The Beer-Lambert Law · 比尔-朗伯定律
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| absorbance/əbˈsɔːbəns/ | 吸光度 | xī guāng dù |
Reading concentration from colour
- A deeper-coloured drink usually means a stronger mix.
- Shine light through it and more colour absorbs more light.
- Measure how much light is swallowed and you know the strength.
- One tidy equation turns absorbed light into concentration.
从颜色读出浓度
- 颜色更深的饮料通常意味着更浓的调配。
- 让光穿过它,颜色越深吸收的光越多。
- 测量有多少光被吞掉,你就知道浓度。
- 一个整洁的方程把吸收的光变成浓度。
The absorbance equation
- Absorbance 吸光度 grows with concentration:
- $\varepsilon$ is how strongly the substance absorbs, $b$ the path length, and $c$ the concentration.
吸光度方程
- 吸光度随浓度增大:
- $\varepsilon$ 是该物质吸收的强弱,$b$ 是光程,$c$ 是浓度。
With $\varepsilon = 300$, $b = 1\ \text{cm}$, $c = 0.002\ \text{M}$, the absorbance $A$? · 给定$\varepsilon = 300$、$b = 1\ \text{cm}$、$c = 0.002\ \text{M}$，吸光度$A$为多少？
$A = \varepsilon b c = 300\times1\times0.002 = 0.6$.
Absorbance tracks concentration
- With everything else fixed, $A$ is directly proportional to $c$.
- Double the concentration and the absorbance doubles.
- A plot of $A$ versus $c$ is a straight line through the origin.
吸光度跟随浓度
- 其他都固定时,$A$ 与 $c$ 成正比。
- 浓度加倍,吸光度加倍。
- $A$ 对 $c$ 的图是一条过原点的直线。
With path length and wavelength fixed, absorbance is proportional to... · 当光程和波长固定时，吸光度与...成正比
$A = \varepsilon b c$, so $A \propto c$ when the rest is fixed. · $A = \varepsilon b c$，所以当其余条件固定时，$A \propto c$也会翻倍。
Doubling the concentration doubles the absorbance (in the linear range). · 在直线范围内，浓度加倍会使吸光度加倍。
$A$ is directly proportional to $c$, so it doubles too. · $A$与$c$成正比，因此它也翻倍。
Finding an unknown
- Measure $A$ for known concentrations to draw a calibration line.
- Read an unknown's concentration off that line from its $A$.
- This is how a spectrophotometer measures a sample.
求未知浓度
- 测量若干已知浓度的 $A$,画出校准直线。
- 根据未知样品的 $A$,从那条线上读出它的浓度。
- 这就是分光光度计测量样品的方式。
A calibration plot of absorbance versus concentration is... · 吸光度对浓度的校准图是...
$A = \varepsilon b c$ is linear in $c$, passing through the origin. · $A = \varepsilon b c$在$c$上是线性的，并通过原点。
A ____ measures a sample's absorbance to find its concentration. · ____用于测量样品的吸光度以确定其浓度。
A spectrophotometer reads absorbance and applies the Beer-Lambert law. · 分光光度计读取吸光度并应用比尔-朗伯定律。
A solution has $\varepsilon = 200$, path length $b = 1\ \text{cm}$, and $A = 0.6$.
- $c = \dfrac{A}{\varepsilon b} = \dfrac{0.6}{200 \times 1}$.
- $c = 0.003\ \text{M}$.
一份溶液 $\varepsilon = 200$,光程 $b = 1\ \text{cm}$,$A = 0.6$。
- $c = \dfrac{A}{\varepsilon b} = \dfrac{0.6}{200 \times 1}$。
- $c = 0.003\ \text{M}$。
The Beer-Lambert law · 比尔-朗伯定律
Absorbance is proportional to concentration - the basis of a calibration curve. · 吸光度与浓度成正比——这是校准曲线的基础。
With $\varepsilon = 100$, $b = 1\ \text{cm}$, and $A = 0.5$, the concentration (in M)? · 给定 $\varepsilon = 100$、$b = 1\ \text{cm}$ 和 $A = 0.5$，浓度（单位为 M）是多少？
$c = A/(\varepsilon b) = 0.5/(100\times1) = 0.005\ \text{M}$.
Absorbance is directly proportional to concentration only over a limited range -- very concentrated solutions bend the line. Keep the path length and wavelength fixed when you compare samples. And use the wavelength the substance absorbs most strongly for the best sensitivity.
吸光度只在有限范围内与浓度成正比——非常浓的溶液会使直线弯曲。比较样品时保持光程和波长固定。而且用该物质吸收最强的波长,灵敏度最好。
The Beer-Lambert law says absorbance $A = \varepsilon b c$, so $A$ is directly proportional to concentration when path length and wavelength are fixed. A plot of $A$ versus $c$ is a straight line, and reading an unknown's $A$ against a calibration line gives its concentration.
比尔-朗伯定律说吸光度 $A = \varepsilon b c$,所以在光程和波长固定时,$A$ 与浓度成正比。$A$ 对 $c$ 的图是一条直线,把未知样品的 $A$ 对照校准直线,就得到它的浓度。