Mechanisms & Complex Reactions

  • Gibbs Free Energy

    • Whether a reaction is spontaneous or not

    • dG: energy between pdt and rxt

    • G=H−TSG = H - TS where H = enthalpy, T = temperature, S = entropy.

    • G changes with concentration. +G non spontaneous, -G spontaneous.

    • Lowest Gibbs free energy usually involves a mixture of reactants and products, so reaction does not proceed to 100% completion.

  • Dynamic Equilibrium:

    • Kc=[C]c[D]d[A]a[B]bK_c = \frac{[C]^c[D]^d}{[A]^a[B]^b}; squares brackets denote equilibrium concentrations.

    • At equilibrium, forward rate = reverse rate, hence Q=KQ = K.

  • Relation between K and Gibbs Free Energy:

    • ΔrG0=−RTln⁡K\Delta_r G^0 = -RT \ln K

    • If \Delta_r G^0 < 0, K >> 1 (product-favored).

    • If \Delta_r G^0 > 0, K << 1 (reactant-favored).

  • Reversible/ Equilibrium Reactions:

    • rate of forward rxn += rate of backward rxn

  • Relaxation Methods (T-jump):

    • Rapid perturbation shifts equilibrium, concentrations relax to new values at rate depending on both forward and reverse rates.

    • k<em>apparent=k</em>1+k−1k<em>{apparent} = k</em>1 + k_{-1}.

  • Consecutive Reactions:

    • Two consecutive, irreversible elementary steps

    • Rate of slow step controls overall reaction rate, leading to a rate law determined by the slow step.

    • Reversible transitions lead to ΔG\Delta G calculations; step with higher activation energy likely slowest.

  • Rate Limiting Step:

    • Identifies the slowest step in a reaction mechanism that dictates reaction rate.