Energetics, rates and driving forces of chemical reactions

• Energy is the capacity to do work or transfer heat; it exists as kinetic (motion) or potential (position).

• Energy is conserved (First Law of Thermodynamics), but can be transformed during chemical reactions.

• Enthalpy (ΔH) measures heat content at constant pressure; ΔH = H_products - H_reactants.

• Exothermic reactions release heat (ΔH < 0); endothermic reactions absorb heat (ΔH > 0).

What is energy and how is it involved in chemical reactions?

• Hess’s Law states that total ΔH is the same whether a reaction occurs in one step or many.

• Equations can be reversed (change sign of ΔH) or multiplied (scale ΔH accordingly).

• Used for ΔcomH (combustion), ΔfusH (melting), ΔvapH (boiling), ΔfH (formation).

What is Hess’s Law and how is it used in enthalpy calculations?

• Standard state: most stable form at 1 bar, 298 K; ΔH° and ΔS° refer to changes under these conditions.

• ΔrH° = ΣΔH°(products) - ΣΔH°(reactants); S° values are nonzero even for elements.

• Standard entropy is given by ΔS° = ΣS°(products) - ΣS°(reactants).

What are standard states and how are standard enthalpy and entropy defined?

• Entropy (S) is a measure of disorder or the number of microstates in a system.

• Gases > liquids > solids in entropy; more disorder = more entropy = more favorable.

• Total entropy of the universe must increase for a process to be spontaneous.

What is entropy and what role does it play in reactions?

• Gibbs energy (ΔG = ΔH - TΔS) determines spontaneity, not ΔS or ΔH alone.

• ΔG < 0: spontaneous; ΔG = 0: equilibrium; ΔG > 0: non-spontaneous.

• ΔH < 0 and ΔS > 0 → always spontaneous; ΔH > 0 and ΔS < 0 → never spontaneous.

• If ΔH and ΔS have same sign, spontaneity depends on temperature.

• Exergonic = ΔG < 0 (energy released); Endergonic = ΔG > 0 (energy required).

What determines whether a reaction is spontaneous

• ΔG < 0 → Q > K: shifts left; ΔG > 0 → Q < K: shifts right; ΔG = 0 → equilibrium.

• At equilibrium, forward and reverse reactions occur at equal rates with no net change.

• ΔG is linked to equilibrium constant: ΔG° = -RTlnK.

How is ΔG related to the reaction quotient Q and equilibrium?

• Thermodynamics determines if a reaction will occur; kinetics determines how fast it happens.

• A reaction can be spontaneous but very slow due to high activation energy.

What is the difference between thermodynamics and kinetics in chemical reactions?

• Rate = change in concentration over time, units mol·L⁻¹·s⁻¹.

• Affected by nature of reactants, surface area, concentration, temperature, and catalysts/inhibitors.

• Catalysts lower activation energy and increase rate without being consumed.

What factors affect the rate of a chemical reaction?

• Rate law: rate = k[A]^x[B]^y; x and y (orders) are determined experimentally.

• Overall order = x + y; stoichiometry doesn’t determine rate law unless step is elementary.

• Pseudo-first order: when [B] ≫ [A], [B] is treated as constant and rate ≈ k’[A].

What is the rate law and how is it determined?

• Use controlled changes in [A] or [B] to find order (x or y); rate = k[A]₀^x[B]₀^y.

• Isolation method: keep one reactant in large excess to simplify rate law.

• Once x and y are known, use any data point to calculate k.

How are reaction rates measured using initial rate and isolation methods?

• Integrated rate law: ln[A] = ln[A]₀ - kt (linear graph → slope = -k).

• Half-life: t½ = ln(2)/k; independent of initial concentration.

• First-order reactions show exponential decay and linear ln[A] vs time.

What are the key equations and properties of first-order reactions

• Elementary steps = single molecular events (uni-/bi-molecular).

• Overall reaction = sum of steps; rate law is based on slow (rate-determining) step only.

• Mechanism must match experimental rate law to be valid.

What are elementary steps and how do they relate to reaction mechanisms?

• Molecules must collide with enough energy (Ea) and correct orientation to react.

• Increasing temperature increases collision frequency and success rate.

• Rate constant k increases with temperature; described by Arrhenius equation.

What is collision theory and how does temperature affect reaction rate?

• k = Ae^(-Ea/RT); shows how rate depends on activation energy and temperature.

• Can be rearranged to find Ea from experimental data.

What is the Arrhenius equation and what does it tell us?

• Oxidation = loss of electrons; reduction = gain of electrons.

• Use oxidation numbers to identify changes in charge and redox agents.

• Oxidizing agent is reduced (e.g., Cl₂ → Cl⁻); reducing agent is oxidized (e.g., Na → Na⁺).

What are redox reactions and how are oxidation numbers used?

• E°cell = E°(cathode) - E°(anode); spontaneous if E°cell > 0.

• Galvanic cell: oxidation at anode, reduction at cathode, electrons flow through circuit.

• Standard hydrogen electrode has E° = 0 V and is used as reference.

How are electrochemical cells and potentials used to analyze redox?

• ΔG° = -nFE°; negative ΔG° → spontaneous reaction.

• E° = (RT/nF)lnK; redox potential links directly to equilibrium constant.

How are ΔG° and E°cell related in redox reactions?

• E = E° - (RT/nF)lnQ; used when concentrations deviate from standard 1 mol·L⁻¹.

• Biological standard = pH 7, which affects redox strength (e.g., MnO₄⁻ is weaker at pH 4)

How is E adjusted for non-standard conditions (Nernst equation)?

1 Balance all atoms except H and O.

2 Add H₂O for O atoms.

3 Add H⁺ for H atoms.

4 Add e⁻ to balance charge.

How do you balance redox half-equations (4 steps)?

• ATP is formed using energy from a proton gradient via ATP synthase. It is Coupled with oxidation of food molecules and electron transfer to O₂ (final electron acceptor).

How is ATP synthesis linked to redox in biological systems?

• NAD⁺, FAD, and CoQ act as mild, reversible oxidants suitable for cells.

• Biological oxidants must accept and later donate electrons (reversible redox).

What are common biological oxidants (3) and how do they function?

• Transition metals (e.g., Fe in cytochromes) change oxidation states to facilitate redox.

• Ligands (from protein side chains or hemes) tune redox potentials of metal centers.

• Ligands are Lewis bases (donate electrons); metal ions are Lewis acids (accept electrons).

What role do transition metals (1) and ligands (1) play in redox biochemistry, and are they Lewis bases or acids?