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Activation energy helps the body to permit the molecules involved in the reaction to give the desired product. The theory of activation energy was first given by Svante Arrhenius and is used as an international unit to measure the energy. Activation energy is simply defined as the minimum amount of energy required to carry out a reaction.
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Key Terms: Activation energy, value of activation energy, Arrhenius Constant, rate expression, half-Life reaction, exothermic reaction, Energy, collide, molecules
Activation Energy
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Activation energy is the minimum energy required by the molecules to react and produce the expected products. The S.I. unit of activation energy is Joules (J) and in moles it is Kj/mol.
According to the activation energy theory, all the reactions have a threshold of minimum energy and all the reactions should possess the molecules to break the bonds and form the desired product.
The threshold energy is acquired when the molecules collide with each other. At high temperature, there is more kinetic energy which helps the molecules reach the threshold much faster than at room temperature.
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Formula of Activation Energy
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The formula used to determine the value of activation energy (Ea) is-
K=Ae-Ea/RT
Where,
K indicates the constant rate
A indicates Arrhenius Constant
Ea indicates Activation energy
R determines Gas constant = 8.34 J/K/mol
K=Ae-Ea/RT
Taking log on both sides
log K = log A - (Ea/RT)log e
2.303 log K = 2.303 log A - Ea/RT
log K = log A - Ea/ 2.303 RT
Derivation of Activation Energy
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Activation energy is derived from the Arrhenius Equation-
k =Ae-Ea/RT
Where,
A = pre-exponent which is a constant.
Ea = Activation Energy
R = Gas Constant
T = Temperature
K = Reaction Rate Constant
Taking log on both sides of the equation.
In k = −Ea/R[1/T]+ In A
Taking the equation y = mx + c, draw the graph to the activation energy
It can also be derived mathematically by taking the A1,A2 and T1,T2 values into the arrhenius equation.
ln K1 = -Ea/RT1 + ln Arr ---(1)
ln K2 = -Ea/RT2 + ln Arr ---(2)
Subtract 2 from 1
ln (K1/K2) = -Ea/R(1/T2-1/T1) ---(3)
From this, we can get Ea as
Ea = R(\(\frac {T1T2} {T1-T2}\)) ln\(\frac {K1} {K2}\)
First Order Reaction
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Concentrations of the molecules change over time. In order to find the changes in the concentration we need the rate law.
Rate expression is given as rate = -d[B]/dt.
According to rate law,
Rate of reaction = K[B]b.
Equating these two we get,
-d[B]/dt = K[B]b
d[B]/[B]= -Kdt
Taking ln on both sides
ln [B]/ [B]o= -Kt
Taking e on both sides,
[B] = [B]oe-Kt
This is called Exponential decay.
First Order Reaction rate is considered to be important as many chemical reactions use this law. This leads to the half-life of the reaction.
Half-Life of First Order Reaction
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Half-Life is generally the time taken by [B]o to become [B]o/2.
[B]o/2 = [B]oe-Kt/2
Taking the log on both sides
ln [1/2] = -Kt1/2
ln [2] = Kt1/2
For 1st order reactions,
ln [2]/K = t1/2 which is constant.
Reactions of Activation Energy
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The chemical reactions are of two types:
- Exothermic reaction
- Endothermic reaction
Exothermic reaction
An exothermic reaction is a type of reaction in which energy is released in the form of light or heat. The energy released will be negative for the change in enthalpy.
The activation energy (Ea) for the forward reaction will be less than the activation energy for the backward reaction.
Let,
Activation energy for Forward reaction (Ea)f
Activation energy for Backward reaction (Ea)b
(Ea)f < (Ea)b
(ROR)f > (ROR)b
ΔH = (Ea)f – (Ea)b
ΔH = -ve value
(Ea)f = ΔH Only one can be possible for Exothermic Reaction
(Ea)f > ΔH
(Ea)f < ΔH
Endothermic reaction
In the endothermic reaction, chemical bonds are formed by absorbing the heat from its surroundings and the energy released will be positive.
The activation energy for the forward reaction will be greater than the energy for the backward reaction
Let,
Activation energy for Forward reaction (Ea)f
Activation energy for Backward reaction (Ea)b
(Ea)f < (Ea)b
(ROR)f < (ROR)b
ΔH = (Ea)b – (Ea)f
ΔH = +ve value
(Ea)f > ΔH (Always)
This value of (Ea)f is universal.
Things to Remember
- Activation energy is defined as the least amount of energy required to carry out the chemical reaction and form the product.
- Activation Energy is denoted by Ea.
- The units of activation energy are LCal/Mol, KJ/mol, J/ mol.
- The activation energy depends on the nature of the reactant and catalyst.
- Endothermic reactions and exothermic reactions are the two types of reactions.
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Previous Year Questions
- The minimum energy required for molecules to enter into a chemical reaction is called
- The effect of a catalyst in a chemical reaction is to change
- The rate of a first order reaction is 0.693×10−2molL−1min−10.693×10−2molL−1min−1 and the initial concentration of the reactants is 1 M, t1/2t1/2 is equal to:
- The unit of rate constant for the reaction, 2H2+2NO?2H2O+N2 which has rate = k[H2][NO]2, is
- If 25% of a radioactive element is left after 40 days, then its half life period is
- The overall order of a reaction which has the rate expression, rate = k[A]1/2[B]1/2 is
- Thermal decomposition of HI on gold surface is a
- In a first order reaction, the time taken for 90% decay is 12 days. The time taken for 99% decay is
- Calculate the activation energy for the reaction (R=8.314JK−1mol−1)
- When a graph is plotted between log K and (1T), the slope of line obtained represents: (K = rate constant, T = temperature)
- Inversion of cane sugar by acid hydrolysis in excess of water is
- For a reaction, the half-life is independent of initial concentration. What is the order of that reaction?
- For a 1st order reaction the unit of rate constant is
- Formula for half life of a zero order reaction is:
- Catalyst increase rate of reaction while photosensitizer initiate a reaction. Catalyst decrease E but photosensitizer act as energy carrier
Sample Questions
Ques: On what does Activation Energy depend and where is it used? (3 Marks)
Ans: Activation Energy depends on chemical transformation and its nature at a given particular temperature. Activation Energy is very important in Catalyst related reactions where they need the theoretical calculation. So it is very needed when it comes to designing different kinds of biological systems like enzyme substrates. Most importantly, we can design systems like that with the help of the activation energy equation we derived above.
Ques: How can we determine Activation Energy? (3 Marks)
Ans: By finding the slope of the line from the graph drawn from the equation In k = −Ea/R[1/T]+ In A . The slope from this equation is -Ea/R.
![k = Ea/R[1/T]+](https://images.collegedunia.com/public/image/0de4790a29dd8d611347515a7625d8d9.gif?tr=w-163,h-129,c-force)
Ques: Can a Catalyst change the activation energy? (3 Marks)
Ans: The catalysts can speed up the chemical reaction by reducing the activation energy. It is usually a substance that is added to speed up the process without getting consumed in the reaction.
There are usually two types of catalyst both positive and negative, while the positive one increases the speed by reducing the activation energy, the negative catalyst will slow down the reaction increasing the activation energy.
Ques: Is activation energy positive or negative and what does each variable represent in the equation k =Ae-Ea/RT? (3 Marks)
Ans: It can be both positive and negative and even Zero. Usually, activation energy is positive.
In the equation,
k =Ae-Ea/RT
A = pre-exponent which is a constant.
Ea = Activation Energy
R = Gas Constant
T = Temperature
k = Reaction Rate Constant.
Ques: Give an Example for activation energy? (3 Marks)
Ans: When you need to start a vehicle you tune in the key and turn it which produces a small spark that helps the gas to burn.
In the same way, we need activation energy for the molecules taking part in the reaction to collide with each other and produce the kinetic energy that will be equal to the minimum threshold required to start the reaction in order to obtain our desired products.
Ques: What is the difference between activation and free energy? (3 Marks)
Ans: Free energy is the amount of energy available to perform thermodynamic work for a thermodynamic system.
Example: Gibbs energy
Application: Physical Chemistry
whereas activation energy is the threshold energy required to obtain required products.
Application: BioChemistry
Example: Exothermic Reactions
Further activation energy is used to beat the energy barrier and obtain products required from the reaction.
Ques: What will happen if activation energy keeps on increasing, and what is rate law? (2 Marks)
Ans: All the molecules which are colliding will have an increase in their kinetic energy if the activation energy keeps increasing.
Concentrations change over time, in order to find how they change we need the rate law.
It is given by
[B] = [B]oe-Kt
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