📚 Masses of Atoms and Molecules | 原子和分子的质量
In chemistry, the quantities we measure in the laboratory – typically in grams – are related to the masses of individual atoms and molecules. Because atoms are incredibly tiny, we use a relative mass scale based on the carbon-12 isotope. This article builds from the unified atomic mass unit to relative atomic mass, isotopic mass, relative molecular mass, the mole concept and calculations linking mass, amount of substance and number of particles.
在化学中，我们在实验室里测量的量（通常以克计）与单个原子和分子的质量相关。因为原子极其微小，我们使用基于碳-12 同位素的相对质量标度。本文从统一原子质量单位出发，逐步讲解相对原子质量、同位素质量、相对分子质量、摩尔概念以及联系质量、物质的量和粒子数的有关计算。
1. The Atomic Mass Scale | 原子质量标准
Atoms are far too small to weigh individually on any balance. Instead, chemists use a relative scale. The modern standard is the unified atomic mass unit (u), defined such that one atom of carbon-12 has a mass of exactly 12 u. Hence, 1 u is equal to one-twelfth of the mass of a ¹²C atom, which is approximately 1.6605 × 10⁻²⁷ kg.
原子实在太小，无法用任何天平单独称量。因此化学家使用相对标度。现代标准是统一的原子质量单位 (u)，定义为一个碳-12 原子的质量恰好为 12 u。因此，1 u 等于一个 ¹²C 原子质量的十二分之一，大约为 1.6605 × 10⁻²⁷ kg。
This choice gives the most precise reference point for measuring masses of all other atoms and molecules. Because the scale is relative, the numbers are dimensionless ratios, which makes calculations straightforward.
这一选择为测量所有其他原子和分子的质量提供了最精确的参考点。由于标度是相对的，数字均为无量纲的比值，这使得计算十分直接。
2. Relative Atomic Mass (Ar) | 相对原子质量 (Ar)
The relative atomic mass, Ar, of an element is defined as the weighted average mass of all the naturally occurring isotopes of that element relative to one-twelfth of the mass of a carbon-12 atom. Because it is a ratio, Ar has no unit.
一种元素的相对原子质量 Ar 被定义为该元素全部天然同位素的加权平均质量与一个碳-12 原子质量的十二分之一的比值。由于是比值，Ar 没有单位。
Most elements consist of a mixture of isotopes, so the Ar value on the periodic table is rarely a whole number. For example, chlorine has two major isotopes: ³⁵Cl (abundance 75 %) and ³⁷Cl (25 %), giving an Ar of about 35.5. Ar values are the ones you use in all stoichiometric calculations.
多数元素由多种同位素组成，因此周期表上的 Ar 值很少为整数。例如氯有两种主要同位素：³⁵Cl（丰度 75 %）和 ³⁷Cl（25 %），得出的 Ar 约为 35.5。所有化学计量计算中用到的就是这些 Ar 值。
3. Relative Isotopic Mass | 相对同位素质量
Relative isotopic mass is the mass of one atom of a specific isotope relative to one-twelfth of the mass of a carbon-12 atom. Unlike Ar, it is not an average; it is the mass number of that isotope, expressed to a high degree of precision when needed. For instance, the relative isotopic mass of ³⁵Cl is 34.969 and that of ³⁷Cl is 36.966.
相对同位素质量是指一个特定同位素的一个原子相对于一个碳-12 原子质量十二分之一的质量。与 Ar 不同，它不是平均值；它就是该同位素的质量数，必要时会以很高的精确度表示。例如 ³⁵Cl 的相对同位素质量为 34.969，³⁷Cl 的为 36.966。
In many A-level problems, you treat the relative isotopic mass as the mass number (e.g. 35 for ³⁵Cl, 37 for ³⁷Cl). The distinction becomes important when interpreting high-resolution mass spectra.
在多数 A-level 习题中，你可以把相对同位素质量当作质量数（例如 ³⁵Cl 为 35，³⁷Cl 为 37）。当解读高分辨质谱时，这一区分就变得重要了。
4. Relative Molecular Mass (Mr) | 相对分子质量 (Mr)
The relative molecular mass, Mr, is the sum of the relative atomic masses of all atoms in a molecule. It is calculated by adding together the Ar values of the constituent atoms according to the molecular formula. Mr is also a dimensionless ratio.
相对分子质量 Mr 是分子中所有原子的相对原子质量之和。它是根据分子式将各组分原子的 Ar 相加而计算得到的。Mr 也是一个无量纲的比值。
For water, H₂O: Mr = (2 × 1.0) + 16.0 = 18.0. For carbon dioxide, CO₂: Mr = 12.0 + (2 × 16.0) = 44.0. The term is used only for substances that consist of discrete molecules, such as simple covalent compounds.
对于水 H₂O：Mr = (2 × 1.0) + 16.0 = 18.0。对于二氧化碳 CO₂：Mr = 12.0 + (2 × 16.0) = 44.0。该术语仅用于由离散分子组成的物质，如简单共价化合物。
5. Relative Formula Mass | 相对式量
For ionic compounds like sodium chloride, we cannot speak of a single molecule. Instead, we use relative formula mass, which is the sum of the relative atomic masses of all atoms in the empirical formula. The symbol is still Mr and it is calculated in exactly the same way.
对于像氯化钠这样的离子化合物，我们不能说单个分子。相反，我们使用相对式量，即最简式（经验式）中所有原子的相对原子质量之和。符号仍然为 Mr，计算方法完全相同。
For NaCl, Mr = 23.0 + 35.5 = 58.5. For magnesium hydroxide, Mg(OH)₂, Mr = 24.3 + 2×(16.0 + 1.0) = 58.3. In examinations, the term ‘relative formula mass’ is often used interchangeably with ‘relative molecular mass’ for giant structures.
对于 NaCl，Mr = 23.0 + 35.5 = 58.5。对于氢氧化镁 Mg(OH)₂，Mr = 24.3 + 2×(16.0 + 1.0) = 58.3。在考试中，对于巨型结构，“相对式量”常与“相对分子质量”混用。
6. The Mass Spectrometer and Isotopic Abundances | 质谱仪与同位素丰度
A mass spectrometer is the instrument that determines relative isotopic masses and their relative abundances. In simple terms, the sample is vaporised, ionised (usually by electron impact to form 1+ ions), accelerated through an electric field, deflected by a magnetic field and detected. The extent of deflection depends on the mass-to-charge ratio (m/z).
质谱仪是测定相对同位素质量及其相对丰度的仪器。简单来说，样品先气化，继而电离（通常通过电子轰击形成 1+ 离子），在电场中加速，由磁场偏转并检测。偏转程度取决于质荷比 (m/z)。
The output is a mass spectrum: a plot of relative abundance (or relative intensity) against m/z. Each peak corresponds to a different isotope, and the peak height (or area) gives the relative abundance. For diatomic elements like Cl₂, you can even see peaks from combinations of isotopes.
输出结果就是质谱图：相对丰度（或相对强度）对 m/z 的图。每个峰对应一种不同的同位素，峰高（或峰面积）给出相对丰度。对于像 Cl₂ 这样的双原子分子，你甚至可以看到由同位素组合产生的峰。
7. Calculating Average Relative Atomic Mass | 计算平均相对原子质量
From the mass spectrum, the average Ar is calculated using the weighted mean of the isotopic masses. The general formula is:
由质谱图，平均 Ar 可通过同位素质量的加权平均值计算出来。通用公式为：
Ar = Σ (isotopic mass × relative abundance) / Σ relative abundances
If abundances are given as percentages, the denominator is 100. Example for chlorine: the spectrum shows peaks at m/z 35 and 37 with relative intensities 3 : 1. Average Ar = (35 × 3 + 37 × 1) / (3 + 1) = 142 / 4 = 35.5.
如果丰度以百分比给出，分母就是 100。以氯为例：质谱图在 m/z 35 和 37 处显示峰，相对强度为 3 : 1。平均 Ar = (35 × 3 + 37 × 1) / (3 + 1) = 142 / 4 = 35.5。
Another common example is boron: ¹⁰B (20%) and ¹¹B (80%). Ar(B) = (10 × 20 + 11 × 80) / 100 = 10.8. Mastering this calculation is essential for A-level data-analysis questions.
另一个常见例子是硼：¹⁰B (20 %) 和 ¹¹B (80 %)。Ar(B) = (10 × 20 + 11 × 80) / 100 = 10.8。掌握这一计算对于 A-level 的数据分析题至关重要。
8. The Mole and Avogadro’s Constant | 摩尔与阿伏伽德罗常数
The mole (mol) is the SI unit for amount of substance. One mole of any substance contains exactly 6.02 × 10²³ specified particles (atoms, molecules, ions or electrons). This number is Avogadro’s constant, L or NA. It is chosen because the mass of one mole of carbon-12 atoms is exactly 12 g, linking the microscopic scale to measurable laboratory masses.
摩尔 (mol) 是物质的量的 SI 单位。1 mol 任何物质精确地含有 6.02 × 10²³ 个指定的微粒（原子、分子、离子或电子）。这个数字就是阿伏伽德罗常数，符号为 L 或 NA。选取这个数值是因为 1 mol 碳-12 原子的质量恰好为 12 g，从而将微观尺度与实验室可测质量联系了起来。
Thus, the magnitude of Avogadro’s constant arises from the definition: it is the number of atoms in exactly 12 g of carbon-12. We use it to convert between the number of particles and the amount in moles.
因此，阿伏伽德罗常数的大小来自其定义：它是恰好 12 g 碳-12 中的原子数目。我们用它来在粒子数与摩尔量之间进行换算。
9. Molar Mass (M) | 摩尔质量 (M)
Molar mass, M, is the mass of one mole of a substance. Its numerical value equals the relative atomic mass (Ar) or relative molecular/formula mass (Mr), but it carries the unit g mol⁻¹. For example, the molar mass of oxygen atoms is 16.0 g mol⁻¹, while that of O₂ molecules is 32.0 g mol⁻¹.
摩尔质量 M 是 1 mol 物质的质量。其数值等于相对原子质量 Ar 或相对分子/式量 Mr，但带有单位 g mol⁻¹。例如，氧原子的摩尔质量是 16.0 g mol⁻¹，而 O₂ 分子的摩尔质量是 32.0 g mol⁻¹。
The relationship is simply: M (g mol⁻¹) = Ar or Mr with units attached. This allows us to weigh out an amount of substance directly in the laboratory; if we need 1 mol of glucose (C₆H₁₂O₆, Mr = 180.0), we weigh 180.0 g.
关系很简单：M (g mol⁻¹) = 加上单位的 Ar 或 Mr。这让我们可以在实验室直接称量出物质的量；若需要 1 mol 葡萄糖 (C₆H₁₂O₆, Mr = 180.0)，我们就称取 180.0 g。
10. Interconverting Mass, Moles and Number of Particles | 质量、摩尔和粒子数的相互换算
The central equation linking mass and amount of substance is:
联系质量和物质的量的核心公式是：
n = m / M
where n is amount (mol), m is mass (g) and M is molar mass (g mol⁻¹). This equation can be rearranged as m = n × M or M = m / n.
其中 n 为物质的量 (mol)，m 为质量 (g)，M 为摩尔质量 (g mol⁻¹)。该式可重排为 m = n × M 或 M = m / n。
To find the number of particles, N, combine with Avogadro’s constant:
要计算粒子数 N，可结合阿伏伽德罗常数：
N = n × L
Worked example: Calculate the number of sodium ions in 4.00 g of NaOH. Mr(NaOH) = 23.0 + 16.0 + 1.0 = 40.0, so M = 40.0 g mol⁻¹. n = 4.00 / 40.0 = 0.100 mol. As each NaOH formula provides one Na⁺, n(Na⁺) = 0.100 mol. N(Na⁺) = 0.100 × 6.02 × 10²³ = 6.02 × 10²² ions.
计算示例：计算 4.00 g NaOH 中钠离子的数目。Mr(NaOH) = 23.0 + 16.0 + 1.0 = 40.0，故 M = 40.0 g mol⁻¹。n = 4.00 / 40.0 = 0.100 mol。因为每个 NaOH 式量提供 1 个 Na⁺，n(Na⁺) = 0.100 mol。N(Na⁺) = 0.100 × 6.02 × 10²³ = 6.02 × 10²² 个离子。
These conversions form the backbone of quantitative chemistry, from titrations to empirical formula determinations. Always ensure you use the correct molar mass and pay careful attention to the chemical formula when counting atoms or ions.
这些换算构成了从滴定到确定最简式的定量化学的支柱。务必使用正确的摩尔质量，并在清点原子或离子时特别注意化学式。
Published by TutorHao | Chemistry Revision Series | aleveler.com
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