Chemistry Chapter on Thermodynamics and Equilibrium

Course Information

• Course name: Applied Introductory and Physical Chemistry
• Course code: CHEM 10130
• Year: Autumn 2024
• Institution: UCD School of Chemistry, University College Dublin (UCD)

Topics covered

• Sources of energy and nature of energy transfer
• Nature of work and heat
• Nature of enthalpy and entropy
• Nature of spontaneous processes and relationship to Gibbs free energy
• Nature of equilibrium reactions and the equilibrium constant
• Nature of binding reactions
• Nature of the relationship between equilibria and Gibbs free energy
• Nature of rates of reaction and relationship to collision theory
• Nature of activation energy and catalysis
• Nature of enzymes, enzyme kinetics, and enzyme inhibition

What is Energy?

• Energy is the capacity to supply heat or do work.
• Energy can be converted from one form to another, but the total energy remains the same.
• During a chemical or physical change energy cannot be created or destroyed, although it can change form.
• The First Law of Thermodynamics states Energy can neither be created nor destroyed.
• The total energy of the universe is constant.

Heat and Specific Heat Capacity

• Heat (q) is energy gained or lost as heat.
• Specific heat capacity (C) is the heat required to raise the temperature of one gram of a substance by one degree Celsius (or Kelvin).

Energy and Changes of State

• Heat of fusion is the energy transferred as heat to convert a substance from a solid to a liquid at its melting point.
• Heat of vaporization is the energy transferred as heat to convert a substance from a liquid to a gas at its boiling point.
• Temperature is constant during a change of state.

Enthalpy (H)

• Enthalpy is the heat content of a chemical reaction carried out at constant pressure.
• ∆H is the change in enthalpy.
• ∆H = H_final - H_initial = q_p
• ∆H is a state function.
• ∆H= H_product - H_reactant

What is a State Function?

• A state function is a system property that depends only on the system's current state, not how it reached that state.
• Examples include energy and enthalpy.
• Work and heat are not state functions, as their values depend on the path taken.

Hess's Law and Energy diagrams

• Manipulate the equation by adding or subtracting reactions to find different enthalpy changes, which can then be added and subtracted to give the enthalpy change for the final reaction.
• Add and subtract reactants and products.
• What you do to reactants and products must be done to the enthalpy values.
• Cancel what appears on both sides of an equation.
• Look at what needs to be cancelled and placed on the correct side.
• Focus on numbers last.

ΔH° is the enthalpy of formation

• ΔH° is the heat required to form one mole of a compound from its elements in their standard states.
• Standard conditions: 1 atm, 1 M, s, l, g
• ΔH° of an element is zero (by definition).

Predicting Spontaneity under standard conditions

• This table predicts whether a reaction is spontaneous under standard conditions by considering if enthalpy (ΔH°) and entropy (ΔS°) are positive or negative.

Quantifying Entropy Changes

• Entropy is the measure of disorder in a system.
• Entropy increases with increasing temperature.

Reaction Quotient

• For a general chemical reaction, aA + bB ⇌ cC + dD, the reaction quotient can be expressed in terms of either the molar concentrations or partial pressures.

Different equilibrium constants

• Equilibrium constants can be expressed in terms of either molar concentrations or partial pressures.
• The relationship between the constants is K_p = K_c(RT)^∆n

Disturbing a Chemical Equilibrium: Le Châtelier's principle

• Equilibrium can be disturbed by changing temperature, concentration, or volume (for systems involving gases).
• If a stress is applied to a system in equilibrium, the system will shift in a direction that reduces the stress.

What is pH?

• pH stands for "potentia hydrogenii" (power of Hydrogen).
• p[H+] = -log₁₀[H+]

Equilibrium constant of water

• 2H₂O ⇌ H₃O⁺ + OH⁻
• K_w = [H₃O⁺] [OH⁻]/[H₂O]₂
• The equilibrium constant at 25°C is K_w =1.0 x 10⁻¹⁴ mol²/L²

Henderson-Hasselbalch equation

• pH = pK_a + log₁₀([A⁻]/[HA]), where HA is the acid and A⁻ is its conjugate base.

Gibbs Free Energy

• Nature favors processes with negative enthalpy (-H) and positive entropy (+S).
• The Gibbs free energy (G) predicts if a process is spontaneous.
• ΔG = ΔH - TΔS where ΔH is enthalpy change, ΔS is entropy change, and T is temperature.

How can we calculate the Gibbs Free Energy?

• ΔG° is a state function.
• ΔG° = Σn∆G°(products) – Σm∆G°(reactants)
• ΔG° = ΔH° − TΔS°
• Enthalpy (ΔH°) and entropy (ΔS°) changes at standard state conditions.

Reaction Rate and Stoichiometry

• Rate = change in concentration/change in time
• aA + bB → cC + dD -1/aΔ[A]/Δt = -1/bΔ[B]/Δt = 1/cΔ[C]/Δt = 1/dΔ[D]/Δt
• Rate of reaction is the change in concentration of a reactant or product over the change in time.

Example: Peroxide decomposition

• 2H₂O₂ → 2H₂O + O₂
• Rate of peroxide decomposition can be calculated

Integrated Rate Laws

• Integrated rate laws relate reactant concentration to time for zero-order, first-order, and second-order reactions.
• The rate of a zero-order reaction is constant.

For 1st order reaction

• For a first-order reaction, the half-life is independent of concentration.

Activation energy (Ea)

• The activation energy is the minimum energy required for a reaction to occur.

Collision theory

• Reaction rates are affected by collisions among molecules, the correct orientation of colliding molecules, and the energy of colliding molecules.

Arrhenius equation

• The Arrhenius equation relates the rate constant (k) to temperature (T), activation energy (Ea), and the frequency factor (A).
• k = Ae^-Ea/RT.

Catalysis

• Catalysts increase reaction rates by lowering the activation energy.
• Enzymes are biological catalysts.

Enzymes – Nature's catalysts

• Enzymes are biological catalysts that accelerate reactions.
• The reactant (substrate) binds to the enzyme, the chemical reaction takes place at the active site, and the products leave, repeating the cycle.

Models for substrate binding to enzymes

• Enzymes can exhibit either lock-and-key or induced-fit models for substrate binding.

This quiz covers important concepts in thermodynamics and chemical equilibrium, including entropy changes, enthalpy, and the reaction quotient. Understand how various factors affect the equilibrium state of reactions and the meaning of equilibrium constants. Test your knowledge on how entropy behaves during phase transitions and the implications of Le Châtelier's principle.