- dA = k[A]1 = 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 ekt
Plot of first order reaction 一级动力反应的图片
• Unimolecular 单分子反应 • CaCO3 Ca2+ + CO32• Bimolecular 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
=
1 d
[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
Rate Laws
A + B + C ===> products
dA = -k ×[A]m ×[B]n ×[C]o dt
“m, n, o” indicate the order of the reaction with respect to each species; determine experimentally
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
- 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 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
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4ementary 基本反应速率定律
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
Wikipedia
Second Order Reaction 二级动力反应
- dA = k"[A]2 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
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
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:
• 伪一级动A力+ B反®应C：+一D种反应物剩余的浓度基本不变 （经常由dA于=它-k与[ A其][他B]物质相比，浓度过量） dt
dA = -k '[A] where k ' = k[B] dt
B浓度不变
ln[A] = ln[A]0 - k 't
Reaction Mechanism反应机理
• Often we write a chemical reaction 我们经 常写化学反应式
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
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
“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
“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)
A ===> products Rate Laws
-
dA
=
k
Reaction
× [ A]m
rate
dt
“m” indicates the order of the reaction with respect to species “A”. Determined experimentally.
• Simple to write 书写简单 • Unimolecular H2CO3 H+ + HCO3-
d[H2CO3]/dt = k[H2CO3] • Bimolecular CO2 + H2O H2CO3
d[CO2]/dt = k[CO2][H2O]
Important Note重要提示
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)
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: