QMonOct06

# QMonOct06 - Thermodynamics 1 Entropy of Equilibrium The...

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1 Thermodynamics

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2 Entropy of Equilibrium The total entropy change is given by: Now just think about the system. Initially the system and the surroundings are at the same temperature. Heat entering the surroundings If a process occurs spontaneously in the system and an amount of heat leaves the system and enters the surroundings then the heat that enters the surroundings is equal and of opposite sign to the heat that leaves the system. 0 = + = surr sys total dS dS dS
3 continued …………. . Remember if heat is added to system q is positive and if it is removed then q is negative. If the surroundings are so big that there is no volume change and we are considering constant temperature: dU surr is a state function and so under these conditions it does not matter if the heat enters the surroundings reversibly or not. surr surr dq dU =

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4 Back to Entropy The entropy in the surroundings is and so surr surr surr T dq dS = sys surr dq dq - = sys surr T T = sys sys surr T dq dS - =
5 At Equilibrium Rewrite this now just in terms of the system: 0 = + = surr sys total dS dS dS 0 = - = sys sys sys total T dq dS dS 0 or 0 = - = - TdS dq T dq dS

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6 The Gibbs (Free) Energy Chemical reactions commonly occur in open vessels at constant pressure. Virtually all reactions that occur in biology occur at constant pressure. Under these conditions: The term H-TS is a state function and is called the Gibbs (free) energy … 0 = - TdS dH TdS dH dG - =
7 Gibbs Energy At constant temperature and pressure at equilibrium dG = 0 Remember the Gibbs energy is a state function. The term “free” is useful since it helps to define G. G is free in the sense that it is available to do work. In a real process the part of a systems energy available to do work must decrease.

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8 Interpretation The Gibbs energy relates enthalpy, entropy and temperature in such a way that the spontaneity of a system my be determined. If G for a process is negative then the change can occur spontaneously.
9 Gibbs Josiah Willard Gibbs (1839 – 1903) Yale’s first professor of Mathematical physics

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10 Examples Lets look at the formation of hydrogen gas: H + H H 2 The standard enthalpy of formation and the standard entropy of the reactants and products are: f H° (kJ mol -1 ) S° (kJ K -1 mol -1 ) H 2 (gas) 0 0.131 H (gas) 218 0.115
Overall H for the reaction is given by the change in enthalpy of the products minus that in the reactants. S for the reaction is given by the change in entropy of the products minus that in the reactants. H = 0 – 436 = – 436 kJ mol

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## This note was uploaded on 03/17/2010 for the course CH 3530 taught by Professor Consors during the Fall '10 term at WPI.

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QMonOct06 - Thermodynamics 1 Entropy of Equilibrium The...

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