Reaction rates
Thermodynamics says whether a reaction can happen; kinetics says how fast. Rates matter for everything from cooking to drug design to explosions.
What a rate is
The rate of a reaction is how fast reactant concentration falls or product concentration rises, in units such as mol/(L s). For \(\text{A} \to \text{B}\), rate \(= -\frac{\Delta[\text{A}]}{\Delta t}\). Rates usually slow down as reactants are used up.
Factors affecting rate
Reactions go faster with higher reactant concentration, higher temperature, larger surface area (powdered solids react faster than lumps), and a catalyst. Flour dust can explode while a bag of flour merely burns, purely because of surface area.
Collision theory
Molecules must collide to react, with enough energy (at least the activation energy) and the right orientation. Higher concentration means more frequent collisions; higher temperature means faster molecules and a larger fraction with enough energy. Only a small fraction of collisions usually succeed.
Activation energy
The activation energy \(E_a\) is the energy barrier reactants must overcome, like pushing a boulder over a hill before it can roll down the other side. A match needs a strike to start burning: the friction supplies the activation energy, then the reaction's own heat keeps it going.
Temperature and the Arrhenius equation
The rate constant depends on temperature: \(k = Ae^{-E_a/RT}\). A rough rule of thumb is that many reactions roughly double in rate for every \(10^\circ\)C rise. This is why food spoils faster in warm weather and refrigeration slows decay.
k = A\,e^{-E_a/RT}Catalysts
A catalyst speeds up a reaction by providing an alternative pathway with a lower activation energy, and is not consumed. Catalytic converters in cars turn toxic carbon monoxide and nitrogen oxides into less harmful gases. Enzymes are biological catalysts, often speeding reactions by factors of millions.
Reaction energy diagrams
An energy diagram plots energy along the reaction path. Reactants climb to a transition state at the top of the barrier, then descend to products. The height of the barrier is \(E_a\); the difference between reactant and product levels is \(\Delta H\). A catalyst lowers the barrier but does not change \(\Delta H\).
Worked example
A reaction's rate doubles from \(20^\circ\)C to \(30^\circ\)C. Using the rule of thumb, at \(50^\circ\)C (three more 10-degree steps from 20) it would be about \(2^3 = 8\) times faster than at \(20^\circ\)C. Real factors vary with the activation energy, but the trend is general.
Key takeaways
Rate measures concentration change per time. Concentration, temperature, surface area, and catalysts raise rates. Collisions must have enough energy (\(E_a\)) and correct orientation. The Arrhenius equation shows rates rise steeply with temperature. Catalysts lower \(E_a\) without changing \(\Delta H\) or being consumed.
Flashcard
Change in concentration per time
Check your understanding
How does a catalyst speed up a reaction?