\[c_1 V_1 = c_2 V_2\]
同种溶液混合mixing two solutions of the same solute
\[c_{\text{混}} = \frac{c_1V_1 + c_2V_2}{V_{\text{混}}}\]\[c_{\text{mix}} = \frac{c_1V_1 + c_2V_2}{V_{\text{mix}}}\]含义Meaning
稀释前后溶质的物质的量不变。
Dilution leaves the amount of solute unchanged.
符号说明Symbols
| 符号Symbol | 含义 Meaning | 单位 Unit |
|---|---|---|
| \(c_1, V_1\) | 稀释前浓度与体积concentration and volume before | mol·L⁻¹, L |
| \(c_2, V_2\) | 稀释后浓度与体积concentration and volume after | mol·L⁻¹, L |
推导Derivation
稀释只加溶剂，溶质物质的量 \(n = cV\) 守恒。
Only solvent is added, so the amount \(n = cV\) is conserved.
令前后 n 相等即得 \(c_1V_1 = c_2V_2\)。
Equate n before and after: \(c_1V_1 = c_2V_2\).
在固定 \(c_1V_1\) 时，\(c_2\) 与 \(V_2\) 成反比（双曲线）。
For fixed \(c_1V_1\), \(c_2\) is inversely proportional to \(V_2\) (a hyperbola).
适用条件与局限Assumptions & limitations
\(V_2\) 是稀释后溶液的总体积，不是加入的水的体积；浓溶液（如浓硫酸）稀释时体积不可加和。
\(V_2\) is the final total volume, not the water added; concentrated solutions (e.g. H₂SO₄) do not have additive volumes.
不适用于发生反应的混合（如酸碱混合要先算反应）。
Not for mixtures that react (do the reaction first).
例题Worked example
用 18.4 mol/L 浓硫酸配 500 mL 1.00 mol/L 稀硫酸：V₁ = 1.00×0.500/18.4 = 27.2 mL。
500 mL of 1.00 mol/L H₂SO₄ from 18.4 mol/L stock: V₁ = 27.2 mL.