B的区别etween Differential Rate Law and Integrated Rate Law

关键差异 - 差异法律与综合利率法

Differential rate law and integrated rate law are two forms of rate laws. The key difference between differential rate law and integrated rate law is that差异速率定律给出了化学反应的速率与特定时间段内一个或多个反应物浓度变化的关系，而综合速率定律给出了化学反应的速率，将化学反应的速率与一个或多个初始浓度的函数有关特定时间后的反应物。

Thereaction rate是化学反应进展过程中反应物或产物浓度变化的度量。不同的速率定律用于解释反应进展。这些速率定律表示为不同参数之间的数学关系。

CONTENTS

1.Overview and Key Difference
2.What is Differential Rate Law
3.综合速率定律是什么
4.Relationship Between Differential Rate Law and Integrated Rate Law
5.Side by Side Comparison – Differential Rate Law vs Integrated Rate Law in Tabular Form
6.概括

什么是差异法律？

差异速率定律用于确定化学反应的速率，这是在特定时间段内一个或多个反应物浓度变化的函数。差异率定律表示化学反应的分子水平上发生了什么。可以使用差异速率定律（反应物转换为产物）确定化学反应的总体机制。

差异法律方程

以下化学反应的差异速率定律可以作为数学表达给出。

→B + C

Rate = – {d[A] / dt} = k[A]ⁿ

Here, [A] is the concentration of reactant “A” and “k” is therate constant. “n” gives theorder of reaction. The differential rate law equation can be integrated to obtain a clear relationship between [A] and time “t”. This integration gives the integrated rate law.

综合速率定律是什么?

The integrated rate law gives the rate of a chemical reaction as a function of the initial concentration of one or more reactants after a specific period of time. The integrated rate law can be used to determine the rate constant of a particular chemical reaction, and the reaction order can be obtained via experimental data.

Integrated Rate Law Equation

For the chemical reaction A → B + C, integrated rate law can be expressed as a mathematical expression as given below.

ln[A] = -kt + ln[A]₀

Here, [A]₀is the initial concentration of the reactant A and [A] is the concentration of reactant “A” after “t” time has passed. However, integrated rate laws are different from each other based on the order of the reaction “n”. The above equation is given for zero order chemical reactions.

Forfirst order reactions, the rate law equation is,

[A] = [A]e^-kt

Forsecond order reactions, the rate law equation is,

1/[A] = 1/[A]₀+ kt

In order to determine therate constant of a reaction, above equations can be used as follows.

对于一阶反应，

k = {ln[A] – ln[A]₀} / t

For second order reactions,

k = {1/[A] – 1/[A]₀} / t

What is the Relationship Between Differential Rate Law and Integrated Rate Law?

• The differential rate law of a chemical reaction can be integrated to obtain the integrated rate law of the same chemical reaction.

What is the Difference Between Differential Rate Law and Integrated Rate Law?

Differential Rate Law vs Integrated Rate Law
Differential rate law is used to determine the rate of a chemical reaction as a function of the change in concentration of one or more reactants during a particular time period.	综合速率定律在特定时间段内给出一个或多个反应物的初始浓度（或特定时刻浓度）的化学反应速率。
Application
差异率定律可用于指示化学反应的分子水平上发生的情况，并且可以使用该速率定律确定化学反应的总体机制。	Integrated rate law can be used to determine the rate constant of a particular chemical reaction.
Usage
与综合利率定律相比，差异率定律很难使用。	Integrated law makes it easy to determine the clear relationship between the concentration of reactants and the time elapsed.

概括– Differential Rate Law vs Integrated Rate Law

化学反应的速率定律给出了反应速率与反应物浓度之间的关系。差异率定律和综合速率定律之间的关键差异是，差异率定律给出了化学反应的速率，这是一个或多个反应物在特定时期内的浓度变化的函数，而综合速率定律则给出了速率。在特定时间段内，化学反应是一个或多个反应物的初始浓度的函数。

Reference:

1. “Rate Laws – Differential.” Chemistry LibreTexts, Libretexts, 17 July 2015,Available here.
2. Libretexts. “12.4: Integrated Rate Laws.” Chemistry LibreTexts, Libretexts, 11 Sept. 2017,Available here。]。

Image Courtesy:

1. “Rateloglogplot” By Fabiuccio~enwikibooks at English Wikibooks – Transferred from en.wikibooks to Commons.(Public Domain) viaCommons Wikimedia