1. Introduction to Chemical Kinetics
Chemical kinetics is the branch of chemistry that deals with the rate of a chemical reaction and the factors that affect the rate. It also helps us understand how a reaction takes place.
Thermodynamics can tell us whether a reaction is possible or favourable under particular conditions, but it does not by itself tell us how fast the reaction will occur.
For example, a reaction may be thermodynamically favourable but extremely slow. Chemical kinetics helps explain this difference.
What does chemical kinetics study?
- Rate of chemical reaction
- Factors affecting reaction rate
- Rate law and rate constant
- Order of reaction
- Molecularity
- Reaction mechanism
- Activation energy
- Effect of temperature
- Effect of catalysts
A simple way to remember the subject is:
2. Rate of a Chemical Reaction
The rate of a reaction tells us how quickly the concentration of reactants decreases or the concentration of products increases with time.
Consider:
If the concentration of A changes from [A]₁ to [A]₂ during a time interval from t₁ to t₂:
The negative sign is used because the concentration of a reactant decreases with time.
For product formation:
For a general reaction
The reaction rate can be written as:
The coefficients are used so that the rate has the same value regardless of which substance is used for calculation.
Units of rate
If concentration is expressed in mol L⁻¹ and time in seconds:
3. Factors Affecting the Rate of Reaction
1. Nature of reactants
Different substances react at different speeds because their bonds, structures and reaction pathways are different.
2. Concentration
Increasing concentration generally increases the number of particles present in a given volume. More frequent effective collisions can occur, so the reaction may become faster.
3. Pressure
For gaseous reactions, increasing pressure generally increases the effective concentration of gases and can increase reaction rate.
4. Temperature
Increasing temperature usually increases reaction rate because particles move faster and a greater fraction of collisions can have enough energy to react.
5. Catalyst
A catalyst provides an alternative reaction pathway with lower activation energy.
6. Surface area
A powdered solid generally reacts faster than a large solid piece because more surface is available for contact with the other reactant.
7. Light
Some photochemical reactions require light to start or accelerate the reaction.
4. Rate Law
The rate law is an equation that relates the reaction rate to the concentrations of reactants.
For:
A possible rate law is:
Here:
- k = rate constant
- [A] = concentration of A
- [B] = concentration of B
- m = order with respect to A
- n = order with respect to B
Overall order
The values of m and n are usually determined experimentally.
5. Order of Reaction
The order of a reaction is the sum of the powers of concentration terms in the experimentally determined rate equation.
If:
Then:
Order may be:
- Zero
- First
- Second
- Third
- Fractional
- Sometimes apparent or experimentally determined values
Importance of order
The order helps determine the mathematical form of the rate equation, the units of the rate constant and the way concentration changes with time.
6. Molecularity of a Reaction
Molecularity is the number of reacting species involved in a single elementary reaction step.
Unimolecular reaction
Molecularity = 1
Bimolecular reaction
Molecularity = 2
Termolecular reaction
Molecularity = 3
Order vs molecularity
| Order | Molecularity |
|---|---|
| Determined experimentally. | Based on an elementary reaction step. |
| Can be zero or fractional. | Usually a positive whole number. |
| Applies to the overall experimentally observed rate law. | Applies to an elementary step. |
| May be obtained from rate experiments. | Obtained from the number of reacting species in an elementary step. |
7. Zero-Order Reaction
For a zero-order reaction, the rate does not depend on the concentration of the reactant.
Integrated rate equation
Where:
- [A]₀ = initial concentration
- [A]t = concentration after time t
- k = rate constant
Half-life
The half-life of a zero-order reaction depends on the initial concentration.
Unit of k
Graph
For a zero-order reaction, a plot of [A] against time gives a straight line.
8. First-Order Reaction
In a first-order reaction, the rate is directly proportional to the concentration of one reactant.
Since:
We have:
On integration:
In common logarithm form:
Half-life of first-order reaction
At half-life:
Substituting in the first-order equation:
Notice that initial concentration does not appear in this expression.
Unit of k
Graphical test
A plot of ln[A] versus time gives a straight line:
9. Second-Order Reaction
For a simple second-order reaction involving one reactant:
The rate law can be:
Integrated rate equation
Therefore:
Half-life
Thus the half-life depends on the initial concentration.
Unit of k
Graphical test
A plot of 1/[A] against time gives a straight line.
Zero order → [A] vs t
First order → ln[A] vs t
Second order → 1/[A] vs t
10. Half-Life of a Reaction
Half-life is the time required for the concentration of a reactant to become half of its initial value.
Zero-order
First-order
Second-order
| Order | Half-life | Depends on [A]₀? |
|---|---|---|
| Zero | [A]₀ / 2k | Yes |
| First | 0.693/k | No |
| Second | 1/(k[A]₀) | Yes |
11. Determination of Order of Reaction
The order of a reaction can be determined by several experimental methods.
1. Initial rate method
Concentrations of reactants are changed systematically and the initial rates are measured.
Suppose:
If [A] is doubled while [B] remains constant and the rate becomes four times:
Therefore the reaction is second order with respect to A.
2. Integrated rate method
Experimental concentration-time data are compared with the integrated equations for zero, first and second order reactions.
3. Half-life method
The relationship between half-life and initial concentration can help identify the order.
4. Graphical method
The graph that gives a straight line indicates the corresponding reaction order.
| Plot | Order indicated |
|---|---|
| [A] vs t | Zero order |
| ln[A] vs t | First order |
| 1/[A] vs t | Second order |
12. Pseudo First-Order Reaction
Sometimes a reaction that actually involves two or more reactants behaves experimentally as a first-order reaction because one reactant is present in very large excess.
Consider:
Suppose:
If B is present in a very large excess, its concentration remains almost constant during the reaction.
Therefore:
The reaction now behaves like a first-order reaction.
Example
Hydrolysis of an ester in a large excess of water can behave as pseudo first-order because water concentration changes very little.
13. Effect of Temperature on Reaction Rate
Reaction rate generally increases when temperature increases.
The important reason is not simply that particles move faster. More importantly, a larger fraction of molecules have energy equal to or greater than the activation energy.
Temperature coefficient
For many reactions, the rate may increase substantially for a temperature rise of 10°C, although the exact change depends on the reaction.
A common approximate rule is:
This is only a rough rule and should not be treated as a universal exact law. The Arrhenius equation gives a better quantitative description.
14. Arrhenius Equation
The Arrhenius equation relates the rate constant to temperature and activation energy.
Where:
- k = rate constant
- A = frequency or pre-exponential factor
- Ea = activation energy
- R = gas constant
- T = absolute temperature in kelvin
Logarithmic form
In common logarithm form:
Two-temperature form
When rate constants at two temperatures are given:
Or:
15. Activation Energy
Activation energy is the minimum energy barrier that reacting particles must overcome for a reaction to occur.
It is represented by Ea.
Why is activation energy important?
If the activation energy is high, fewer molecules have enough energy to react at a particular temperature, so the reaction may be slow.
If activation energy is lower, a larger fraction of molecules can react.
Effect of catalyst
A catalyst provides a different pathway with lower activation energy.
The catalyst does not change the overall thermodynamic energy difference between reactants and products.
16. Collision Theory
Collision theory explains reaction rate in terms of collisions between reacting particles.
Not every collision produces a reaction.
Conditions for an effective collision
- The reacting particles must collide.
- The collision must have sufficient energy.
- The particles must have a suitable orientation.
Energy requirement
The collision must provide enough energy to overcome the activation energy barrier.
If the collision energy is below the activation energy, the particles usually separate without forming products.
Orientation
Even when particles have enough energy, they must collide in a suitable orientation so that the necessary bonds can break and form.
17. Activated Complex and Transition State
During a chemical reaction, reactants pass through a high-energy arrangement before forming products. This unstable arrangement is called the activated complex or transition state.
A simplified representation is:
The energy required to reach this state from the reactants is related to the activation energy.
Energy profile
In an energy profile diagram, the vertical axis usually represents potential energy and the horizontal axis represents reaction progress.
The highest point corresponds approximately to the transition state.
A catalyst lowers the height of the energy barrier by providing another pathway.
18. Reaction Mechanism
The reaction mechanism is the sequence of elementary steps through which reactants are converted into products.
A reaction that appears simple overall may actually occur through several smaller steps.
Example of a two-step mechanism
Overall reaction:
Step 1:
Step 2:
C is formed in one step and consumed in another. Therefore it is an intermediate.
Elementary step
An elementary step represents a single molecular event in the mechanism.
Slow step and rate-determining step
In a simple mechanism, the slowest elementary step can control the overall reaction rate and is often called the rate-determining step.
However, for more complicated mechanisms, deriving the overall rate law requires careful treatment and cannot always be done simply by assuming the slow step.
19. Catalysis
A catalyst is a substance that changes the rate of a reaction without being consumed permanently in the overall reaction.
The main kinetic role of a catalyst is to provide an alternative pathway with lower activation energy.
What a catalyst does
- Changes reaction rate.
- Provides an alternative reaction pathway.
- Lowers the activation energy of that pathway.
What a catalyst does not do
- It does not change the overall reaction equation.
- It does not change the equilibrium constant for a reaction at a fixed temperature.
- It does not change the final equilibrium composition when equilibrium is reached.
- It does not make an impossible reaction thermodynamically possible simply by being present.
Homogeneous catalysis
Catalyst and reactants are in the same phase.
Heterogeneous catalysis
Catalyst and reactants are in different phases.
Enzyme catalysis
Enzymes are biological catalysts. They can accelerate biochemical reactions under relatively mild conditions and often show high specificity for their substrates.
20. Worked Numerical Problems
The concentration of A decreases from 0.80 mol L⁻¹ to 0.50 mol L⁻¹ in 30 seconds. Calculate the average rate.
Given:
Formula:
Change in concentration:
Substitution:
Therefore, the average rate is 1.0 × 10⁻² mol L⁻¹ s⁻¹.
For a reaction:
When [A] is doubled, the rate becomes four times. Find m.
Given:
Therefore:
Since:
The reaction is second order with respect to A.
A first-order reaction has an initial concentration of 0.80 mol L⁻¹. After 20 minutes the concentration becomes 0.40 mol L⁻¹. Calculate k.
Formula:
Substitution:
Since:
Therefore:
The rate constant of a first-order reaction is 0.020 min⁻¹. Calculate its half-life.
Formula:
Substitution:
Therefore, the half-life is approximately 34.7 minutes.
A zero-order reaction has [A]₀ = 0.50 mol L⁻¹ and k = 0.010 mol L⁻¹ min⁻¹. Find the concentration after 20 minutes.
Formula:
Substitution:
For a second-order reaction, [A]₀ = 0.50 mol L⁻¹ and [A]t = 0.25 mol L⁻¹ after 10 seconds. Calculate k.
Formula:
Substitution:
For a reaction, k₁ = 2.0 × 10⁻³ s⁻¹ at 300 K and k₂ = 8.0 × 10⁻³ s⁻¹ at 320 K. Calculate the activation energy.
Use:
Step 1: Calculate k₂/k₁
Step 2:
Since:
And:
Therefore:
Therefore the activation energy is approximately 55.3 kJ mol⁻¹.
21. Common Mistakes
1. Forgetting the negative sign for reactant rate
Reactant concentration decreases with time, so its rate expression contains a negative sign.
2. Confusing order with molecularity
Order is obtained from the experimentally determined rate law. Molecularity refers to an elementary reaction step.
3. Assuming stoichiometric coefficients always give the rate-law powers
This is not generally correct for an overall complex reaction.
4. Using Celsius in the Arrhenius equation
Always convert:
5. Forgetting the unit of k
The unit of the rate constant depends on the overall order.
6. Thinking catalyst changes equilibrium constant
A catalyst changes how quickly equilibrium is reached. It does not change K at a fixed temperature.
7. Saying every collision causes reaction
Only effective collisions have suitable energy and orientation.
8. Using the first-order half-life formula for every reaction
This expression is specifically for a first-order reaction.
22. TU Examination Preparation
Important 2-Mark Questions
- Define chemical kinetics.
- Define rate of reaction.
- What is rate constant?
- Define order of reaction.
- Define molecularity.
- What is activation energy?
- What is an effective collision?
- State Arrhenius equation.
- Define half-life.
- What is a catalyst?
- What is a pseudo first-order reaction?
Important 5-Mark Questions
- Explain the factors affecting reaction rate.
- Differentiate order and molecularity.
- Derive the integrated rate equation for a first-order reaction.
- Explain the half-life of a first-order reaction.
- Explain collision theory.
- Explain the Arrhenius equation.
- Explain pseudo first-order reactions with an example.
- Explain the effect of temperature on reaction rate.
Important 10-Mark Questions
- Derive the integrated rate equations for zero-order and first-order reactions and discuss their half-lives.
- Explain Arrhenius equation and derive the two-temperature form.
- Explain collision theory and discuss the conditions required for an effective collision.
- Explain reaction mechanism, elementary reactions, intermediates and rate-determining step.
- Explain the methods used for determination of order of a chemical reaction.
23. Quick Revision
- Chemical kinetics studies reaction rate and reaction mechanism.
- Rate describes concentration change with time.
- Rate law connects rate with reactant concentrations.
- Rate = k[A]^m[B]^n.
- Overall order = m + n.
- Order is determined experimentally.
- Molecularity refers to an elementary reaction step.
- Zero-order equation: [A]t = [A]₀ − kt.
- First-order equation: k = 2.303/t log([A]₀/[A]t).
- First-order half-life: t1/2 = 0.693/k.
- Second-order equation: 1/[A]t − 1/[A]₀ = kt.
- Second-order half-life: t1/2 = 1/(k[A]₀).
- Arrhenius equation: k = Ae−Ea/RT.
- Higher temperature generally increases k.
- Higher activation energy generally means a slower reaction at the same temperature, all else being comparable.
- Effective collision requires sufficient energy and proper orientation.
- Catalyst provides an alternative pathway with lower activation energy.
- Catalyst does not change the equilibrium constant at a fixed temperature.
- Reaction mechanism consists of elementary reaction steps.
Zero order → [A]t = [A]₀ − kt
First order → ln([A]₀/[A]t) = kt
First-order half-life → 0.693/k
Second order → 1/[A]t − 1/[A]₀ = kt
Arrhenius → k = Ae−Ea/RT