Chemical Kinetics
Why do some reactions finish almost instantly while others take years? Chemical kinetics studies reaction rates, the factors that affect them, and the mechanisms through which reactions occur.
1. Rate of a Chemical Reaction
Reaction rate describes how quickly the concentration of a reactant or product changes with time.
Average rate = Δ[Product] / Δt
The negative sign for a reactant accounts for its decreasing concentration. Product concentration generally increases as the reaction proceeds.
A common unit of reaction rate is mol L⁻¹ s⁻¹. For a general reaction aA + bB → cC + dD, the rate can be written as:
= −(1/b) d[B]/dt
= (1/c) d[C]/dt
= (1/d) d[D]/dt
These expressions describe the same reaction rate after accounting for the stoichiometric coefficients.
2. Factors Affecting Reaction Rate
Concentration
A higher reactant concentration can increase the frequency of effective collisions.
Temperature
Increasing temperature generally increases the fraction of particles energetic enough to react.
Surface area
For reactions involving solids, greater exposed surface area can allow more frequent collisions.
Catalyst
A catalyst provides an alternative reaction pathway with lower activation energy and is regenerated overall.
Pressure can also affect rates for reactions involving gases, particularly when changing pressure changes the gases' concentrations.
3. Rate Law and Rate Constant
For a reaction involving reactants A and B, an experimentally determined rate law may take the form:
- k is the rate constant at a specified temperature.
- [A] and [B] are reactant concentrations.
- m and n are experimentally determined reaction orders with respect to A and B.
The exponents in a rate law generally cannot be obtained from the balanced chemical equation alone. They must be established experimentally, except for suitable elementary reaction steps.
Suppose Rate = k[A]²[B].
- Doubling [A], with [B] unchanged, makes the rate four times as large.
- Doubling [B], with [A] unchanged, doubles the rate.
4. Order and Molecularity
| Feature | Reaction order | Molecularity |
|---|---|---|
| Meaning | Sum of powers in the experimental rate law | Number of reacting entities in an elementary step |
| How obtained | Experiment | Mechanism of the elementary step |
| Possible values | Can be zero, fractional or integer | Positive integer for a conventional elementary step |
For Rate = k[A]²[B], the overall order is 2 + 1 = 3.
5. Integrated Rate Equations
Integrated rate equations describe how reactant concentration changes over time for reactions with particular rate laws.
Zero-order reaction
t½ = [A]₀ / 2k
The rate is independent of reactant concentration. A plot of [A] against time is linear, with slope −k.
First-order reaction
k = (2.303/t) log₁₀([A]₀ / [A]t)
t½ = 0.693 / k
Here, [A]₀ is the initial concentration and [A]t is the concentration at time t. For a first-order reaction, the half-life does not depend on the initial concentration.
Second-order reaction
For the simple rate law Rate = k[A]²:
t½ = 1 / (k[A]₀)
These equations assume the corresponding rate law applies under the conditions considered.
6. Half-Life
Half-life is the time required for the concentration of a reactant to decrease to half its initial value.
Zero order
Depends on the initial concentration.
First order
Independent of the initial concentration.
Second order
For Rate = k[A]², it depends inversely on initial concentration.
7. Collision Theory and Activation Energy
Collision theory suggests that reacting particles must collide with suitable orientation and sufficient energy for a reaction to occur.
Activation energy, Ea, is the energy barrier associated with a reaction pathway. A catalyst can provide an alternative pathway with a lower activation energy.
Raising temperature increases the proportion of particles with enough energy to overcome this barrier.
8. Arrhenius Equation
The Arrhenius equation describes the relationship between the rate constant and absolute temperature for many reactions.
ln k = ln A − Ea/(RT)
- k is the rate constant.
- A is the pre-exponential factor.
- Ea is activation energy.
- R is the gas constant.
- T is absolute temperature in kelvin.
A plot of ln k against 1/T is linear for a system following the Arrhenius relationship, with slope −Ea/R.
This two-temperature form can be used to estimate how the rate constant changes with temperature when the activation energy is known and the Arrhenius model applies.
9. Reaction Mechanisms
A reaction mechanism is a sequence of elementary steps that describes how a chemical reaction proceeds.
- An intermediate is formed in one step and consumed in another.
- The slowest step can limit the overall rate in a simplified mechanism.
- The rate law must be consistent with experimental observations.
- A catalyst participates in the mechanism and is regenerated overall.
10. Quick Revision
- Reaction rate measures concentration change per unit time.
- Rate law: Rate = k[A]ᵐ[B]ⁿ.
- Overall order is the sum of the exponents in the rate law.
- First-order half-life: t½ = 0.693/k.
- Second-order integrated equation for Rate = k[A]²: 1/[A]t = 1/[A]₀ + kt.
- Arrhenius equation: k = Ae⁻ᴱᵃ⁄ᴿᵀ.
- Catalysts provide an alternative pathway with lower activation energy.