溶质质量分数 Mass fraction (percentage by mass) — 公式推导、符号与局限

\[w = \frac{m_{\text{溶质}}}{m_{\text{溶液}}}\times 100\% = \frac{m_{\text{溶质}}}{m_{\text{溶质}} + m_{\text{溶剂}}}\times 100\%\]\[w = \frac{m_{\text{solute}}}{m_{\text{solution}}}\times 100\% = \frac{m_{\text{solute}}}{m_{\text{solute}} + m_{\text{solvent}}}\times 100\%\]

稀释前后溶质质量不变dilution: solute mass is conserved

\[m_1 w_1 = m_2 w_2\]

含义Meaning

溶质质量占溶液总质量的百分比。初中最常用的浓度表示法。

The percentage of the solution’s mass that is solute — the standard concentration measure in junior high.

符号说明Symbols

符号Symbol	含义 Meaning	单位 Unit
\(w\)	质量分数mass fraction	%
\(m\)	质量mass	g

推导Derivation

溶液质量 = 溶质质量 + 溶剂质量。
Mass of solution = mass of solute + mass of solvent.
按定义取比值并乘以 100%。
Take the ratio and multiply by 100 %.
加水稀释时溶质质量不变：\(m_1w_1 = m_2w_2\)；同理可求浓缩、混合问题。
On dilution the solute mass is unchanged: \(m_1w_1 = m_2w_2\); the same balance handles concentrating and mixing.

适用条件与局限Assumptions & limitations

溶质必须真正溶解；未溶解的固体、结晶析出的部分不计入。
Only dissolved solute counts; undissolved or crystallised material does not.
饱和溶液中 \(w\) 有上限 \(w_{\max} = \frac{S}{100+S}\)（\(S\) 为溶解度，g/100 g 水）。
A saturated solution caps \(w\) at \(w_{\max} = \frac{S}{100+S}\) (S = solubility in g per 100 g water).
体积不能直接相加：混合后溶液体积一般不等于两体积之和，计算要用质量。
Volumes are not additive; work in masses.

例题Worked example

把 50 g 20% 的 NaCl 溶液稀释到 5%，需加水：50×20% = (50+x)×5%，x = 150 g。

Diluting 50 g of 20 % NaCl to 5 %: 50 × 20 % = (50 + x) × 5 %, so x = 150 g of water.