Half-life and the rate constant · 半衰期和速率常数
| English | 中文 | Pinyin · 拼音 |
|---|---|---|
| half-life/hɑːf laɪf/ | 半衰期 | bàn shuāi qī |
| first-order/fɜːst ˈɔːdə/ | 一级 | yī jí |
| rate constant/reɪt ˈkɒnstənt/ | 速率常数 | sù lǜ cháng shù |
The constant countdown
- The half-life 半衰期 is the time for a concentration to halve.
- For a first-order 一级 reaction it is constant — the same every time.
- That constant half-life both identifies first order and gives you the rate constant 速率常数.
恒定的倒计时
- 半衰期(half-life)是一个浓度减半的时间。
- 对一个一级反应它是恒定的——每次都相同。
- 那个恒定的半衰期既识别一级,也给你速率常数。
A first-order reaction has a constant half-life. · 一个一级反应有一个恒定的半衰期。
The half-life is independent of concentration. · 半衰期与浓度无关。
Constant half-life
- For a first-order reaction, the half-life does not depend on concentration.
- So the concentration halves in the same time, again and again — a quick way to spot first order.
A first-order reaction has a constant half-life
恒定的半衰期
- 对一个一级反应,半衰期不取决于浓度。
- 所以浓度在相同的时间一次又一次地减半——一个发现一级的快速方式。
一个一级反应有一个恒定的半衰期
Half-life & rate constant · 半衰期和速率常数
[A] = [A]₀·bᵗ
Each · 每个 half-life halves the concentration. · 每个半衰期使浓度减半。
A reaction whose half-life stays the same as it proceeds is: · 一个半衰期随它进行保持相同的反应是:
A constant half-life (independent of concentration) is the signature of a first-order reaction. · 一个恒定的半衰期(与浓度无关)是一个一级反应的标志。
A constant half-life can be used to identify a first-order reaction. · 一个恒定的半衰期能被用来识别一个一级反应。
Only first-order reactions have a half-life that is independent of the concentration. · 只有一级反应有一个与浓度无关的半衰期。
Finding k
- You can also find $k$ by putting initial-rate data into the rate equation.
A first-order reaction has a half-life of 20 s.
- Rate constant: $k = 0.693 / 20 =$ 0.035 per second.
- After 60 s (that's 3 half-lives), the concentration has fallen to $(\tfrac{1}{2})^3 =$ one-eighth of the start.
找 k
- 你也能通过把初始速率数据放进速率方程找到 $k$。
一个一级反应有一个 20 s 的半衰期。
- 速率常数:$k = 0.693 / 20 =$ 0.035 每秒。
- 在 60 s 后(那是 3 个半衰期),浓度已经下降到起始的 $(\tfrac{1}{2})^3 =$ 八分之一。
For a first-order reaction, the rate constant is: · 对一个一级反应,速率常数是:
k = 0.693 / t½ for a first-order reaction. · 对一个一级反应 k = 0.693 / t½。
A first-order reaction has a half-life of 100 s. What is k? (k = 0.693/t½) · 一个一级反应有一个 100 s 的半衰期。k 是多少?(k = 0.693/t½)
k = 0.693 / 100 = 0.00693 (per second). · k = 0.693 / 100 = 0.00693(每秒)。
Reading it off a graph
- Plot concentration against time, then read the time for it to fall to half.
- Read it again from that point to a quarter — if the two half-lives are equal, the reaction is first order.
- Equal successive half-lives on the curve is the visual fingerprint of first order.
从一个图读出它
- 画浓度对时间,然后读出它下降到一半的时间。
- 从那一点再读到四分之一——如果两个半衰期相等,反应是一级。
- 曲线上相等的连续半衰期是一级的视觉指纹。
You've got it
- half-life = time for the concentration to halve
- a first-order reaction has a constant half-life (independent of concentration)
- $k = \dfrac{0.693}{t_{1/2}}$ — e.g. $t_{1/2} = 20\,\text{s}$ gives $k = 0.035$ per second
- check it on a graph: equal successive half-lives ⇒ first order
你掌握了
- 半衰期 = 浓度减半的时间
- 一个一级反应有一个恒定的半衰期(与浓度无关)
- $k = \dfrac{0.693}{t_{1/2}}$——例如 $t_{1/2} = 20\,\text{s}$ 给出 $k = 0.035$ 每秒
- 在一个图上检查它:相等的连续半衰期 ⇒ 一级