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240_l12 - Entropy Changes Processes Chapter 4 of Atkins The...

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Entropy Changes & Processes Sectios 4.4 - 4.7, 7th ed.; Sections 3.3-3.6, 8th ed. Third Law of Thermodynamics Nernst Heat Theorem Third-Law Entropies Reaching Very Low Temperatures Helmholtz and Gibbs Energies Helmholtz Energy Maximum Work Gibbs Energy Maximum Non-Expansion Work Standard Molar Gibbs Energies Chapter 4 of Atkins: The Second Law: The Concepts Oct. 25, 2006: Updated slide 1

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The Third Law of Thermodynamics At absolute zero, or when T = 0 K, all energy of thermal motion has been quenched, and all atoms or ions in a perfect crystalline lattice are in a perfect continuous array # No spatial disorder # No thermal motion # Entropy is zero: if S = 0, there is only one way of arranging the molecules Cannot actually reach absolute zero - everything has some internal energy!! Perfect continuous array of atoms in solid NaOH What good is the Third Law? It allows us to realize that as T approaches zero, the absolute entropy tends towards zero. The effects of the third law are most keenly felt at very low temperatures (not everyday stuff). The third law also lets us define some entropies of substances relative to their perfect crystals at 0 K. Useful book keeping device!
Nernst Heat Theorem The entropy change accompanying a physical or chemical transformation approaches zero as the temperature approaches zero ) S 6 0 as T 6 0 Consider transition from orthorhombic sulfur S ( " ) to monoclinic sulfur S ( \$ ) in the solid state. At the transition temperature (369 K): ) trs S ' S m ( " ) & S m ( \$ ) ' ( & 402 J mol & 1 ) 369 K ' & 1.09 J K & 1 mol & 1 Two entropies can be determined from measuring heat capacities from T = 0 K to T = 369 K: So at the transition temperature: ) S trs ' S m ( " ,0) & S m ( \$ ,0) & 1 J K & 1 mol & 1 S m ( " ,0) & S m ( \$ ,0) . 0 S m ( " ) ' S m ( " ,0) % 37 J K & 1 mol & 1 S m ( \$ ) ' S m ( \$ ,0) % 38 J K & 1 mol & 1

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Third Law & The Nernst Heat Theorem If we decide to assign a value zero to entropies of elements in their perfect crystalline form at T = 0, then all perfect crystalline compounds have entropy = 0 at T = 0 Third Law of Thermodynamics If the entropy of every element in its most stable state at T = 0 is taken as zero, then every substance has a positive entropy which at T = 0 may become zero, which is also zero for all perfect crystalline substances, including compounds This does not mean that the entropy at T = 0 is really zero! It means that all perfect crystalline substances have the same entropy at T = 0 (choosing the value S = 0 at this temperature is a convenience, and as mentioned, leads to some very neat bookkeeping for comparing relative entropies)
Third Law Entropies The choice S (0) = 0 for perfect crystal is made from now on, and entropies reported relative to this value are called Third Law Entropies (or just standard entropies ) A substance in its standard state at temperature T has a standard entropy which is denoted as S o ( T ) Standard reaction entropies are defined as ) r S o ' j products < S o m & j reactants < S o m ' j J < J S o m (J) and are weighted by stoichoimetric coefficients in the same way that enthalpies are weighted Example : Calculate ) r S o of H 2 (g) + ½O 2 (g) 6 H 2 O(l) at 25 o C ) r S o = S m o (H 2 O, l) - S m o (H 2 , g) - ½ S m o (O 2 , g) = 69.9 - {130.7 + ½(205.0)} J K -1

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240_l12 - Entropy Changes Processes Chapter 4 of Atkins The...

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