Notes on Jones/Atkins Chapter 17: The Direction of Chemical Change
Handout 17.2: 3/12/01

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Spontaneous Reactions

• Every chemical reaction has a spontaneous natural direction in which it occurs. These reactions can be reactant-favored or product-favored.
• Note that not all spontaneous reactions are rapid ones or go completely to products!
• Product-favored reactions are usually exothermic and are usually accompanied by an increase in disorder or randomness of the system.
• Spontaneous endothermic reactions must be accompanied by an increase in disorder.

• Disorder or randomness is called entropy and assigned the symbol “S”.
• From tables of entropy values it can be seen that there is more entropy or “energy of disorder” when thermal or positional disorder is increased such as when:
  • a solid is converted to a liquid or gas
  • a liquid is converted to a gas
  • larger, more complex molecules are formed
  • intra- and intermolecular bonds are weakened
  • the formation of a solution

• The second law of thermodynamics states that: the total entropy of the universe is always increasing. In other words, ÆS_total = ÆS_system+ ÆS_surroundings.
• The second law can also be interpreted to mean that since heat leaves the system and creates disorder, ÆS_surroundings = ÆH/T.
• ÆS_system can decrease giving localized order but ÆS_{surroundings will be that much larger}.
• The third law of thermodynamics: S = 0 for a perfect crystalline solid at absolute zero. All absolute entropies are positive.

• Standard state conditions for entropy are 1.00 atm and 298 K.
• A table of standard molar entropy values is in the appendix and has values in Joules/K*moles.
• ÆS_system = · [a ÆS°(products)] - · [b ÆS°(reactants)].
• A positive ÆS_system indicates an overall increase in disorder even if individual compounds have a negative S°.
• Example: CaBr₂(s) ---> Ca⁺²(aq) + 2 Br^-(aq); ÆS° Ca⁺²(aq) = -53.1 J/K*mole; ÆS° for reaction is +242 J/K*mole

• Since both enthalpy and entropy affect the spontaneous nature of a reaction, we can combine them into one energy term.
• This terms is called the “Gibb’s Free Energy”, symbolized by G and has the relationship: ÆG = ÆH - TÆS.
• Spontaneous reactions have a ÆG which is negative, non-spontaneous reactions have a ÆG which is positive and reactions with ÆG = 0 are at equilibrium.
• ÆG°_rxn = · [a ÆG°_f(products)] - · [b ÆG°_f(reactants)] or use ÆG° = ÆH° - TÆS°
• Note that ÆG°_f for elements at standard state condition = 0. However, in general, ÆG°_f does not equal ÆH°_f.

• While ÆG_r° is the free energy change of the pure reactants to create pure products, ÆG_r is the free energy change at any composition in which reactants and products are both present.
• These are related by the expression: ÆG_r = ÆG_r° + RT ln Q where R = 8.314 J/K-mole and Q is the reaction quotient.
• At equilibrium ÆG_r = 0 and K = Q so that this relationship becomes: ÆG_r° = -RT ln K.
• An important conclusion from this is that when ÆG_r° > 0, then K < 1 and reactants are favored; also when ÆG_r° < 0, then K > 1 and products are favored.

• If the enthalpy change for a reaction is (-) and entropy change is (+) the reaction is spontaneous at all temperatures.
• If the enthalpy change for a reaction is (-) and entropy change is (-) the reaction is spontaneous if |TÆS| < |ÆH| .
• If the enthalpy change for a reaction is (+) and entropy change is (+) the reaction is spontaneous if TÆS > ÆH.
• If the enthalpy change for a reaction is (+) and entropy change is (-) the reaction is non-spontaneous at all temperatures.

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