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
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” Hobbementary 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]
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
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，
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）
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
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:
“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
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]
Example of 2nd order reaction 二级动力反应范例
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
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
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
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