15.2 ENTROPY & SPONTANEITY *SPONTANEOUS CHANGE defined one that, given the necessary ______________________ energy, proceeds without continuous outside assistance *WHAT CONDITIONS FAVOUR A SPONTANEOUS CHANGE? 1. Enthalpy and Spontaneous Changes: When a change lowers the energy of a system, events tend to occur _______________. In chemical reactions, ________________ reactions tend to be spontaneous. *However, not every exothermic reaction is spontaneous and not every endothermic reaction is non-spontaneous. The important thing to consider is that an energy decrease works as one factor in favour of spontaneity. 2. Entropy and Spontaneous Changes: *Entropy, S, a measure of the randomness or _________________ of a system An ordered arrangement of particles (atoms, ions or molecules) has lower entropy (less disorder) than the same number of particles in random arrangements. The greater the _______________ of movement, the larger the entropy. Unlike enthalpy, absolute entropy values can actually be measured, but usually it is the change in entropy that is important. The Formula: [ΔS˚ = *Units of entropy = ______________ *Any event that is accompanied by an _____________in the entropy of the system tend to occur spontaneously. (*Second Law of Thermodynamics = The entropy of the universe is constantly increasing / Third Law of Thermodynamics = As the temperature of a system approaches zero, the entropy of a system approaches zero.) In general, a system will experience an increase in entropy (i.e. disorder / freedom of movement / S > 0) if: the _______________of a gaseous system increases, the ________________ of a system increases (e.g. heating a liquid, solid, or gas) there is a change of physical _____________ where the distance between the particles increases (e.g. solid to liquid or gas, or liquid to gas (Sgas > Sliquid > Ssolid) different types of particles mix (e.g. a solute dissolving in a solvent. (There are some exceptions.) the number of particles increases (e.g. N2O4(g) 2NO2(g)) the number of moles of gas increases *Activity: Determine whether the following reactions/changes show an increase or decrease in entropy (Hint: disorder = +ve S ; disorder = -ve S) 1. 2KClO3(s) 2KCl(s) + 3O2(g) 2. H2O(l) H2O(s) 3. N2(g) + 3H2(g) 2NH3(g) 4. NaCl(s) Na+(aq) + Cl-(aq) 5. KCl(s) KCl(l) 6. Ag+(aq) + Cl-(aq) AgCl(s) 7. 2OH-(aq) + CO2(g) H2O(l) + _________ _________ _________ _________ _________ _________ CO32-(aq) ___________ 1 GIBBS FREE ENERGY (G) the amount of energy available to do work *For a reaction to be spontaneous, the sign of G has to be ______________________. To calculate Gibbs Free Energy use: G˚ = Where: G˚ = change in free energy; H˚ = enthalpy change; OR ΔG˚ = ΣnG˚products - ΣnG˚reactants S˚ = entropy change T = temperature in _________________ ; ***Note that H˚ values are given terms of ________ and S˚ values are given in terms of ________. (Therefore, divide S˚ value by 1000 before calculating G˚.) When G is ______________, the forward reaction is SPONTANEOUS. When G is ______________, the forward reaction is NON-SPONTANEOUS. When G is ______________, the reverse reaction is SPONTANEOUS. When G is __________________, the reaction has established equilibrium….more on this in grade 12. *PREDICTING SPONTANEITY SUMMARY: H S G SPONTANEITY - + Always ________________________ __________________ spontaneous + - Always _______________________ ___________________ spontaneous - - Depends on ____________________ Spontaneous ____________ a specific, calculated, threshold temperature; spontaneous when TS<H + + Depends on ____________________ Spontaneous ____________ a specific, calculated threshold temperatures; when TS>H *MEMORIZE [negative, negative, below] and [positive, positive, above] *Other scenario: (i) MIXING GASES ∆H =_____ ; ∆S = _____ therefore ∆G =____ and process occurs___________________ *Useful rearrangement of G˚ =H˚ - TS˚ : *By setting G˚ = 0, the temperature at which a reaction becomes spontaneous or non-spontaneous can be determined. When G˚ = 0, T= *Remember: the T you attain will be in _____________. *PRACTICE Questions: 6.8 & 6.9 Questions (IB Text) and the following: 1. a) Write the equation for the combustion of one mole of hydrogen to form water under standard conditions, and state whether you would expect the entropy change to have a positive or negative value. b) The standard enthalpy of combustion of hydrogen is -286 kJ mol-1. The standard entropy values for hydrogen, oxygen, and water are 131, 205, and 69.9 J K-1 mol-1, respectively. Calculate the value for the Gibbs free energy at 298 K to show that this reaction is spontaneous at this temperature. **Be sure to be consistent with units! c) Above what temperature will this reaction become non-spontaneous? 2. For the melting of ice, ΔH = +6.00 kJ mol-1 and ΔS = 22.0 J K-1 mol-1. a) Calculate ΔG for the process at -10˚C. (2 marks) b) Use this to explain which form of water is stable at this temperature. (1 mark) c) Repeat this for water at +10˚C. (1 mark) d) Calculate the temperature at which ΔG = 0. What is the significance of this temperature? (2 marks) e) Suppose that the entropy of liquid water was increased by the presence of a solute such as sodium chloride. How would this affect ΔS and the temperature at which ΔG is zero? Does this correspond to any common phenomenon? (2 marks) 2