Concentration Over Time · 浓度随时间变化
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| half-life/hɑːf laɪf/ | 半衰期 | bàn shuāi qī |
How amounts fade with the clock
- Watch a reactant disappear and plot it against the clock.
- The shape of that curve reveals the reaction's order.
- A straight line, of the right kind, pins it down.
- One special time, the half-life, sums up the pace.
量如何随时钟消退
- 看着某反应物消失,把它对时钟作图。
- 那条曲线的形状揭示反应的级数。
- 一条正确类型的直线把它确定下来。
- 一个特殊的时间——半衰期——概括了节奏。
Which plot is a straight line
- First order: a plot of $\ln[A]$ versus time is straight.
- Second order: a plot of $1/[A]$ versus time is straight.
- Zero order: a plot of $[A]$ versus time is straight.
哪张图是直线
- 一级:$\ln[A]$ 对时间的图是直线。
- 二级:$1/[A]$ 对时间的图是直线。
- 零级:$[A]$ 对时间的图是直线。
If a plot of $\ln[A]$ versus time is a straight line, the reaction is... · 如果$\ln[A]$对时间的作图是一条直线，则该反应为...
A linear $\ln[A]$-versus-time plot indicates first order. · $\ln[A]$对时间的线性作图表明这是一级反应。
A straight-line plot of $1/[A]$ versus time indicates which order? · $1/[A]$对时间的直线作图指示的是哪一级反应？
The $1/[A]$ linear plot is the signature of second order. · $1/[A]$的线性作图是二级反应的特征。
The half-life
- The half-life 半衰期 is the time for half the reactant to be used up.
- For a first-order reaction, the half-life is constant.
- Every half-life, the amount halves again.
半衰期
- 半衰期是消耗掉一半反应物所需的时间。
- 对一级反应,半衰期是恒定的。
- 每过一个半衰期,量再次减半。
Only a first-order reaction has a constant half-life. · 只有具有一级反应才具有恒定的半衰期。
For other orders the half-life changes as concentration drops. · 对于其他级数的反应，随着浓度降低，半衰期会发生变化。
Each half-life, the amount of reactant is cut in . · 每经过一个半衰期，反应物的量就减少为。
A half-life halves whatever is present. · 半衰期会使任何现有的量减半。
Finding the order from data
- Try each plot; whichever is straight gives the order.
- The slope of that line relates to the rate constant $k$.
- This is how experiments reveal the reaction order.
从数据求级数
- 试每一张图;哪一张是直线就给出级数。
- 那条直线的斜率与速率常数 $k$ 有关。
- 这就是实验揭示反应级数的方式。
Concentration over time · 浓度随时间的变化
A first-order reactant decays exponentially: it falls by the same fraction in each equal time step. · 一级反应物的浓度呈指数衰减：在每一个相等的时间间隔内，其减少的比例相同。
The slope of the straight-line plot is related to the rate constant. · 直线的斜率与速率常数有关。
The magnitude of the slope gives $k$. · 斜率的绝对值给出$k$。
A first-order reaction has a half-life of $20\ \text{s}$, starting at $8\ \text{M}$.
- After $20\ \text{s}$ it is $4\ \text{M}$; after $40\ \text{s}$, $2\ \text{M}$; after $60\ \text{s}$, $1\ \text{M}$.
- It halves every $20\ \text{s}$, no matter the amount.
一级反应半衰期为 $20\ \text{s}$,起始 $8\ \text{M}$。
- $20\ \text{s}$ 后是 $4\ \text{M}$;$40\ \text{s}$ 后 $2\ \text{M}$;$60\ \text{s}$ 后 $1\ \text{M}$。
- 无论量多少,它每 $20\ \text{s}$ 减半。
A first-order reaction starts at $16\ \text{M}$ with a $10\ \text{s}$ half-life. Concentration after $20\ \text{s}$ (in M)? · 一级反应起始浓度为$16\ \text{M}$，半衰期为$10\ \text{s}$。经过$20\ \text{s}$（单位M）后的浓度是多少？
Two half-lives give $16 \to 8 \to 4\ \text{M}$. · 两个半衰期后剩余$16 \to 8 \to 4\ \text{M}$。
Only a first-order reaction has a constant half-life -- for other orders the half-life changes as the concentration drops. Match the straight-line plot to the order ($\ln[A]$, $1/[A]$, or $[A]$). And a steeper line means a bigger rate constant.
只有一级反应才有恒定的半衰期——对其他级数,半衰期随浓度下降而变化。把直线图与级数对应($\ln[A]$、$1/[A]$ 或 $[A]$)。而且直线越陡,速率常数越大。
The order shows up in which plot is a straight line: $\ln[A]$ (first), $1/[A]$ (second), or $[A]$ (zero) versus time. The half-life is the time to use up half the reactant, and it is constant only for a first-order reaction, halving the amount again each period.
级数体现在哪张图是直线:$\ln[A]$(一级)、$1/[A]$(二级)或 $[A]$(零级)对时间。半衰期是消耗掉一半反应物的时间,它只在一级反应中恒定,每个周期把量再次减半。