Chemical Kinetics: MDCAT Chemistry notes
Chemical Kinetics MDCAT notes: reaction rate, average and instantaneous rate, rate expressions, activation energy, activated complex and energy profiles.
Rate of reaction
Chemical kinetics is the study of the rates of chemical reactions, the factors that affect them and their mechanisms.
The rate of reaction is the change in concentration of a reactant or product per unit time:
$$\text{rate} = \frac{\text{change in concentration}}{\text{time taken}}\qquad \text{unit: } \mathrm{mol\,dm^{-3}\,s^{-1}}$$
- The rate usually decreases as the reaction proceeds, because reactants are used up. It is highest at the start.
- In autocatalytic reactions, where a product catalyzes the reaction, the rate can increase at first. So in general the rate may decrease or increase with time.
- A graph of concentration against time is a curve, not a straight line. Its slope is the rate; a steeper slope means a faster reaction.
Average and instantaneous rate
| Average rate | Instantaneous rate |
|---|---|
| Rate between two specific time intervals | Rate at one particular instant |
| $\dfrac{\Delta[\mathrm{A}]}{\Delta t}$ | $\dfrac{d[\mathrm{A}]}{dt}$, slope of the tangent to the curve |
At the start of a reaction the instantaneous rate is at its highest. As the time interval gets very small, the average rate approaches the instantaneous rate.
Writing the rate in terms of each species
For $a\mathrm{A} + b\mathrm{B} \rightarrow c\mathrm{C} + d\mathrm{D}$:
$$\text{rate} = -\frac{1}{a}\frac{d[\mathrm{A}]}{dt} = -\frac{1}{b}\frac{d[\mathrm{B}]}{dt} = +\frac{1}{c}\frac{d[\mathrm{C}]}{dt} = +\frac{1}{d}\frac{d[\mathrm{D}]}{dt}$$
Reactants take a minus sign (their concentration falls); products take a plus sign. Example: for $\mathrm{N_2 + 3H_2 \rightarrow 2NH_3}$, rate $= -\dfrac{d[\mathrm{N_2}]}{dt} = -\dfrac13\dfrac{d[\mathrm{H_2}]}{dt} = +\dfrac12\dfrac{d[\mathrm{NH_3}]}{dt}$.
The equation that gives the rate in terms of reactant concentrations, rate $= k[\mathrm{A}]^x[\mathrm{B}]^y$, is the rate law.
Collision theory and activation energy
- Molecules must collide to react, but only effective collisions lead to products. These need enough energy and the correct orientation.
- Activation energy ($E_a$): the minimum energy that colliding particles must have for an effective collision; the energy needed to weaken existing bonds so they can break.
- At ordinary temperature only a few molecules possess energy equal to $E_a$.
- High $E_a$: slow reaction. Low $E_a$: fast reaction, because more collisions are effective.
Activated complex
- A high-energy, unstable, short-lived arrangement of atoms at the top of the energy barrier (transition state).
- Its potential energy is maximum.
- Forming it requires energy input, so its formation is endothermic.
Energy profile
$$\Delta H = E_a(\text{forward}) - E_a(\text{backward})$$
- Exothermic: products lie below reactants, so $E_a$(backward) > $E_a$(forward).
- Endothermic: products lie above reactants, so $E_a$(backward) < $E_a$(forward).
- Forward and backward activation energies are always different (unless $\Delta H = 0$).
Key formulas
- Average rate $= \Delta c/\Delta t$; instantaneous rate $= dc/dt$
- $\Delta H = E_{a,f} - E_{a,b}$
Common MDCAT traps
- Rate is concentration change ÷ time, not time ÷ concentration.
- A product's rate term has a positive sign; a minus sign in front of a product term is wrong.
- The activated complex is unstable, not stable.
- Low activation energy means more effective collisions, not "no transition state".
Quick revision
- Unit of rate: $\mathrm{mol\,dm^{-3}\,s^{-1}}$.
- Rate between two times is the average rate.
- Instantaneous rate is highest at the start.
- Formation of the activated complex is endothermic.
- For an endothermic reaction, backward $E_a$ is less than forward $E_a$.