物质的量与粒子数 Amount of substance from number of particles — 公式推导、符号与局限

\[n = \frac{N}{N_A}, \qquad N_A = 6.02214076\times10^{23}\ \mathrm{mol^{-1}}\]

含义Meaning

1 mol 任何粒子都含有阿伏加德罗常数个粒子。2019 年起 \(N_A\) 被定义为精确值，摩尔由它定义。

One mole of any entity contains Avogadro’s number of entities. Since 2019 \(N_A\) is exact and defines the mole.

符号Symbol	含义 Meaning	单位 Unit
\(N\)	粒子数number of entities	1
\(N_A\)	阿伏加德罗常数Avogadro constant	mol⁻¹

摩尔被定义为含 \(N_A\) 个基本单元的物质的量，所以 N 个粒子相当于 \(N/N_A\) mol。
The mole is the amount containing \(N_A\) entities, so N entities are \(N/N_A\) mol.
与 \(n = m/M\) 联立：\(N = \frac{m}{M}N_A\)，可在质量与粒子数之间换算。
Combined with \(n = m/M\): \(N = \frac{m}{M}N_A\), converting mass to particle count.

必须指明粒子种类（分子、原子、离子、电子）。
Always state the entity (molecules, atoms, ions, electrons).
历史上 \(N_A\) 是测量值（X 射线晶体密度法、电解法），约 \(6.022\times10^{23}\)；高中计算取 6.02×10²³。
Historically \(N_A\) was measured (X-ray crystal density, electrolysis); use 6.02×10²³ in school calculations.

1.204×10²⁴ 个 CO₂ 分子是 2.00 mol，含 4.00 mol 氧原子。

1.204×10²⁴ CO₂ molecules = 2.00 mol, containing 4.00 mol of O atoms.