Kinetics: Energy, Catalysis & Mechanisms

Activation Energy and Arrhenius

The activation energy $E_a$ is the barrier from the reactant valley to the transition state, and $\Delta H = E_a(\text{fwd}) - E_a(\text{rev})$. In $k = Ae^{-E_a/RT}$ the exponential is the fraction of collisions energetic enough to react, and $A$ carries collision frequency and orientation, so higher $T$ or lower $E_a$ raises $k$; an Arrhenius plot of $\ln k$ vs $1/T$ has slope $-E_a/R$. A transition state is a peak that cannot be isolated; an intermediate sits in a valley.

Mechanisms and Catalysis

The slowest elementary step sets the rate law; an intermediate in it is replaced using a fast pre-equilibrium. Intermediates are made then used up, catalysts used then remade. A catalyst lowers $E_a$ in both directions, leaving $\Delta H$ and $K$ unchanged. Enzymes follow Michaelis-Menten kinetics: $K_m$ is the [S] giving $V_{\text{max}}/2$; competitive inhibitors raise $K_m$, noncompetitive inhibitors lower $V_{\text{max}}$.

Key Takeaways

• Barriers set the speed; $\Delta G$ and $\Delta H$ do not.
• The rate-determining step sets the rate law.
• A catalyst changes kinetics, never equilibrium.