k 速率常数计算器（零级、一级、二级与阿伦尼乌斯）Rate Constant Calculator (Zero, First, Second Order & Arrhenius)

使用说明与常见问题How-to & FAQ

「速率常数计算器（零级、一级、二级与阿伦尼乌斯）」是什么？What is the Rate Constant Calculator (Zero, First, Second Order & Arrhenius) tool?

由浓度随时间的变化按积分速率方程求零级、一级或二级反应的速率常数 k 和半衰期；也可用阿伦尼乌斯方程 k = A·e^(−Ea/RT) 求 k，或由一个温度下的 k 换算另一温度下的 k。本地处理。Find the rate constant k and half-life of a zero-, first- or second-order reaction from how the concentration changes over time (integrated rate laws), or get k from the Arrhenius equation k = A·e^(−Ea/RT), or convert a known k to another temperature. Processed locally.

如何使用「速率常数计算器（零级、一级、二级与阿伦尼乌斯）」？How do I use the Rate Constant Calculator (Zero, First, Second Order & Arrhenius) tool?

在「速率常数计算器（零级、一级、二级与阿伦尼乌斯）」中，填写「计算」、「反应级数」、「初始浓度 [A]₀」、「t 时浓度 [A]」、「时间 t」等参数，结果会随输入实时计算并显示在下方。In the Rate Constant Calculator (Zero, First, Second Order & Arrhenius): Fill in "Calculate", "Reaction order", "Initial concentration [A]₀", "Concentration [A] at time t", "Time t"; results are recalculated instantly as you type.

怎么知道反应级数？How do I know the reaction order?

级数要由实验确定，不能直接从化学方程式看出。常用方法：ln[A] 对 t 是直线就是一级，1/[A] 对 t 是直线就是二级，[A] 对 t 是直线就是零级。The order comes from experiment, not from the balanced equation. A common check: if ln[A] against t is a straight line the reaction is first order, if 1/[A] against t is straight it is second order, and if [A] against t is straight it is zero order.

k 的单位是什么？What unit does k have?

零级 k 的单位是 浓度/时间（如 mol·L⁻¹·s⁻¹），一级是 1/时间（如 s⁻¹），二级是 1/(浓度·时间)（如 L·mol⁻¹·s⁻¹）。时间单位和你输入的 t 一致。Zero order: concentration per time (such as mol·L⁻¹·s⁻¹); first order: 1/time (such as s⁻¹); second order: 1/(concentration·time) (such as L·mol⁻¹·s⁻¹). The time unit is whatever you used for t.

阿伦尼乌斯方程怎么用？How is the Arrhenius equation used?

k = A·e^(−Ea/RT)，Ea 用 kJ/mol 输入，T 用开尔文。已知某温度下的 k 和 Ea 时，用“换算到另一温度”模式：ln(k₂/k₁) = −(Ea/R)(1/T₂ − 1/T₁)。经验上很多反应温度每升高 10 K 速率约翻一倍。k = A·e^(−Ea/RT), with Ea in kJ/mol and T in kelvin. If you know k at one temperature and Ea, use the other-temperature mode: ln(k₂/k₁) = −(Ea/R)(1/T₂ − 1/T₁). As a rule of thumb many reactions roughly double in rate for every 10 K rise.

能举个计算实例吗？Can you show a worked example?

例如在「速率常数计算器（零级、一级、二级与阿伦尼乌斯）」中填 计算 = 由浓度变化求 k，反应级数 = 一级，初始浓度 [A]₀ = 1，t 时浓度 [A] = 0.5，时间 t = 10，结果区显示：速率常数 k：0.06931 1/时间；半衰期 t½（从 [A]₀ 开始）：10 （与 t 同一时间单位）；ℹ ln([A]₀/[A]) = kt · t½ = ln 2 / kFor example, entering Calculate = k from concentrations, Reaction order = First order, Initial concentration [A]₀ = 1, Concentration [A] at time t = 0.5, Time t = 10 in the Rate Constant Calculator (Zero, First, Second Order & Arrhenius) gives: Rate constant k: 0.06931 1/time; Half-life t½ (from [A]₀): 10 (same time unit as t); ℹ ln([A]₀/[A]) = kt · t½ = ln 2 / k

哪些输入会被检查？Which inputs are validated?

「速率常数计算器（零级、一级、二级与阿伦尼乌斯）」会检查这些输入——「初始浓度 [A]₀」、「t 时浓度 [A]」、「时间 t」、「指前因子 A」、「活化能 Ea（kJ/mol）」、「温度 T₁（K）」、「T₁ 时的速率常数 k₁」、「温度 T₂（K）」：所选方式用到时必须填写；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The Rate Constant Calculator (Zero, First, Second Order & Arrhenius) checks its inputs — "Initial concentration [A]₀", "Concentration [A] at time t", "Time t", "Pre-exponential factor A", "Activation energy Ea (kJ/mol)", "Temperature T₁ (K)", "Rate constant k₁ at T₁", "Temperature T₂ (K)": required when the chosen option uses it; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.

有哪些选项可以调整？What options can I adjust?

「速率常数计算器（零级、一级、二级与阿伦尼乌斯）」的设置：「计算」可选 由浓度变化求 k、阿伦尼乌斯方程求 k、换算到另一温度（默认 由浓度变化求 k）；「反应级数」可选 零级、一级、二级（默认 一级）；「初始浓度 [A]₀」默认 1；「t 时浓度 [A]」默认 0.5；「时间 t」默认 10；「指前因子 A」默认 1e13；「活化能 Ea（kJ/mol）」默认 75；「温度 T₁（K）」默认 298；「T₁ 时的速率常数 k₁」默认 0.01；「温度 T₂（K）」默认 310。每次生成结果都按当前设置处理。Settings in the Rate Constant Calculator (Zero, First, Second Order & Arrhenius) — "Calculate": k from concentrations, k from the Arrhenius equation, k at another temperature (default k from concentrations); "Reaction order": Zero order, First order, Second order (default First order); "Initial concentration [A]₀" default 1; "Concentration [A] at time t" default 0.5; "Time t" default 10; "Pre-exponential factor A" default 1e13; "Activation energy Ea (kJ/mol)" default 75; "Temperature T₁ (K)" default 298; "Rate…

计算结果可以用于作业或工程吗？Can I use the results for homework or engineering?

「速率常数计算器（零级、一级、二级与阿伦尼乌斯）」使用教科书标准公式（公式写在说明和常见问题中），适合学习和估算核对；涉及安全的工程设计请以规范和实测为准。The Rate Constant Calculator (Zero, First, Second Order & Arrhenius) uses standard textbook formulas (given in the description and FAQ), which is good for learning and checking estimates; for safety-critical engineering follow codes and measured values.

「速率常数计算器（零级、一级、二级与阿伦尼乌斯）」免费吗？需要注册吗？Is the Rate Constant Calculator (Zero, First, Second Order & Arrhenius) free? Do I need an account?

「速率常数计算器（零级、一级、二级与阿伦尼乌斯）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The Rate Constant Calculator (Zero, First, Second Order & Arrhenius) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.