\[\bar M_n = \frac{\sum_i N_iM_i}{\sum_i N_i} = \sum_i x_iM_i\]
含义Meaning
按分子数目加权的平均摩尔质量，对低分子量组分敏感。用端基分析、渗透压、凝固点降低等依数性方法测定。
Molar mass averaged over the number of molecules; sensitive to small chains and measured by end-group analysis or colligative methods such as osmometry.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(N_i\) | 摩尔质量为 M_i 的分子数number of molecules of mass M_i | 1 |
| \(x_i\) | 数量分数number fraction | 1 |
推导Derivation
总质量除以总分子数（物质的量）。
Total mass divided by total number of molecules.
依数性只“数”粒子数目：\(\Pi/c \to RT/\bar M_n\)（c → 0），所以给出数均值。
Colligative properties count particles, so osmometry gives \(\bar M_n\).
适用条件与局限Assumptions & limitations
对少量低分子杂质（残余单体、溶剂）非常敏感。
Very sensitive to small amounts of low-mass impurities.
例题Worked example
等摩尔的 10 kg/mol 与 100 kg/mol 链：M_n = 55 kg/mol。
Equal numbers of 10 and 100 kg/mol chains: M_n = 55 kg/mol.