# General Treatment of the Effect of Temperature on the Enthalpy of Reaction

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General Treatment of the Effect of Temperature on the Enthalpy of Reaction. The equation is only applicable if there is no change in phase in going from T 1 to T 2. Entropy: the Second and Third Laws of Thermodynamics.
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General Treatment of the Effect of Temperature on the Enthalpy of ReactionThe equation is only applicable if there is no change in phase in going from T1 to T2.Entropy: the Second and Third Laws of Thermodynamics
• Spontaneous changes, e.g water running down-hill, a chemical reaction going to equilibrium
• Non-spontaneous changes, e.g. water running up-hill
• Non-spontaneous changes can be made to occur only by supplying energy from outside the system.
• Clausius statement of the second law: It is impossible to use a cyclic process to transfer heat from a colder to a hotter body without at the same time converting a certain amount of work into heat.
• The Entropy of the Universe and a System tends to increase
• Entropy is an extensive thermodynamic quantity designated S. An extensive property is one which depends on the size of the system.
• Entropy
• Entropy is a function of the state of a system and have the following properties, where T is the thermodynamic temperature of the surroundings:
• For an infinitesimal reversible process: dS ≡ dq/dT
• For an infinitesimal spontaneous process: dS >dq/dT
• Entropy thus has the units of Energy divided by Temperature
• q is not a perfect differential but depends upon the path used in making the change.
• Entropy
• For an infinitesimal reversible process dS = 0
• For an infinitesimal spontaneous process dS > 0
• For a finite reversible process ∆S = 0
• For a finite spontaneous process ∆S > 0
• Entropy Changes for Reversible Processes
• The fusion of a solid at its melting point
• The evaporation of a liquid at constant partial pressure of the substance equal to its vapor pressure
• These are isothermal reversible process since they can be reversed by an infinitesimal change in temperature
• Entropy Changes for Reversible Processes
• This equation can be used to calculate the entropy of fusion, sublimation or for the entropy change for transition between two forms of solid.
• The heat gained for the system is equal to the heat lost by the surroundings and together ∆S = 0
• E.g. n-Hexane boils at 68.7oC and the heat of vaporisation is 6896 cal mole-1. Calc. the entropy change for vaporisation into a gas at this temperature
• Entropy Changes for Reversible Processes
• The molar entropy of a vapor is always greater than the liquid and the molar entropy of the liquid is always greater than the solid.
• The increase in entropy of a system due to and increase in temperature can be calculated since the temperature change can be carried out in a reversible manner.
• Entropy Changes for Reversible Processes
• If C is independent of temperature
• The fact that entropy is always larger at the higher temperature agrees with the increased disorder of motion of the molecules.
• Calculate the increase in entropy of gaseous O2 when a mole is heated from 25o to 600oC, using data from the Table
• Entropy Changes for Reversible Processes= 6.56 + 1.87 - 0.36= 8.07 cal deg-1 mole-1The change in entropy may be obtained graphically by plotting and determining the area under the curve from one temperature to the next.Entropy Changes for Irreversible Processes
• The entropy change for an irreversible process may be calculated by considering a path by which the process can be carried out in a series of reversible steps. This is illustrated for the freezing of water below its freezing point, to -10oC which is an irreversible process.
• Entropy Changes for Irreversible ProcessesFor crystallization of liquid water @ 0oC, qrevs = -79.7 cal g-1. The specific heat of water is 1.0 cal deg-1 g-1 and ice 0.49 cal deg-1 g-1 over this range.The decrease in entropy corresponds to an increase structural orderCooling the waterFreezing the waterCooling the iceThird Law of Thermodynamics
• If the entropy of each element is some crystalline state is taken as zero at absolute zero temperature the entropy may become zero, and does so in the case of perfect crystalline substances.
• For a perfect crystal at absolute zero the entropy = 0
• The third law of entropy of a gas at temperature T may be calculated from integrating dqrev/T from 0oK to T.
• Third Law of Thermodynamics
• The third law entropy of a gas at temperature T may be calculated by integrating dq/T from 0oK to the desired temperature.
• The entropy can be calculated from the third law if data on the heat capacity is known, the enthalpy of fusion at melting point Tm, and the enthalpy of vaporization at boiling point Tb
• Third Law of ThermodynamicsThe Entropy of SO2Third Law Entropies @ 25oCThird Law Entropies @ 25oC
• Calculate the entropy change for formation of water vapor at 25oC from oxygen and hydrogen
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