Thermodynamics and Equilibrium

GENERAL CHEMISTRY

Chapter 17: Thermodynamics and Equilibrium

1. Entropy and Gibbs Free Energy
1.1 Sign Convention for Heat (q)
  • Negative q: When heat is evolved by the system, it is considered negative, signifying a decrease in the internal energy of the system.
  • Positive q: When heat is absorbed by the system, it is considered positive, indicating an increase in the internal energy of the system.
1.2 Spontaneous Processes
  • A spontaneous process is a physical or chemical change that occurs on its own without external intervention. It continues until the system reaches equilibrium.
2. First Law of Thermodynamics
  • The First Law of Thermodynamics states that whenever a thermodynamic system undergoes a change, the change in internal energy is the sum of heat transferred and work done.
  • Equation:

     riangle U = q + w
3. Entropy (S)
  • Entropy (S) is a thermodynamic quantity that measures the dispersion of energy within a system and the number of ways a system can contain energy. The concept of entropy is essential for determining the spontaneity of reactions.
4. Second Law of Thermodynamics
  • The Second Law of Thermodynamics states that the total entropy (S) of a system and its surroundings will always increase for a spontaneous process.
5. Entropy and Molecular Disorder
  • Entropy relates to energy dispersal within a system. When energy changes from concentrated states to dispersed states, the entropy increases.
  • A system's entropy can transition from having energy concentrated in few states to being spread across many states, which increases the total energy of the system.
6. Criteria for a Spontaneous Reaction
  • For a reaction to be spontaneous, the total change in entropy of the universe must increase, which can be denoted as:
      - +riangleS=extspontaneous+ riangle S = ext{spontaneous}
      - −riangleS=extnonspontaneous- riangle S = ext{nonspontaneous}
7. Helpful Equations
  • Total Universe Entropy Change:

     riangle S_{universe} = riangle S_{system} + riangle S_{surroundings}
  • Surroundings Entropy Change:

     riangle S_{surroundings} = - rac{ riangle H}{T}
8. Third Law of Thermodynamics
  • According to the Third Law of Thermodynamics, a perfectly crystalline substance at absolute zero (0 K) has an entropy of zero.
9. Entropy Change for a Reaction
  • Entropy typically increases in three scenarios:
      1. A molecule breaking into two or more smaller molecules.
      2. An increase in the number of moles of gas.
      3. A phase change such as a solid turning into a liquid or gas.
10. Free Energy (G)
  • The concept of Free Energy (G) introduced by physicist J. Willard Gibbs is defined by the equation:
      -
     riangle G^ heta = riangle H^ heta - T riangle S^ heta
10.1 Gibbs Free Energy as a Criterion for Spontaneity
  • The spontaneity of a reaction can be assessed using the sign of Gibbs Free Energy (G):
      - riangleGheta<−10extkJ:extspontaneousriangle G^ heta < -10 ext{ kJ}: ext{spontaneous}   - riangleGheta>+10extkJ:extnonspontaneousriangle G^ heta > +10 ext{ kJ}: ext{nonspontaneous}
      - For very small or zero values (between +10 kJ and -10 kJ), the system is at equilibrium.
11. Coupling of Reactions
  • Nonspontaneous processes often occur in nature, balanced by spontaneous ones providing the necessary energy. Examples include:
      - ATP synthesis
      - Photosynthesis
      - Cooking processes
12. Calculating Entropy Change (riangleShetariangle S^ heta) of a Reaction
  • The change in entropy can be calculated based on moles from the balanced equation:
      -
     riangle S^ heta = ext{Sum of } nS^ heta_{products} - ext{Sum of } nS^ heta_{reactants}
13. Example Calculation of riangleShetariangle S^ heta
  • Given a reaction:
    CH3CH2OH(l)+O2(g)→CH3COOH(l)+H2O(l)CH_3CH_2OH(l) + O_2(g) → CH_3COOH(l) + H_2O(l)
  • Standard entropies (S°) at 25°C:
      - CH3CH2OH(l)=161extJ/(Kmol)CH_3CH_2OH(l) = 161 ext{ J/(K mol)}
      - O2(g)=205extJ/(Kmol)O_2(g) = 205 ext{ J/(K mol)}
      - CH3COOH(l)=160extJ/(Kmol)CH_3COOH(l) = 160 ext{ J/(K mol)}
      - H2O(l)=69.9extJ/(Kmol)H_2O(l) = 69.9 ext{ J/(K mol)}
14. Free Energy and Spontaneity
  • If riangle G < 0, the forward reaction is spontaneous.
  • If riangleG=0riangle G = 0, the reaction is at equilibrium.
  • If riangle G > 0, the reaction is nonspontaneous.
15. Spontaneity and Completion of Reaction
  • Spontaneous reactions might not go to completion due to reaching equilibrium, where the rate of forward and reverse reactions are equal.
16. Example of Reaction Entropy Change Prediction
  • For:
    Ba(OH)2imes8H2O(s)+2NH4NO3(s)→2NH3(g)+10H2O(l)+Ba(NO3)2(aq)Ba(OH)_2 imes 8H_2O(s) + 2NH_4NO_3(s) → 2NH_3(g) + 10H_2O(l) + Ba(NO_3)_2(aq)
  • The system transitions from 3 moles of reactants to 13 moles of products indicating a positive riangleShetariangle S^ heta.
17. Energy Exchanges in Thermodynamics
  • Energy exchange comes in two main forms: heat (q) and work (w). The first law of thermodynamics can be concisely expressed as:
      -
     riangle U = q + w
18. Sign Convention for Work (w)
  • For work done by the system on the surroundings:
      - extWhenriangleVextispositive,wextisnegative.ext{When } riangle V ext{ is positive, } w ext{ is negative.}
  • For work done on the system by the surroundings:
      - extWhenriangleVextisnegative,wextispositive.ext{When } riangle V ext{ is negative, } w ext{ is positive.}
19. Constant Pressure Conditions
  • At constant pressure, the heat absorbed or evolved can be expressed as:
      - qP=riangleHq_P = riangle H
20. Work Example Calculation
  • Consider the reaction of HCl and Zn:
      - The reaction evolves hydrogen gas, increasing volume, therefore, work is done by the system as the piston lifts.
21. Heat Flow Example
  • A cup of coffee releasing heat to its environment demonstrates spontaneous heat flow, thus increasing total entropy.
22. State Function Nature of Entropy
  • Entropy is recognized as a state function, which signifies it relies on temperature and pressure, and it is an extensive property depending on the amount of substance.
23. Units of Entropy
  • Entropy is measured in units of J/K, with changes in entropy calculated using:
      - riangleS=Sf−Siriangle S = S_f - S_i
  • Examples will involve calculating changes in entropy for phase changes.
24. Transition Phase Entropy Change
  • For phase transitions near equilibrium, changes in entropy can be captured as slow heat absorption or release:
      - riangle S = rac{q}{T}
25. Entropy Change for Vaporization Example
  • For acetone:
    extCH<em>3extCOCH3(l)→extCH3extCOCH3(g)ext{CH}<em>3 ext{COCH}_3(l) → ext{CH}_3 ext{COCH}_3(g)   where the values of enthalpy of vaporization (riangleH</em>vapriangle H</em>{vap}) and standard entropy (ShetaS^ heta) lead to subsequent calculations of riangleSriangle S and Gibbs free energy ( riangle G) for the reaction.
26. Standard Free Energy of Formation
  • The standard free energy of formation (GfhetaG_f^ heta) is the change that occurs when 1 mol of a substance is formed from its elements in their standard states at 1 atm and 25°C.
27. Calculating riangleGriangle G Using Standard-Free Energies
  • The calculation of riangleGriangle G based on the formulation of reactants and products is crucial for assessing reaction spontaneity.
28. Relation Between Free Energy Change and Equilibrium Constant
  • At equilibrium:
      - riangleG=0extandQ=Kriangle G = 0 ext{ and } Q = K
      - The relationship is defined as:
      - riangleGheta=−RTextlnKriangle G^ heta = -RT ext{ln } K
29. Example Calculation of Equilibrium Constant
  • For the reaction, use standard free energies of formation to calculate the equilibrium constant using:
  • Values of Gibbs free energy provide insight into reactants and products concentrations in equilibrium conditions.