Introduction to Biochemistry: Activation Energy and Reaction Rates

Part 1: Understanding Chemical Reactivity

  1. Atoms of a chemical element form bonds with other atoms to achieve greater stability, typically by completing their electron octet.

  2. Bond formation occurs when atoms come sufficiently close together for their electronic orbitals to overlap.

  3. Overlapping orbitals lead to the release of energy. The energy conversion involves both potential and kinetic energy, which is dissipated as heat. This relaxation signifies a transition to a lower energy state (stabilization).

  4. Bonds in reactants are stable by definition; they would not exist if they were unstable.

  5. A chemical reaction entails breaking of existing bonds in reactants to form new bonds in the products.

  6. Activation Energy (Eₐ): This is defined as the initial energy input necessary to disrupt stable bonds in the reactants to initiate the reaction process.

Example of Reactivity in Elements

Sodium (Na)

  • Stability Gain: Sodium (Na) attains stability by losing one electron, transforming into a Na⁺ ion, leading to an electronic configuration analogous to that of the inert gas Neon (Ne).

  • Ionization Energy: The energy needed to remove an electron from Na is approximately 11 eV.

  • Example: Formation of Sodium Chloride (NaCl) occurs after sodium loses an electron, resulting in Na⁺.

Chlorine (Cl)

  • Stability Gain: Chlorine (Cl) becomes stable upon gaining one electron, becoming Cl⁻, with a configuration similar to Argon (Ar).

  • Ionization Energy: The energy needed for an electron to be added to Cl is around 17 eV.

  • This reaction leads to the formation of NaCl as well.

Part 2: Activation Energy (Eₐ) and Reaction Rates

Activation Energy and its Role

  • Activation energy is defined as the threshold energy needed for a reactant molecule to initiate bond cleavage and new bond formation.

  • Reaction rates define the speed at which reactants are converted into products. Activation energy might vary significantly between reactions, being large for slower reactions and small for quicker reactions.

Example of Reaction

  • Consider the decomposition of hydrogen peroxide: 2H2O2 → 2H2O + O2

    • Gibbs Free Energy: The reaction has a negative Gibbs energy, indicating its spontaneity but with a high activation energy, hence it proceeds slowly over weeks.

Exothermic vs Endothermic Reactions

Exothermic Reaction: Combustion of Methane

  • Reaction formula:
    CH4 + 2 O2
    → CO2 + 2 H2O

  • This process is characterized by a release of energy (ΔH) and is marked by Gibbs Free Energy (ΔG) = -212 kcal/mol.

Endothermic Reaction: Formation of Nitric Oxide

  • Reaction formula:
    N2 + 2O2 → 2NO2

  • Characterized by a positive Gibbs Free Energy (ΔG = +22 kcal/mol). Despite being non-spontaneous, this indicates that it requires energy input, but it does not make the reaction impossible.

Transition States

  • These states are formed when reactants acquire enough energy to rearrange into products. The transition state is a structure with localized energy that signifies the molecular conformation needed for the conversion as bonds break and new bonds form thereafter.

  • Transition states are typically short-lived, existing in the femtosecond timescale.

The Eyring-Polanyi Equation

The relationship between activation energy and reaction rates is captured in the Eyring-Polanyi equation, which expresses how the rate constant (k) depends on temperature (T), activation energy (ΔG≠), the Boltzmann constant (k_B), and Planck's constant (h):

  • Eyring-Polanyi Equation

  • In the equation:

    • k: rate constant (s^-1)

    • k_B: Boltzmann constant

    • T: absolute temperature in Kelvin (K)

    • h: Planck's constant

    • R: universal gas constant

    • ΔG: activation energy or Gibbs free energy change.

Conclusion

  • The interplay of bond breaking, the concept of activation energy, and the Eyring-Polanyi equation is essential for understanding the kinetics and dynamics of biochemical reactions. An understanding of the transition state provides insights into the speed of reaction rates, vital for many biological processes.