abundance is actually 24.24% of a mixture whose other component is 75.76%. Always check that your fractional abundances add up to 1.000, or that your percentages add up to 100%.
要小心正确换算每个百分数。很容易把 75.76 输成 0.757（常见失误），或者在另一种组分占 75.76% 时把丰度误写成 24.24。始终检查你的分数丰度之和是否为 1.000，或者百分数之和是否为 100%。
7. Worked Examples: Chlorine, Copper and Boron | 实例演算：氯、铜和硼
Worked example 1: chlorine. Using 34.969 at 75.76% and 36.966 at 24.24%:
实例 1：氯。使用 34.969（75.76%）和 36.966（24.24%）：
Aᵣ = (75.76 × 34.969 + 24.24 × 36.966) ÷ 100 = (2649.3 + 896.1) ÷ 100 = 35.45
Worked example 2: copper. Using 62.930 at 69.15% and 64.928 at 30.85%:
实例 2：铜。使用 62.930（69.15%）和 64.928（30.85%）：
Aᵣ = (69.15 × 62.930 + 30.85 × 64.928) ÷ 100 = (4351.6 + 2003.0) ÷ 100 = 63.55
Worked example 3: boron. Using 10.013 at 19.9% and 11.009 at 80.1%:
实例 3：硼。使用 10.013（19.9%）和 11.009（80.1%）：
Aᵣ = (19.9 × 10.013 + 80.1 × 11.009) ÷ 100 = (199.26 + 881.82) ÷ 100 = 10.81
101) = 24.32. Using the accurate relative isotopic masses 23.985, 24.986 and 25.983 gives 24.305, which rounds to 24.31.
实例 4：镁，用以说明准确度的影响。使用质量数和取整的丰度得到 (24 × 0.7899) + (25 × 0.1000) + (26 × 0.1101) = 24.32。使用准确的相对同位素质量 23.985、24.986 和 25.983 则得到 24.305，取整为 24.31。
These four examples show a consistent pattern: the accurate answer is within about 0.05 of the estimate, but a question demanding an accurate value will not accept the estimate.
这四个例子显示出一致的规律：准确答案与估算值相差约 0.05 以内，但要求给出准确数值的题目不会接受估算结果。
8. Mass Defect, Binding Energy and Decimal Places | 质量亏损、结合能与小数位
Why is the relative isotopic mass of ³⁵Cl 34.969 rather than 35.000? The answer lies in the nucleus. When protons and neutrons come together to form a nucleus, a small amount of mass is converted into binding energy, according to Einstein's relationship.
为什么 ³⁵Cl 的相对同位素质量是 34.969 而不是 35.000？答案在于原子核。当质子和中子结合形成原子核时，少量的质量按照爱因斯坦的关系式转化为了结合能。
ΔE = Δm × c²
This difference between the sum of the masses of the separate nucleons and the actual mass of the nucleus is called the mass defect. Because the mass defect differs from one nuclide to another, the packing fraction differs too, and the relative isotopic masses are not whole numbers.
各个独立核子的质量之和与原子核实际质量之间的这个差值称为质量亏损。由于不同核素的质量亏损不同，其"堆积分数"也不同，因此相对同位素质量并非整数。
This is also why the mass of a proton, 1.00728 u, and the mass of a neutron, 1.00866 u, are not exactly 1. For accurate work, chemists use tabulated relative isotopic masses measured to six or seven significant figures, and they never round them before the final step of the calculation.
这也解释了为什么质子的质量 1.00728 u 和中子的质量 1.00866 u 都不正好是 1。在需要准确度的工作中，化学家使用测定到六到七位有效数字的相对同位素质量表，并且在计算的最后一步之前绝不对其取整。
9. Relative Molecular Mass, Formula Mass and Molar Mass | 相对分子质量、式量与摩尔质量
The relative molecular mass, symbol Mᵣ, is the sum of the relative atomic masses of all the atoms in a molecule. For covalent substances this value is exact for the particular formula being considered.
相对分子质量（符号 Mᵣ）是分子中所有原子的相对原子质量之和。对于共价物质，该值对所考虑的特定化学式而言是准确的。
e formula unit. Sodium chloride therefore has a relative formula mass of 22.99 + 35.45 = 58.44, not a relative molecular mass.
对于离子化合物，不存在独立的分子，因此我们使用相对式量，其计算方式完全相同，但指的是化学式单元。因此氯化钠的相对式量为 22.99 + 35.45 = 58.44，而不是相对分子质量。
The molar mass, symbol M, is the mass in grams of one mole of a substance. Numerically it equals Aᵣ or Mᵣ, but it carries the unit g mol⁻¹, which makes it usable in calculations.
摩尔质量（符号 M）是一摩尔物质以克计的质量。其数值等于 Aᵣ 或 Mᵣ，但它带有单位 g mol⁻¹，因而可以用于计算。
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