\[w_\text{待测} = \frac{m_\text{称量形} \times F}{m_\text{试样}}\times 100\%,\qquad F = \frac{a\,M_\text{待测}}{b\,M_\text{称量形}}\]\[w_\text{analyte} = \frac{m_\text{weighed form} \times F}{m_\text{sample}}\times 100\%,\qquad F = \frac{a\,M_\text{analyte}}{b\,M_\text{weighed form}}\]
含义Meaning
把称量形式（如 BaSO₄）的质量换算为待测组分（如 S 或 SO₃）质量的系数，a、b 使两者所含关键元素原子数相等。
Converts the weighed form (e.g. BaSO₄) into the analyte (e.g. S or SO₃); a and b balance the key element.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(F\) | 换算因数gravimetric factor | 1 |
| \(a, b\) | 使关键元素数目相等的系数coefficients balancing the key element | 1 |
推导Derivation
关键元素守恒：\(a\) mol 待测物 ↔ \(b\) mol 称量形。
The key element is conserved between analyte and weighed form.
质量比 = \(aM_\text{待测}/(bM_\text{称量形})\)。
Mass ratio = \(aM_\text{analyte}/(bM_\text{weighed})\).
适用条件与局限Assumptions & limitations
要求沉淀完全（溶解损失可忽略）、称量形组成确定且纯净（共沉淀、吸附杂质会造成误差）。
Needs complete precipitation and a pure, stoichiometric weighed form.
例题Worked example
由 Fe₂O₃ 求 Fe₃O₄：F = 2M(Fe₃O₄)/(3M(Fe₂O₃)) = 2×231.5/(3×159.7) = 0.9666。
Fe₃O₄ from Fe₂O₃: F = 0.9666.