Entropy, Spontaneity, and Gibbs Free Energy Study Guide

Predicting Changes in Entropy (Topic 14)

  • Definition of Entropy (SS): Entropy is defined as a measure of disorder or randomness within a chemical or physical system.
  • General Rules for Predicting an Entropy Increase (ΔS>0\Delta S > 0):     - An increase in disorder occurrs when gases are produced or when the total number of moles of gas increases during a reaction.         - Example Reaction: H2O2(l)→H2O(l)+O2(g)H_2O_{2(l)} \rightarrow H_2O_{(l)} + O_{2(g)}     - An increase in disorder occurs when solids dissolve into their constituent ions in a solution.         - Example Reaction: NaCl(s)→Na+<em>(aq)+Cl−</em>(aq)NaCl_{(s)} \rightarrow Na^{+}<em>{(aq)} + Cl^{-}</em>{(aq)}     - A substance undergoes a phase transition to a more disordered phase. The progression of disorder is as follows: solid→liquid→gas\text{solid} \rightarrow \text{liquid} \rightarrow \text{gas}.
  • General Rules for Predicting an Entropy Decrease (ΔS<0\Delta S < 0):     - A decrease in disorder occurs when gases are consumed, leading to a decrease in the change in moles of gas (Δngas\Delta n_{gas}).         - Example Reaction: 3H2(g)+N2(g)→2NH3(g)3H_{2(g)} + N_{2(g)} \rightarrow 2NH_{3(g)}     - A substance undergoies a phase transition to a more ordered phase.         - Examples: gas→liquid→solid\text{gas} \rightarrow \text{liquid} \rightarrow \text{solid}.         - Specific processes include freezing, condensation, and deposition.
  • General Rules for Predicting No Change in Entropy (ΔS=0\Delta S = 0):     - Entropy remains effectively unchanged when there is no net change in the number of gas moles between the reactants and the products.         - Example Reaction: CH4(g)+2O2(g)→CO2(g)+2H2O(g)CH_{4(g)} + 2O_{2(g)} \rightarrow CO_{2(g)} + 2H_2O_{(g)}

Second Law Theory and Spontaneity (Topic 15)

  • The Second Law of Thermodynamics: This law states that a process is spontaneous if the entropy of the universe increases (\Delta S_{univ} > 0).
  • The Universe Calculation: The total entropy change of the universe is the sum of the entropy change of the system and the entropy change of the surroundings.     - Formula: ΔSuniv=ΔSsys+ΔSsurr\Delta S_{univ} = \Delta S_{sys} + \Delta S_{surr}
  • Criteria for Spontaneity:     - If \Delta S_{univ} > 0, the process is spontaneous.     - If \Delta S_{univ} < 0, the process is nonspontaneous.

Second Law Calculation for Entropy of Surroundings (Topic 16)

  • Relationship Between System Heat and Surrounding Entropy: The entropy of the surroundings is inversely proportional to the temperature and directly related to the negative of the heat flow of the system.     - Formula: ΔSsurr=−qsysT\Delta S_{surr} = -\frac{q_{sys}}{T}
  • Heat Exchange Principles:     - Exothermic Reactions: When heat leaves the system, the heat variable is negative (qsys<0q_{sys} < 0). Based on the negative sign in the calculation, this results in a positive entropy change for the surroundings (ΔSsurr>0\Delta S_{surr} > 0).     - Endothermic Reactions: When heat enters the system, the heat variable is positive (q_{sys} > 0). This results in a negative entropy change for the surroundings (\Delta S_{surr} < 0).
  • Numerical Calculation Example:     - Problem: Find the ΔSsurr\Delta S_{surr} for a process where 200 kJ200\,kJ of heat leaves a system at a temperature of 200 K200\,K.     - Step 1: Set value for qsysq_{sys}. Since heat leaves the system, qsys=−200,000 Jq_{sys} = -200,000\,J.     - Step 2: Apply the formula:         - ΔSsurr=−qsysT\Delta S_{surr} = -\frac{q_{sys}}{T}         - ΔSsurr=−−200,000 J200 K\Delta S_{surr} = -\frac{-200,000\,J}{200\,K}         - ΔSsurr=+1000 J/K\Delta S_{surr} = +1000\,J/K

Relating Reaction Spontaneity to Temperature for Phase Changes (Topic 17)

  • Gibbs Free Energy (ΔG\Delta G): This state function relates the spontaneity of a process to the enthalpy, entropy, and absolute temperature of the system.     - Governing Equation: ΔGsys=ΔHsys−TΔSsys\Delta G_{sys} = \Delta H_{sys} - T\Delta S_{sys}
  • Predicting Spontaneity via ΔG\Delta G:     - Spontaneous Process: ΔG<0\Delta G < 0     - Nonspontaneous Process: ΔG>0\Delta G > 0     - Equilibrium: ΔG=0\Delta G = 0
  • Relation to Intermolecular Forces (IMF):     - Stronger intermolecular forces lead to more order in a substance, which corresponding to lower entropy.     - As a substance transitions from stronger IMF to weaker IMF states (such as a liquid transitioning to a gas), the entropy of the system increases.
  • Spontaneity and Temperature Table:     - Condition 1: ΔHsys=+\Delta H_{sys} = + and ΔSsys=+\Delta S_{sys} = +         - Spontaneity: The process is spontaneous at high values of TT.         - Phase Change Examples: Melting and Vaporization.     - Condition 2: ΔHsys=−\Delta H_{sys} = - and ΔSsys=−\Delta S_{sys} = -         - Spontaneity: The process is spontaneous at low values of TT.         - Phase Change Examples: Freezing and Condensation.     - Condition 3: ΔHsys=−\Delta H_{sys} = - and ΔSsys=+\Delta S_{sys} = +         - Spontaneity: The process is always spontaneous.         - Examples: Combustion and Salt dissolution.     - Condition 4: ΔHsys=+\Delta H_{sys} = + and ΔSsys=−\Delta S_{sys} = -         - Spontaneity: The process is never spontaneous.         - Example: Deposition.