Reaction rate is defined as the change in concentration per unit time and depends greatly on the concentrations of reactants, temperature, and catalysts.
Basic Knowledge
The rate of the reaction aA + bB → cC + dD is expressed as v = -(1/a)·dCA/dt = (1/c)·dCC/dt. The exponents α and β in the rate law(v = k[A]α[B]β) are the experimentally determined reaction orders and are independent of the stoichiometric coefficients.
The rate constant k strongly depends on temperature and is expressed by the Arrhenius equation k = A·exp(-Ea/RT)(Ea=activation energy). As a guideline, the rate approximately doubles or triples when the temperature rises by 10℃.
Reaction rate v（[mol/(L·s)]）
Rate law（v = k[A]α[B]β）
Reaction order（α, etc.; determined experimentally）
Rate constant k（Depends on temperature and catalysts; independent of concentration）
Arrhenius equation（k = A·exp(-Ea/RT)）
Activation energy Ea（Threshold energy required for the reaction）
Further Exploration (Principles and Applications)
For a reaction to occur, colliding molecules must have (1) an appropriate orientation and (2) kinetic energy greater than or equal to the activation energy(collision theory). When the temperature rises, the high-energy side of the Maxwell–Boltzmann distribution increases, and the fraction of molecules exceeding Ea increases exponentially, so the reaction rate rises sharply.
Food lasts longer in a refrigerator because the k of decomposition reactions becomes smaller at low temperatures.
- v = k[A]α[B]β
- Reaction order=determined experimentally (different from coefficients)
- k changes with temperature and catalysts
- Arrhenius: k=A·exp(-Ea/RT)
- Rate increases approximately 2–3 times per 10℃
- Collision theory=orientation+Ea
- Transition-state theory=via an activated complex
Points to Note (Common Confusions and Frequent Mistakes)
① Reaction order ≠ stoichiometric coefficient (the two agree only for elementary reactions). ② The rate constant k changes with temperature but remains unchanged by concentration. ③ The unit changes with the order: s-1 for a first-order reaction and L/(mol·s) for a second-order reaction. ④ The Arrhenius equation shows a linear relationship between ln k and 1/T.
Practice
- In the second-order reaction v=k[A][B], by how many times does the rate change when both [A] and [B] are doubled?
- When the temperature is raised from 27℃ to 57℃, approximately how many times does the rate of a reaction with Ea=50 kJ/mol increase?(R=8.31).
- For the first-order reaction v=k[A] (k=0.02 s-1), find the reaction rate when [A]=0.10 mol/L.