Thermodynamics and Entropy Quiz

Learning Outcomes

• Reactivity 1.4.1: Entropy, S, is a measure of the dispersal or distribution of matter and/or energy in a system. Higher entropy means more ways energy can be distributed. Gases have greater entropy than liquids, which have greater entropy than solids under the same conditions.
• Predict whether physical or chemical changes increase or decrease the entropy of a system.
• Calculate standard entropy changes (ΔS) using standard entropy values (S).
• Reactivity 1.4.2: Change in Gibbs energy (ΔG) relates the energy obtainable from a chemical reaction to enthalpy change (ΔH), entropy change (ΔS), and absolute temperature (T).
• Apply the equation ΔG = ΔH – TΔS to calculate unknown values.
• Reactivity 1.4.3: At constant pressure, a change is spontaneous if the change in Gibbs energy (ΔG) is negative.
• Interpret the sign of ΔG from thermodynamic data.
• Determine the temperature at which a reaction becomes spontaneous.
• Reactivity 1.4.4: As a reaction approaches equilibrium, ΔG becomes less negative and eventually reaches zero.
• Perform calculations using ΔG = ΔG° + RTlnQ and its application to a system at equilibrium (ΔG = −RTlnK).

Overview

• Entropy
• Gibbs energy
• ΔG and equilibrium

Entropy

• Entropy (S) is a measure of dispersal or distribution of total available energy or matter in a system.
• Low entropy: energy and matter localized in one place.
• High entropy: energy and matter randomly distributed throughout a system.
• Entropy is a measure of the disorder of a system.

Entropy and Physical Change

• Changes in entropy are associated with every physical and chemical process.
• Solid < Liquid < Gas (increasing entropy).

Equilibrium

• Many physical and chemical changes are reversible.
• Interconversion of reactants and products can proceed simultaneously in both directions.
• In reversible equations, the arrow is replaced by the equilibrium sign (=) to symbolize the bidirectional nature of the reaction.
• If a reversible change occurs in a closed system, it will eventually reach a state of dynamic equilibrium where:
  • The change continues at the microscopic level.
  • Forward and reverse reaction rates are the same.
  • Concentrations of reactants and products remain constant.
  • Macroscopic properties of the system remain unchanged.
  • Equilibrium can be achieved from either direction.

Entropy Change

• Total entropy change (ΔS_total) during a reaction is the sum of the entropy changes of the system and the surroundings. (ΔS_total = ΔS_system + ΔS_surroundings)
• A reaction is spontaneous when it moves toward either completion or dynamic equilibrium under a set of conditions without any external intervention (e.g., change in temperature, pressure, or concentration of a reactant).

Predicting Entropy Change

• Changes in state (solid → liquid → gas) affect entropy.
• Change in the number of moles of gaseous species affects entropy. More gaseous product moles usually leads to a positive entropy change, while fewer gaseous product moles usually mean a negative change.

Calculating Entropy Changes

• Standard entropy change (ΔS°) of a system can be calculated from standard entropy values (S°) for the reactants and products: ΔS° = ΣS°(products) – ΣS°(reactants).
• Standard entropy values have units of J K⁻¹ mol⁻¹.
• Coefficients used in balanced equations must be considered in entropy calculations.

Gibbs Energy

• Gibbs energy (G) is a state function that combines enthalpy, entropy, and temperature.
• Change in Gibbs energy (ΔG) is calculated as ΔG° = ΔH° – TΔS°.
• The unit of change in Gibbs energy is kJ mol⁻¹.
• ΔG takes into account the direct entropy change of the system and any direct entropy changes in the surroundings resulting from heat transfer.
• At constant pressure a reaction is spontaneous if the change in Gibbs energy has a negative value.

Gibbs Energy Change & Spontaneity

• A table showing the relationship between ΔH°, ΔS°, and ΔG° to spontaneity.

Worked Example 3 (Enthalpy and Entropy)

• Calculation of standard enthalpy change (ΔH°) for the combustion of propane using bond enthalpy data or enthalpy of formation data.
• Prediction of the sign of the standard entropy change (ΔS°) for the reaction.

Worked Example 5 (Ammonia Synthesis)

• Calculating the standard Gibbs energy change (ΔG°) for the synthesis of ammonia.
  • Calculation of the equilibrium constant (K) from ∆G.

ΔG and Equilibrium

• Reaction quotient (Q): ratio of product concentrations to reactant concentrations.
• When a chemical system has reached equilibrium, the ratio of product concentrations to reactant concentrations is the equilibrium constant (K).
• Q > K: The system is not in equilibrium; to reach it, the reverse reaction will be favored.
• Q = K: The system is at equilibrium; no net change in either direction of the reaction.
• Q < K: The system is not in equilibrium; to reach it, the forward reaction will be favored.
• Relationship between ΔG, Q, K, and T.
• At equilibrium, ΔG = 0, Q=K