📚 Counting Particles by Mass: The Mole | 用质量计数微粒：摩尔
In chemistry, we need a bridge between the macroscopic world of grams and the invisible world of atoms and molecules. The mole provides that bridge, allowing us to count particles by weighing them.
在化学中，我们需要一座连接宏观的克世界和微观的原子、分子世界的桥梁。摩尔提供了这座桥梁，让我们能够通过称量来计数微粒。
1. Why Do We Need the Mole? | 为什么我们需要摩尔？
Atoms and molecules are incredibly small. It is impossible to count them individually in a laboratory. Chemists needed a way to relate the mass of a substance, which we can measure on a balance, to the number of particles it contains.
原子和分子极其微小，在实验室里不可能逐个计数。化学家们需要一种方法，将我们能用天平测量的物质质量与其所含的微粒数联系起来。
The mole solves this problem by setting a fixed number of particles – Avogadro's constant – and linking it to the atomic mass scale. We can then use the mass of a sample to calculate how many atoms, molecules or formula units are present.
摩尔通过设定一个固定的微粒数——阿伏伽德罗常数——并将其与原子质量标度联系起来，解决了这一问题。这样我们就可以通过样品的质量计算出其中含有多少个原子、分子或式单元。
2. Avogadro's Constant: The Chemist's Dozen | 阿伏伽德罗常数：化学家的“打”
Avogadro's constant, symbol Nₐ (or L in some IB resources), has the value 6.02214076 × 1023 mol⁻¹. You will often use the rounded value 6.02 × 1023 for calculations. It represents the number of specified particles in exactly one mole of a substance.
阿伏伽德罗常数，符号为 Nₐ（某些IB资源中用 L），数值为 6.02214076 × 1023 mol⁻¹。计算时你通常会使用四舍五入后的值 6.02 × 1023。它表示恰好一摩尔任何物质中所含指定微粒的个数。
Just as a dozen means 12 items, a mole means 6.02 × 1023 items – whether those items are eggs, electrons, or water molecules. The only difference is the sheer magnitude of the number.
正如一打表示12个一样，一摩尔表示 6.02 × 1023 个——无论这些个体是鸡蛋、电子还是水分子。唯一的区别在于这个数字的巨大数量级。
3. Defining the Mole | 摩尔的定义
The mole is the SI unit for amount of substance. One mole contains exactly 6.02214076 × 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, Nₐ, when expressed in mol⁻¹, and is called the Avogadro number.
摩尔是国际单位制中物质的量的单位。一摩尔恰好含有 6.02214076 × 1023 个基本单元。这个数字是阿伏伽德罗常数 Nₐ 在以 mol⁻¹ 为单位时的固定数值，称为阿伏伽德罗数。
Importantly, we must always specify the entities we are counting. They can be atoms (e.g., Ar), molecules (e.g., H₂O), ions (e.g., Na⁺), electrons, or any other specified particle.
重要的是，我们必须始终指明所计数的实体。它们可以是原子（如 Ar）、分子（如 H₂O）、离子（如 Na⁺）、电子或任何其他指定的微粒。
4. Molar Mass – The Mass of One Mole | 摩尔质量——一摩尔的质量
The molar mass, M, is the mass of one mole of a substance. It has units of g mol⁻¹. The numerical value of the molar mass of an element in g mol⁻¹ is equal to its relative atomic mass (Aᵣ). For example, the Aᵣ of carbon is 12.01, so the molar mass of carbon is 12.01 g mol⁻¹.
摩尔质量 M 是一摩尔某物质的质量，单位为 g mol⁻¹。某种元素的摩尔质量在数值上等于其相对原子质量（Aᵣ）。例如，碳的 Aᵣ 是 12.01，因此碳的摩尔质量是 12.01 g mol⁻¹。
sses of all the atoms in the formula. For water (H₂O): M = 2×1.01 + 16.00 = 18.02 g mol⁻¹.
对于分子和化合物，摩尔质量是化学式中所有原子的摩尔质量之和。对于水（H₂O）：M = 2×1.01 + 16.00 = 18.02 g mol⁻¹。
5. Calculating Number of Moles from Mass | 由质量计算物质的量
The key formula linking mass (m in grams), molar mass (M in g mol⁻¹) and amount of substance (n in moles) is:
n =
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