一级反应动力学、二级反应动力学基本原理

Further Reading (Chapter 3 in Hobbs)
• Rate of reaction is typically measured as the change in concentration (moles/L) with time 反应速率通常通过浓度(mol/L)随时间的变化来测量 This change may be a decrease or an increase •改变可能是增加的也可能是减小的 • Likewise the concentration change may be of reactants or products 同样，改变浓度的物质可能是反应物也可能是生成物
Rate of = - 1 [N2O5] = 1 [NO2] = reaction 2 4 t t
[O2] t
• Rate may be expressed in three main ways: •反应速率主要有以下三个表达方式： 1. Average reaction rate: a measure of the change in concentration with time 1、平均反应速率：浓度随时间变化的度量 2. Instantaneous rate: rate of change of concentration at any particular instant during the Reaction 2、瞬时速率：反应过程中某一特定瞬间的浓度变化速率 3. Initial rate: instantaneous rate at t = 0 - that is, when the reactants are first mixed 3、初始速率：t=0时即反应物最初混合时的瞬时速率，
Rate Laws
A + B + C ===> products
“m, n, o” indicate the order of the reaction with respect to each species; determine experimentally
dA m n o = -k × [ A ] × [ B ] × [ C ] dt
半衰期的长度固定
t½ = 0.693 / k
Example of 1st order reaction 1级动力反应范例
H2O2 (l) H2O(l) + 1/2O2(g)
If a reaction has a single reactant and the value of the exponent is one, then it is said to be a first-order reaction. 如果反应物只有一种，而且指数为1，那么称这种反应为一级动 力反应 Write rate law for above equation:
Single Step (Elementary) Reaction Process 单步（基本）反应过程
• • • • • Unimolecular 单分子反应 CaCO3 Ca2+ + CO32Bimolecular 双分子反应 CO2 + H2O H2CO3 Termolecular 三分子反应 2 FeS2 + 3 O2 + 2 H2O 2 Fe3+ + 4H2SO4 • No four or more molecule processes have been identified because chances of 4 molecules colliding is very, very small (making reaction rate super small) • 没有4或者4以上的分子反应被检测到，因为4分子同时碰撞的 机会非常非常小（使得反应速率非常小）
Important Note重要提示
Reaction order is not necessarily related to the stoichiometry of the reaction, unless the reaction is elementary. 反应级数不一定和反应的化学计量数有关，除非反应是基本反应 In single step process, reaction order = coefficient of reactant in chemical equation 在单步反应过程中，反应级数=化学式中反应物的系数 Complex reactions may or may not have reaction orders equal to their stoichiometric coefficients 复杂反应的反应级数可能和化学计量系数相等 Not all first order reactions, are single step, monomolecular reactions 不是所有的一级反应都是单步反应、单分子反应
A ===> products
Rate Laws
Reaction rate
dA m = k × [ A] dt
“m” indicates the order of the reaction with respect to species “A”. Determined experimentally.
Rate Laws For Elementary 基本反应速率定律
• Simple to write 书写简单
• Unimolecular H2CO3 H+ + HCO3d[H2CO3]/dt = k[H2CO3]
• Bimolecular CO2 + H2O H2CO3
d[CO2]/dt = k[CO2][H2O]
Rate of = - 1 [A] = - 1 [B] = a t reaction b t 1 [C] = 1 [D] c t d t
• Note the use of the negative sign •注意负号的使用 - rate is defined as a positive quantity 反应速率被定义为正量 - rate of disappearance of a reactant is negative 那么，反应物的消耗速率就是负的 2N2O5(g) 4NO2(g) + O2(g)
Wikipedia
Pseudo first order reactions 伪一级反应
• pseudo-first order: concentration of one reactant remains essentially constant over time (often because it is in large excess compared to the other reactant) • 伪一级动力反应：一种反应物剩余的浓度基本不变（经常由 于它与其他物质相比，浓度过量）
May or may NOT have a theoretical basis可能有或没有 理论基础 “Many reactions occur at a decreasing rate with increasing time because the reaction rate diminishes as the concentrations of the reactants diminish” “很多反应随着时间的增加反应速率逐渐减小？，因为反应物浓 度减小会降低反应速率” Hobbs (2000)
concentration change Rate = time change
反应速率=△浓度/△时间
in [products] in [reactants] Rate = ______________ = ______________ change in time change in time
• Rate has units of moles per liter per unit time - M s-1, M h-1 速率的单位是摩尔每升每单位时间，如M s-1、M h-1 Consider the hypothetical reaction 对于这个假设的反应 aA + bB cC + dD • We can write
Plot of second order reaction 2级动力反应图
[A]
time
Half lives are not constant with time for second order reactions 二级反应动力学反应物质的半衰期随时间推移变化
t½ = 1 / k [Ao]
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Example of 2nd order reaction 二级动力反应范例
Rate Laws 速率定律
Rate law = a mathematical function describing the turnover rate of the compound of interest as a function of the concentrations of the various species participating in the reaction 速率定律：用来描述相关的化合物的转化速率的数学函数，即各 种参与反应的物质的浓度的函数
dA 1 = k[ A] = k[ A] dt
Take integral of equation above, and get equation below: 将以上等式积分，得到下面的等式：
[ A]t [ A]0 e
kt
Plot of first order reaction 一级动力反应的图片
Kinetics动力学
• Thermodynamics determines whether and in which direction a reaction will happen, and what the concentrations of constituents are involved in the reaction • 热力学决定了反应是否发生、反应的方向以及参与到反应 之中的物质浓度问题。 • Kinetics say how fast a reaction happens, sequence of steps in the reaction, and some of the factors that control the rates of reactions • 动力学则说明反应发生的速率有多快、反应步骤的顺序以 及控制反应速率的一些因素
overall reaction order = m+n+o
“m, n, o”分别是关于每种物质的反应级数，实验确定的总反 应级数=m+n+o Reaction orders can be: first, second, third
反应级数可以是一级、二级、三级
First order reactions 一级动力反应
Wikipedia
Second Order Reaction 二级动力反应
dA 2 = k "[ A] dt
• If integrated如果积分:
– 得到1/[A]t = k”t + 1/[A]o – Inverse concentration linear in time – 浓度的倒数和时间程线性关系
“m”指关于物质A的反应级数，由实验确定。
“k” = rate coefficient (or specific reaction rate coeff.); determined for a specific reaction at a specific temp
“K”=速率常数（或特定的速率系数），由特定温度下的具体反应 确定
A+B®C+D dA = -k[ A ][ B ] dt dA = -k '[ A] where k ' = k[ B ] dt ln[ A ] = ln[ A]0 - k ' t
B浓度不变
Reaction Mechanism反应机理
• Often we write a chemical reaction 我们经 常写化学反应式 • How we write it is often not how it happens • 但是我们所写的通常不是它如何发生的 • Many kinds of reaction mechanisms • 有很多反应的机理
2NO2 (g) 2NO(g) + O2(g)
CO2 + H2O H2CO3
A second-order reaction depends on the concentrations of one second-order reactant, or two first-order reactants. 二级动力反应取决是否有一个二级反应物或者两个一级反应物？ Write rate law for above equations: