📚 The Mole Concept Explained & Basic Calculation Techniques | 摩尔概念详解与基础计算技巧
The mole is one of the most important ideas in chemistry because it connects the invisible world of atoms and molecules to the measurable world of grams, litres and concentrations. In this article, you will learn the definition of the mole, the Avogadro constant, and the core calculations involving mass, particle number, gas volume and solution concentration.
摩尔是化学中最重要概念之一，因为它把看不见的原子、分子世界与可称量的克、升、浓度联系起来。本文将讲解摩尔的定义、阿伏伽德罗常数，以及涉及质量、粒子数、气体体积和溶液浓度的基础计算技巧。
1. What Is a Mole? | 什么是摩尔
The mole is the SI base unit for the amount of substance. One mole of any substance contains exactly the same number of elementary entities as the number of atoms in exactly 12 g of carbon-12. This number is known as the Avogadro constant, NA = 6.022 × 10²³ mol⁻¹.
摩尔是物质的量的SI基本单位。任何物质的一摩尔所含有的基本单元数目，与12 g碳-12中所含的原子数目完全相同。这个数目称为阿伏伽德罗常数，NA = 6.022 × 10²³ mol⁻¹。
Elementary entities may be atoms, molecules, ions, electrons or formula units.
基本单元可以是原子、分子、离子、电子或式量单元。
The amount of substance is given the symbol n and is measured in moles (mol).
物质的量用符号 n 表示，单位是摩尔（mol）。
The mole acts as a bridge between the microscopic world and the macroscopic world of laboratory measurements.
摩尔是连接微观粒子世界与实验室宏观测量之间的桥梁。
2. The Avogadro Constant and Number of Particles | 阿伏伽德罗常数与粒子数
number of particles N and the amount of substance n. The central relationship is N = n × NA, or n = N / NA.
阿伏伽德罗常数使我们能在粒子数 N 与物质的量 n 之间进行换算。核心关系为 N = n × NA，即 n = N / NA。
N = n × 6.022 × 10²³
but because each molecule has two oxygen atoms, it contains 2 × 6.022 × 10²³ oxygen atoms.
例如，2.00 mol水分子含有2.00 × 6.022 × 10²³ = 1.204 × 10²⁴个水分子。注意：1 mol O₂ 含有6.022 × 10²³个氧分子，但由于每个氧分子含两个氧原子，所以其中氧原子数目为2 × 6.022 × 10²³个。
3. Molar Mass | 摩尔质量
Molar mass, M, is the mass of one mole of a substance. Its unit is g mol⁻¹. Numerically, the molar mass of a substance is equal to its relative atomic mass, Ar, or its relative molecular/formula mass, Mr.
摩尔质量 M 指一摩尔物质所具有的质量，单位是 g mol⁻¹。在数值上，摩尔质量等于物质的相对原子质量 Ar，或相对分子质量／式量 Mr。
98.1, so its molar mass is 98.1 g mol⁻¹. This means one mole of H₂SO₄ has a mass of 98.1 g.
例如，H₂SO₄ 的相对分子质量为2 × 1.0 + 32.1 + 4 × 16.0 = 98.1，因此其摩尔质量为98.1 g mol⁻¹。也就是说，1 mol H₂SO₄ 的质量为98.1 g。
4. Converting Between Mass, Moles and Particles | 质量、物质的量与粒子数的换算
The most important mole calculation equation relates mass m, molar mass M and amount of substance n:
最重要的摩尔计算公式将质量 m、摩尔质量 M 与物质的量 n 联系起来：
n = m / M and m = n × M
To convert between particles and grams, combine this equation with the Avogadro constant. A useful summary of the main relationships is shown below.
要在粒子数与质量之间换算，可把上式与阿伏伽德罗常数结合使用。下面表格总结了主要关系。
| Quantity | Symbol | Unit | Useful relationship |
| Mass | m | g | m = n × M |
| Amount of substance | n | mol | n = m/M = N/NA = V/Vₘ = c × V |
| Number of particles | N | no unit | N = n × NA |
| Gas volume | V | dm³ | V = n × Vₘ |
| Concentration | c | mol dm⁻³ | c = n / V |
sing the concentration equation, always convert cm³ to dm³ before performing the calculation.
请记住1 cm³ = 0.001 dm³。使用浓度公式时，务必先把 cm³ 换算成 dm³ 再进行计算。
5. Molar Volume of Gases | 气体摩尔体积
Under the same conditions of temperature and pressure, equal volumes of different gases contain equal numbers of moles. This idea is captured by the molar volume of a gas, Vₘ.
在相同的温度和压力条件下，相同体积的不同气体含有相同的物质的量。这个概念可以用气体摩尔体积 Vₘ 来表达。
