Activation Energy Formula, Derivation, Effect of Temperature on Rate Constant, Solved Problems

Define Activation Energy

Activation energy of a chemical reaction is defined as the least amount of energy necessary to initiate the reaction. It can be interpreted as the differential in energy content between molecules and atoms that causes it to be in an activation or transition-state configuration while the associated atoms and molecules stay in their initial configuration. It is known that to initiate a reaction, molecules must collide with other molecules and exchange kinetic energy or velocity. There will be no response if the collision does not occur or if the molecules do not have enough kinetic energy. This forms the basis for the concept of activation energy. Its standard unit of measurement is kilojoules per mole (kJ/mol).

Activation Energy Formula

Ea = 2.303 R (log k2/k1) [T1T2 / (T2 – T1)]

where,

Ea is the activation energy of the reaction,

R is the ideal gas constant with the value of 8.3145 J/K mol,

k1,k2 are the rates of reaction constant at initial and final temperature,

T1 is the initial temperature,

T2 is the final temperature.

This is also known as the Arrhenius equation.

Activation Energy Derivation

Suppose a reaction takes place between two reactants P and Q to give a product R. The completion of a reaction is ensured and denoted by its rate constant.

We know the formula for rate constant is given by,

k = Ae−EaRT

Taking log on both sides we get,

ln k = −EaRT + ln A

For initial temperature T1 and rate of constant k1, the equation is written as,

ln k1 = −Ea/RT1 + ln A   …….. (1)

For final temperature T2 and rate of constant k2, the equation is written as,

ln k2 = −Ea/RT2 + ln A   …….. (2)

Subtracting (2) from (1) we get,

ln k2 – ln k1 = −Ea/RT2 + ln A − (− Ea/RT1 + ln A)

ln (k2/k1) = EaR (1/T1 − 1/T2)

2.303 log (k2/k1) = EaR (1/T1 − 1/T2)

Ea = 2.303 R (log k2/k1) [T1T2 / (T2 – T1)]

This derives the formula for activation energy.

Sample Problems

Problem 1. Calculate the activation energy of a reaction if its rate doubles when there is a temperature change from 200K to 400K. 

Solution:

We have,

k2 = 2k1,

T1 = 200

T2 = 400

Using the formula we get,

Ea = 2.303 R (log k2/k1) [T1T2 / (T2 – T1)]

= 2.303 (8.3145) (log 2) (80000/200)

= 461090.907/200

= 2305.45 KJ/mol

Problem 2. Calculate the activation energy of a reaction if its rate triples when there is a temperature change from 100K to 300K.

Solution:

We have,

k2 = 3k1,

T1 = 100

T2 = 300

Using the formula we get,

Ea = 2.303 R (log k2/k1) [T1T2 / (T2 – T1)]

= 2.303 (8.3145) (log 3) (30000/200)

= 274012.079/200

= 1370.060 KJ/mol

Problem 3. Calculate the activation energy of a reaction if its rate quadruples when there is a temperature change from 150K to 400K.

Solution:

We have,

k2 = 4k1,

T1 = 150

T2 = 400

Using the formula we get,

Ea = 2.303 (8.3145) (log 4) (60000/250)

= 691636.36/250

= 2766.55 KJ/mol

Problem 4. Calculate the activation energy of a reaction if its rate becomes five times when there is a temperature change from 300K to 600K.

Solution:

We have,

k2 = 5k1,

T1 = 300

T2 = 600

Using the formula we get,

Ea = 2.303 (8.3145) (log 5) (180000/300)

= 2405791.59/300

= 8019.30 KJ/mol

Problem 5. Calculate the change in the rate of reaction if the activation energy of a reaction is 500 KJ/mol when there is a temperature change from 120K to 360K.

Solution:

We have,

Ea = 500

T1 = 120

T2 = 360

Using the formula we get,

=> 3000 = 2.303 (log k2/k1) [43200/240]

=> log (k2/k1) = (500/2.303) (240/43200)

=> log (k2/k1) = 7.23

=> k2/k1 = 16

=> k2 = 16 k1

Problem 6. Calculate the change in the rate of reaction if the activation energy of a reaction is 200 KJ/mol when there is a temperature change from 50K to 100K.

Solution:

We have,

Ea = 200

T1 = 50

T2 = 100

Using the formula we get,

=> 200 = 2.303 (log k2/k1) [5000/50]

=> log (k2/k1) = (200/2.303) (50/5000)

=> log (k2/k1) = 0.86

=> k2/k1 = 7.37

=> k2 = 7.37 k1

Problem 7. Calculate the change in the rate of reaction if the activation energy of a reaction is 450 KJ/mol when there is a temperature change from 100K to 200K.

Solution:

We have,

Ea = 450

T1 = 100

T2 = 200

Using the formula we get,

=> 450 = 2.303 (log k2/k1) [20000/100]

=> log (k2/k1) = (450/2.303) (100/20000)

=> log (k2/k1) = 0.97

=> k2/k1 = 9.33

=> k2 = 9.33 k1

Er. Neeraj K.Anand is a freelance mentor and writer who specializes in Engineering & Science subjects. Neeraj Anand received a B.Tech degree in Electronics and Communication Engineering from N.I.T Warangal & M.Tech Post Graduation from IETE, New Delhi. He has over 30 years of teaching experience and serves as the Head of Department of ANAND CLASSES. He concentrated all his energy and experiences in academics and subsequently grew up as one of the best mentors in the country for students aspiring for success in competitive examinations. In parallel, he started a Technical Publication "ANAND TECHNICAL PUBLISHERS" in 2002 and Educational Newspaper "NATIONAL EDUCATION NEWS" in 2014 at Jalandhar. Now he is a Director of leading publication "ANAND TECHNICAL PUBLISHERS", "ANAND CLASSES" and "NATIONAL EDUCATION NEWS". He has published more than hundred books in the field of Physics, Mathematics, Computers and Information Technology. Besides this he has written many books to help students prepare for IIT-JEE and AIPMT entrance exams. He is an executive member of the IEEE (Institute of Electrical & Electronics Engineers. USA) and honorary member of many Indian scientific societies such as Institution of Electronics & Telecommunication Engineers, Aeronautical Society of India, Bioinformatics Institute of India, Institution of Engineers. He has got award from American Biographical Institute Board of International Research in the year 2005.

CBSE Class 12 Chemistry Syllabus Download PDF

Below is the CBSE Class 12 Syllabus along with the marking scheme and time duration of the Chemistry exam.

S.NoTitleNo. of PeriodsMarks
1Solutions107
2Electrochemistry129
3Chemical Kinetics107
4d -and f -Block Elements127
5Coordination Compounds127
6Haloalkanes and Haloarenes106
7Alcohols, Phenols and Ethers106
8Aldehydes, Ketones and Carboxylic Acids108
9Amines106
10Biomolecules127
Total70

CBSE Class 12 Chemistry Practical Syllabus along with Marking Scheme

The following is a breakdown of the marks for practical, project work, class records, and viva. The total number of marks for all parts is 15. The marks for both terms are provided in the table below.

Evaluation Scheme for ExaminationMarks
Volumetric Analysis08
Salt Analysis08
Content-Based Experiment06
Project Work and Viva04
Class record and Viva04
Total30

CBSE Class 12 Chemistry Syllabus (Chapter-wise)

Unit -1: Solutions

  • Raoult's law.
  • Colligative properties - relative lowering of vapour pressure, elevation of boiling point, depression of freezing point, osmotic pressure, determination of molecular masses using colligative properties, abnormal molecular mass.
  • Solutions, Types of solutions, expression of concentration of solutions of solids in liquids, solubility of gases in liquids, solid solutions.
  • Van't Hoff factor.

Unit -2: Electrochemistry

  • Redox reactions, EMF of a cell, standard electrode potential
  • Nernst equation and its application to chemical cells
  • Relation between Gibbs energy change and EMF of a cell
  • Kohlrausch's Law
  • Electrolysis and law of electrolysis (elementary idea)
  • Dry cell-electrolytic cells and Galvanic cells
  • Conductance in electrolytic solutions, specific and molar conductivity, variations of conductivity with concentration.
  • Lead accumulator
  • Fuel cells

Unit -3: Chemical Kinetics

  • Rate of a reaction (Average and instantaneous)
  • Rate law and specific rate constant
  • Integrated rate equations and half-life (only for zerfirst-order order reactions)
  • Concept of collision theory (elementary idea, no mathematical treatment)
  • Factors affecting rate of reaction: concentration, temperature, catalyst;
  • Order and molecularity of a reaction
  • Activation energy
  • Arrhenius equation

Unit -4: d and f Block Elements  

  • Lanthanoids- Electronic configuration, oxidation states, chemical reactivity and lanthanoid contraction and its consequences.
  • Actinoids- Electronic configuration, oxidation states and comparison with lanthanoids.
  • General introduction, electronic configuration, occurrence and characteristics of transition metals, general trends in properties of the first-row transition metals – metallic character, ionization enthalpy, oxidation states, ionic radii, color, catalytic property, magnetic properties, interstitial compounds, alloy formation, preparation and properties of K2Cr2O7 and KMnO4.

Unit -5: Coordination Compounds  

  • Coordination compounds - Introduction, ligands, coordination number, color, magnetic properties and shapes
  • The importance of coordination compounds (in qualitative analysis, extraction of metals and biological system).
  • IUPAC nomenclature of mononuclear coordination compounds.
  • Bonding
  • Werner's theory, VBT, and CFT; structure and stereoisomerism

Unit -6: Haloalkanes and Haloarenes  

  • Haloarenes: Nature of C–X bond, substitution reactions (Directive influence of halogen in monosubstituted compounds only). Uses and environmental effects of - dichloromethane, trichloro methane, tetrachloromethane, iodoform, freons, DDT.
  • Haloalkanes: Nomenclature, nature of C–X bond, physical and chemical properties, optical rotation mechanism of substitution reactions.

Unit -7: Alcohols, Phenols and Ethers   

  • Phenols: Nomenclature, methods of preparation, physical and chemical properties, acidic nature of phenol, electrophilic substitution reactions, uses of phenols.
  • Ethers: Nomenclature, methods of preparation, physical and chemical properties, uses.
  • Alcohols: Nomenclature, methods of preparation, physical and chemical properties (of primary alcohols only), identification of primary, secondary and tertiary alcohols, mechanism of dehydration, and uses with special reference to methanol and ethanol.

Unit -8: Aldehydes, Ketones and Carboxylic Acids   

  • Carboxylic Acids: Nomenclature, acidic nature, methods of preparation, physical and chemical properties; uses.
  • Aldehydes and Ketones: Nomenclature, nature of carbonyl group, methods of preparation, physical and chemical properties, mechanism of nucleophilic addition, the reactivity of alpha hydrogen in aldehydes, uses.

Unit -9: Amines    

  • Diazonium salts: Preparation, chemical reactions and importance in synthetic organic chemistry.
  • Amines: Nomenclature, classification, structure, methods of preparation, physical and chemical properties, uses, and identification of primary, secondary and tertiary amines.

Unit -10: Biomolecules     

  • Proteins -Elementary idea of - amino acids, peptide bond, polypeptides, proteins, structure of proteins - primary, secondary, tertiary structure and quaternary structures (qualitative idea only), denaturation of proteins; enzymes. Hormones - Elementary idea excluding structure.
  • Vitamins - Classification and functions.
  • Carbohydrates - Classification (aldoses and ketoses), monosaccharides (glucose and fructose), D-L configuration oligosaccharides (sucrose, lactose, maltose), polysaccharides (starch, cellulose, glycogen); Importance of carbohydrates.
  • Nucleic Acids: DNA and RNA.

The syllabus is divided into three parts: Part A, Part B, and Part C. Part A consist of Basic Concepts of Chemistry, which covers topics such as atomic structure, chemical bonding, states of matter, and thermochemistry. Part B consists of Topics in Physical Chemistry, which includes topics such as chemical kinetics, equilibrium, and electrochemistry. Part C consists of Topics in Organic Chemistry, which covers topics such as alkanes, alkenes, alkynes, and aromatic compounds.

Basic Concepts of Chemistry:

  • Atomic structure: This section covers the fundamental concepts of atomic structure, including the electronic configuration of atoms, the Bohr model of the atom, and the wave nature of matter.
  • Chemical bonding: This section covers the different types of chemical bonds, including ionic, covalent, and metallic bonds, as well as the concept of hybridization.
  • States of the matter: This section covers the three states of matter - solid, liquid, and gas - and the factors that influence their properties.
  • Thermochemistry: This section covers the principles of thermochemistry, including the laws of thermodynamics and the concept of enthalpy.

Chapters in Physical Chemistry:

  • Chemical kinetics: This section covers the study of the rate of chemical reactions and the factors that influence it, including the concentration of reactants, temperature, and the presence of catalysts.
  • Equilibrium: This section covers the principles of chemical equilibrium, including the concept of Le Chatelier's principle and the equilibrium constant.
  • Electrochemistry: This section covers the principles of electrochemistry, including the concept of half-cell reactions, galvanic cells, and electrolysis.

Chapters in Organic Chemistry:

  • Alkanes: This section covers the properties and reactions of alkanes, including their structure, isomerism, and combustion.
  • Alkenes: This section covers the properties and reactions of alkenes, including their structure, isomerism, and addition reactions.
  • Alkynes: This section covers the properties and reactions of alkynes, including their structure, isomerism, and addition reactions.
  • Aromatic compounds: This section covers the properties and reactions of aromatic compounds, including their structure, isomerism, and electrophilic substitution reactions.

In addition to the topics covered in the syllabus, the CBSE Class 12 Chemistry exam also tests students on their analytical and problem-solving skills, as well as their ability to apply the concepts learned in the classroom to real-world situations.

Students can also check out the Tips for the Class 12 Chemistry Exam. They can easily access the Class 12 study material in one place by visiting the CBSE Class 12 page at ANAND CLASSES (A School Of Competitions). Moreover, to get interactive lessons and study videos, download the ANAND CLASSES (A School Of Competitions) App.

Frequently Asked Questions on CBSE Class 12 Chemistry Syllabus

Q1

How many chapters are there in the CBSE Class 12 Chemistry as per the syllabus?

There are 10 chapters in the CBSE Class 12 Chemistry as per Syllabus. Students can learn all these chapters efficiently using the study materials provided at ANAND CLASSES (A School Of Competitions).

Q2

What is the marking scheme for CBSE Class 12 Chemistry practical exam according to the syllabus?

The marking scheme for CBSE Class 12 Chemistry practical exam, according to the syllabus, is 8 marks for volumetric analysis, 8 marks for salt analysis, 6 marks for the content-based experiment, 4 marks for the project and viva and 4 marks for class record and viva.

Q3

Which is the scoring chapter in Chemistry as per CBSE Class 12 syllabus?

The chapter Electrochemistry in Chemistry is the scoring chapter as per CBSE Class 12 syllabus.