19.1 - Spontaneous Processes Clausius - The total energy of the universe is constant (energy cannot be created or destroyed) while the total energy of an isolated system is constant ∆E = q + w Spontaneous processes proceed without any outside intervention Gasses, if spontaneous, will move from higher pressure to lower pressure All spontaneous processes are so in one direction and non-spontaneous in the opposite direction A spontaneous process can be used to do work while a non-spontaneous process can occur if work is done to the system Increase in entropy and exothermic reactions (negative enthalpy change) create spontaneous processes The evolution of heat (release) from a system increases the entropy of the surroundings due to vibrational motion 2nd Law of Thermodynamics: Overall, a net increase in entropy of system and surroundings is what makes a process spontaneous Heat is transferred spontaneously from a region of higher temperature to a region of lower temperature and can do work State functions are those that can be expressed with a ∆ If ∆T is high, heat transfer occurs more quickly If a system is far from equilibrium, a process is irreversible Processes near equilibrium are reversible due to a small ∆T in heat transfer for an easy change in direction of heat transfer At equilibrium, ∆T = 0 Reversible processes are extremely slow processes Spontaneity depends on temperature, so a process might be non-spontaneous at one temperature and spon- taneous at another (think of the melting of ice)

19.2 - Entropy and the Second Law of Thermodynamics q ∆S = rev T Heat transfer occurs spontaneously only if ∆S ≥ 0

For an irreversible spontaneous process: ∆Suniv = ∆Ssys + ∆Ssurround > 0

For a reversible spontaneous process: ∆Suniv = ∆Ssys + ∆Ssurround = 0

For any spontaneous process: ∆Suniv = ∆Ssys + ∆Ssurround ≥ 0 Entropy in the universe is not conserved and is constantly growing Entropy is an extensive property (depends on amount) ∆H Entropy for Phase Changes: ∆S = T

19.3 - Molecular Interpretation of Entropy Temperature is a measure of the average kinetic energy of the molecules in a sample Translational: Movement of the entire molecule from one place to another (not in solids) Vibrational: Periodic motion of atoms within a molecule (most important in gases) Rotational: Rotation of the molecule about an axis or rotation about σ bonds (not much in solids) R S = k ln(W ), where k = NA W  ∆S = k ln f Wi

1 When a solid is dissolved in liquid, entropy generally increases A solution is typically more disordered than pure solute and solvent separately Exceptions: Anhydrous ionic compounds with ions of charge greater than +2 dissolve with a decrease in entropy because several water molecules are strongly bounds to the ions in solution. Charge of +2 is borderline.

19.4 - Entropy Changes in Chemical Reactions Third Law of Thermodynamics: The entropy of most pure crystalline substances at absolute zero (0 K) is 0 Entropy changes gradually when temperature increases without a phase change but jumps up for phase changes Standard entropies tend to increase with increasing molar mass (for the same physical state) while S(g)  S(l)  S(s) for the same molar mass Larger and more complex molecules have greater entropies Standard molar entropies of elements at 298K are NOT zero even though they are for enthalpies of formation ∆S◦ = P nS◦(products) − P mS◦(reactants) −q −∆H For an isothermal process, ∆S = sys and ∆S = sys for constant-pressure processes surr T surr T

19.5 - Gibbs Free Energy ∆G = ∆H − T ∆S When ∆G < 0, a process is spontaneous, when ∆G = 0 the system is at equilibrium, and ∆G > 0 has the reverse direction spontaneous G is a form of energy that tends to reach a minimum for any spontaneous process at constant T and P When ∆G < 0 (spontaneous processes), ∆G is equal to the maximum work that can be obtained from the process When ∆G = 0, no work can be obtained If ∆G > 0, ∆G is equal to the minimum work that should be applied to the system to force the process to occur ◦ for all elements ∆Gf = 0 ◦ P ◦ P ◦ ∆G = nGf (products) − mGf (reactants)

19.6 - Free Energy and Temperature

19.7 - Free Energy and the Equilibrium Constant The standard free energy change for a reaction is one that starts at standard conditions and goes to equilib- rium ∆G = ∆G◦ + RT ln(Q)

2 If ∆G < 0 then Q < K (forward reaction spontaneous) If ∆G = 0 then Q = K (at equilibrium) If ∆G > 0 then Q > K (reverse reaction spontaneous)

−∆G◦ Free energy at equilibrium at 298 kelvins: K = e RT −∆H◦ ∆S◦ Free energy at other temperatures: ln(K ) ≈ 298K + 298K T RT R −∆H◦ ∆S◦ ln(P ) ≈ vap + vap RT R ∆G = 0 for phase changes since it's at equilibrium

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