Login with Facebook

The kinetics of the transformation processes

The kinetics of the reactions study, the speed of development of a transformation reaction, which, starting from certain reagents, gives rise to certain products. In fact, all reactions take place at a certain characteristic speed k = 1 / Δtr, where Δt r is a characteristic time of the reaction considered. A typical characteristic time is that of half-life, that is, the time necessary for 50% of the reactants to be transformed into the products, also called t50. This time must be compared with the time scales typical of other processes, transport processes such as advection and diffusion, which take place, together with the transformation reactions, within the surface water body. Self Δtp is the time scale of the transport processes, 3 cases can occur:

- if the reaction takes place very quickly, on a time scale lower than that of the transport processes, i.e., it is Δtr << Δtp, you can make the hypothesis that the products are formed as soon as the reagents are available and, therefore, the reaction kinetics can be neglected. The reactions of this type are called snapshots and are controlled by the availability of reagents. In other words, the speed of formation of the products depends on that of formation of the reactants and not on the intrinsic speed of the transformation reaction:

 - if the reaction takes place slowly, on a time scale to that of the transport processes, i.e., it is Δtr >> Δtp, the presence of the reaction can be neglected, and the substance can be considered conservative, i.e., non-reactive.

- If the reaction time scale is similar to that of the transport processes, i.e., Δt r = Δtp, the reaction must be considered, and its kinetics also plays an essential role. Assuming that the reactants are available, the reaction is controlled precisely by its kinetics, and the rate of formation of the products depends precisely on the kinetics of the transformation reaction.

Consider again the generic reaction, which takes place under conditions of complete mixing:

aA + b B↔ c C + d D  (1)

Where abc, and’s’ are the stoichiometric coefficients of the reaction, and ABC, and ‘D’ are the substances involved in the reaction. The reaction law or kinetic law of generic substance A is:

D[A]/dt= RA       (2)

Where RA is a function that describes the reaction law for species A

At this point, it is necessary to define the expression of the reaction law Ri of the generic species i. The general form of the kinetic law for the generic product formed from a number of reagents A equal to j is:

Ri=kr-i[A1]n1 A2]n2 A3]n3……. Aj]nj     (3)

Where k r-i is the speed constant of the reaction [T -1], and n j is the order of the reaction with respect to the generic constituent j. The sum of the orders of reactions of all constituents, namely:

It is the total order of the reaction, which therefore serves to identify the influence that the concentration of some or all of the reactants has on the speed of the reaction. The law of reaction is often determined on an experimental basis.

The kinetics of transformation processes

In the simple case of the reaction:

A+B -àP  (4)

It is reaction law for P holds:

D[p]/dt=kr[A]nA [B]ns    (4)

The rate constant of a reaction k r depends on the temperature and, in particular, generally increases with it. To define the relationship between k r and T, we can use the Arrhenius-Van't Hoff equation:

Kr= A exp( -Ea/Rgas T)    (5)

Where A is the frequency factor, E a,  are the activation energy characteristic of the reaction, R gas the universal constant of the gases, and T the absolute temperature. Therefore, a slow reaction can be due to a low-frequency factor value or a high activation energy value.

The zero-order kinetics

When the speed of a reaction is independent of the concentration of the reagents, it is called zero-order kinetics. This is typical, for example, of heterogeneous reactions, where the exchange surface controls the speed of the reaction. Consider, again, the simple reaction:

A+B -àP  (4)

Its reaction law for P always holds:

D[p]/dt=kr[A]nA [B]ns    (4)

In this case, since the exponents of (4) are all null, the reaction law becomes:

-d[A]/dt= -d[B]/dt= d[P]/dt= kr  (6)

Therefore, if one refers to one of the reactants, the zero-order kinetics establishes that this reactant decreases over time with constant speed. Therefore, for example, if the field data of the concentration of a pollutant are arranged, plotted against time, according to a straight line, it can be deduced that the reaction that determines the progressive disappearance of the contaminant follows a zero-order kinetics, which is constant andS exactly equal to the inclination of the straight line.

First-order kinetics

When the speed of a reaction depends on the concentration of only one of the reagents, it is called first-order kinetics. Consider, again, the simple reaction:

A+B -àP  (4)

If, in this case, for example, the speed of the reaction depends only on A, the reaction law for A becomes:

d[A]/dt=kr[A]nA =kr[A]    (7)


RA=kr[A]   (8)

Where the unknown k r that is the reaction constant can be determined by different methods

The (7) can be expressed in a similar way to the transport equations examined so far, in terms of concentration, if C is the concentration of the generic contaminant, such as:

dC/dt=± krC (9a)

Where the negative sign describes the case in which the chemical reaction tends to make the contaminant progressively disappear, while the positive sign refers to the opposite case in which the reaction produces this contaminant.

First-order kinetics

This equation can be easily solved by assigning an initial condition, represented by the initial value of the contaminant at a certain preset time, usually t = 0. In fact, let this condition:

C(t=0)=Co   (10)

By separating the variables, (10) takes the form:

dC/C=± kr, dt  (9b)

Which integrating both members, provides, after defining the reaction constant through the initial condition:

C(t)=Co exp(± kr,t)   (11)

for k r negative, represents an exponential decay of the concentration over time. For the case of C 0 = 1 and k r = -1, where the concentration tends asymptotically to the null value.

The second-order kinetics

When the speed of a reaction depends on the concentration of two of the reagents, this is called second-order kinetics. Consider, once again, the simple reaction:

A+B -àP  (4)

in this case, the speed of the reaction depends on both A that B. The reaction law is:

-d[A]/dt= d[P]/dt =kr[A]nA[B]nB  (12)

Also (12) can be expressed in terms of the concentration C of a generic contaminant such as:

dC/dt=±kr, C2   (13)

Here the negative sign refers to a reaction that tends to make the contaminant progressively disappear, and k r has dimensions of [L 3 · M -1 · T -1]. Here, too, an initial condition like the first one must be assigned. The (13) has the form:

C(t)= 1/ ∓krt+1/Co (14)

If you need a scholarly article like this onescientist, you can contact us for a cheap reliable essay writing service.


Send Comment

Need a custom

We will write it for you.
Order now

Free Essay Examples

Free essays:

Analysis of Business Cycles
Analysis of Fiscal and Monetary Policies
An Overview Of Economic Studies
A Guide to Pricing Strategies
Biosensors for cancer diagnosis
Business Analysis: Pricing strategies and Demand Curve
Broadcasting: How to Be Good In Front of the Camera
Bioconjugates for the Drugs Delivery
Cells of Immune system
Challenges that IT Managers are facing
Cochlear implant: what it is and how it works
Current challenges to the health of women
Doppler ultrasound or simply eco Doppler
DNA extraction
Dynamic Systems Modeling with Machine Learning
Digital Imaging: What Is It?
Economy analysis: Business Cycle and Economic Trends
Exchange rate and foreign currency risk
Economic Factors Affecting Decision Making In A Business
Economy Analysis: Inflation, Unemployment And Policies
Factors Influencing Interest and Exchange Rates
Fiscal and Monetary Policies in Response to 2008/2009
Fermentation: how it works and what it is used for
Financial Markets and Functions
Genetic regulation networks: modeling in biology
How can immigrants blend in the American society?
How to make your business survive at economic crisis
How to choose the topic of the senior capstone project
Importance of corporate sustainability
Interaction of Consumer and Firm Choices in Markets
Introduction to Microeconomics
Introduction of Microfabrication techniques
Journalism: What is News?
Journalism: Broadcast media and Television Presenters
Journalism: Sources of News
Journalism and Law
Key Determinants of National Income
Key Factors That Affect Pricing Decisions
Kinetic models in biology and Related fields
Know about the different forms of traditional African dances
Latest technology trends
Latest dance trends
Methods of labeling of nucleic acid that enable their detection
Macroeconomics: International Economic Issues
Neuromuscular disorders
National Economies, Fluctuation, and Responses to Fluctuations
Neurotransmitters: what they are and different types
Nanomedicines to target tumors
Overcoming Hiring Challenges for Nonprofit Organization
Principles of Microeconomics - Producer Theory
Principles of Microeconomics - Consumer Theory
Principles of Economics
Role of technology in the modern business environment
Role of Homeostasis in Human Physiology
Role of a digital artist
Role of gender studies
Skills in Journalism: Effective Interview
Systems biology - An understanding the functioning of biological systems
Self-assembly for biological systems
School of American Ballet
Types of corporate responsibility
The Role of Government Policy in Improving Economic Outcomes
Types of bioreactors and their applications
Technological perspectives and reflections of neural engineering
Understanding Perfect and Imperfect Competition
Ultrasound: physical principles and image formation
Understanding social entrepreneurship
Understand the importance of investigative journalism
Various theoretical perspectives of sociology
Virtual reality, what it is and how it works
What are the Causes of financial instability?
What is business ethics and code of ethics
4 Facts about Origin of Mathematics!
5 techniques to create an animation
10 strategies to maximize corporate profits
13 Best colleges for political science in the world
6 Medical Technologies that revolutionized the healthcare in 2020
All you need to know about the ACA Code of ethics
Architecture and Democracy: An Introduction
Architecture and Democracy: Democratic Values
Architecture and Democracy: Democratic Procedures
All You Need to Know About a Synthesis Essay
An essential guide to understanding Film Theory
Application of Artificial Intelligence in Cyber Security
Applications of electrical engineering
Augmented reality: what it is, how it works, examples
Advantages And Disadvantages Of Social Networking
All you need to know about Cryptography
Applications of astrophysical science
All you need to know about architecture engineering
Applications of geological engineering
Artificial intelligence and medicine: an increasingly close relationship
An insight into Computational Biology
ACA code of conduct
A Rose for Emily
Applications of Mathematics in daily life
Architecture mistakes to avoid
All you need to know about Toxicology
All you need to know about Holistic Medicine
All you need to know about linguistics
An introduction to Linguistics and its subfields
All you need to know about Anxiety disorder
All you need to know about Drones
A Brief Insight into Political Science
Assumptions related to feminism
All you need to know about Byzantine emperors
All you need to know about labour economics
An insight into xenobots -the first-ever robots
An ultimate guide about Biomaterials
A Comprehensive Introduction to the Mona Lisa
Analysis methods of Transport through biological membranes
An ultimate guide about biochemical reactions
Analysis of brain signals
Artificial Gene Synthesis
Application to synthetic biology of CAD methods
All you need to know about metabolic pathways
Applications of BIOMEMS
All you need to know about the epidemiology
Asian vs. western leadership styles
All you need to know about Smart prosthesis
Analysis of Economy: Output of Goods and Services (GNP), and GDP on Economic success
A Guide to Pricing Strategies
An Overview Of Economic Studies
Analysis of Fiscal and Monetary Policies
Analysis of Business Cycles
How to Write a Personal Essay
Housing Needs in America
How to Write a Description Essay
How to Create an Excellent Scholarship Essay?
How to write a cause and effect essay
How to Hire the Best Essay Writing Service Provider?
How to Write a College Application Essay?
How to get the most out of your English lectures
How to write Expository Essay
How to succeed in your psychology class?
How to Write an Academic Essay in the Shortest Time?
History of Journalism
How Different Sectors are Using Artificial intelligence (AI)
How to write an informative essay
How to deliver persuasive essays?
How to Give a Convincing Presentation
How to write an essay on leadership?
Historical Art Still Around Today
Humanoid robot: what it is, how it works and price
History of Chemistry
Healthcare Advanced Computer Power: Robotics, Medical Imaging, and More
Healthcare AI: Game Changers for Medical Decision-Making and Remote Patient Monitoring
How to understand different types of English
How to Cope with Chronic Pain
How African American choreographers and dancers have influenced American dance
How mobile robot can do in logistics or in production
How To Become a Successful Entrepreneur
History of the Philosophy of Feminism
How is the climate changing?
How to Track Your Content Marketing ROI
How to Gun control In the USA?
Historical and contemporary role of labour in the modern world
How breast cancers are classified?
How the cells of our body communicate?
How the Lymphatic System Works?
How Digestive System Works
How to complete your capstone projects effectively?
How to write a research project
Healthcare technologies that help patients with better self-management
How to choose the topic of the senior capstone project
How to make your business survive at economic crisis
How can immigrants blend in the American society?
The Looming Energy Crisis in America
Top benefits of performance-based engineering
The More Languages You Know, The More Times You Are a Man
Things to consider while writing an Argumentative Essay
Top Ways to Improve Your Academic Writing Skills
Tips to Excel in Creative Writing
The origins of films in the early 19th century
Top career options in Architecture
The Elevator Pitch
Top finance trends 2020
The basic Structure and functionality of robots
The Way to Success
The election system of the President in the United States of America
Two-party System in United States of America
Top trends in urban design
The history and theory of African American filmmaking
Top benefits of creative writing
Tinnitus Guide: Common Symptoms and Treatment Options
The language of dance
The digital image processing management
Top famous politicians of the World
Top methods of political science!
The history of the feminist movement
The blood flow in cardiovascular system - Biofluid Mechanics
The best of Leonardo Da Vinci
The Structure and Function of Macromolecules
The structure of cell: a research on the bricks of the human body!
Tissue and organ construction: Adhesion and recognition between cells
The kinetics of the transformation processes
The Modeling of Biological Systems
Tips for writing a great thesis statement
The Defense mechanisms against infections
The impact of the technological innovations in medicine
Top journalism trends to know about
The relation between mass media & politics
Theranostics: Diagnosis and Care through Nanoparticles
The practical Applications of X-rays
The applications of Ultrasound in medicine
Transfer mechanisms of genetic information in Bacteria
The regulation of cellular metabolism in the diagnosis
The Principles of MRI Contrast agents
The technical basis of optical coherence imaging
The New Media: Emerging Trends
The Structure of Interest Rates and the Yield Curve
Technological perspectives and reflections of neural engineering
Types of bioreactors and their applications
The Role of Government Policy in Improving Economic Outcomes
Types of corporate responsibility
What is a Definition Essay?
What are diagnostic essays?
What is the relation between art structural engineering?
What is a Narrative Essay
What are robotics and intelligence systems?
What are the benefits of studying health sciences?
What is artificial intelligence and why it matters?
What is comparative Literature?
Why study neuroscience
What is Wi-Fi and how does it works
What is French history famous for?
What are Humanistic Studies?
What is covered in Biophysics?
What is modern journalism?
What is Virtualization? Benefits & Applications
What are modern public relations?
What is plasma physics?
What is teacher preparation?
What is rapid prototyping for 3D printing?
What is contemporary European Politics?
Why should you learn American Ballet?
What is engineering physics?
What is the purpose of African American Literature?
Ways to learn the Rhythm
What is digital art used for?
What are Enzymes and how do they work
Who is the father of political science?
Why Study Political Science - Job?
What is the Philosophy of Feminism?
What is a quantum computer?
Ways B2B Startups Streamline Their Conversion Strategies
Why do biomedical signals need processing?
What are the long term effects of climate change?
Why study labour relations
What is Holoprosencephaly?
What is antisocial disorder?
What are the important principles of evolution?
What is the cytoplasm and its function?
What is biopolymers?
What Makes a Good Leader
Women empowerment in modern generation
What is the history of political thought?
What is Gene recombination
What is synthetic biology
What is business cost analysis?
What is Inflation
What are the consequences of unemployment?
What is lithotripsy and its types?
What is transition elastography?
What is the purpose of deep brain stimulation?
What is a Brain-Computer Interface (BCI)
What is neuroethics?
What is Market and Supply and Demand
What is optogenetics?
What are the techniques to record brain activity?
What happens if the interest rate increases?
What is immunotherapy?
What is the economic role of the financial market?
What are the factors behind illegal immigration?
What is the lymphocyte activation?
What is financial market and its types?
What is the structure of financial markets?
What are the methods of measuring business performance?
What is the Credit market?
What is business ethics and code of ethics
What are the Causes of financial instability?