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The Laws of Thermodynamics No one breaks the Laws… You can’t win… you can’t break even… and you can’t even get out of the game. Wouldn’t it be nice to know if a reaction has a chance of working before you even try it? What makes reactions go? Reactions tend to a position of minimum energy, that is… So this must be what makes reactions go. 1 In thermodynamics, we define the System as that part of the universe in which we are interested. That which is not the System constitutes the Surroundings. Taken together the System and the Surroundings constitute the… But First… The First Law of Thermodynamics: The (internal) energy (U) of an isolated system is constant. An isolated system has a fixed volume and is thermally insulated from the surroundings. Any change to the energy of a system must take place by a transfer of heat (q) or work (w) to/from the surroundings. U q w • Heat and work are path functions (not state functions). • Heat at a constant pressure is called enthalpy. By definition, at constant pressure: q H • Imagine a reaction done in a balloon. The volume of the balloon may change over the course of the reaction. – If the balloon shrinks, work has been done on the system. – If the balloon expands, the system has done work (can be restated as “negative work has been done on the system”). – The amount of work done on the system depends on the pressure and on the change in volume. At constant pressure: w PV 1st Law: Heat and Work • Recalling that U q w and that q H at constant pressure, we can relate enthalpy and internal energy: q U w H U PV This is the strict definition of enthalpy - a state function. And we have pointed out the correlation between enthalpy and the whether reactions go. The Second Law of Thermodynamics… For any spontaneous process, the entropy of the universe increases. Suniverse 0 This is a truly profound observation with important implications. S univ erse S sy stem S surroundin gs The macrostate of a system has macroscopic properties such as temperature, volume, density and pressure. To try to get a handle on Entropy and to quantitate it, we must consider the system and its microstates. Macroscopic versus microscopic states We can describe the system’s microscopic state, or its microstate as a specific ensemble of particles and their states: 1 atom gas It is also: 2. Moving (translation) 3. Rotating 4. Vibrating Every time it hits another atom or the wall of the balloon it changes to a new microstate. Each microstate has the same total energy. 1 mol gas 6 Macroscopic versus microscopic states The system’s microstate is described by: o Positions of all particles o Momenta of all particles (p = mv) o Occupied energy levels for each particle This would be a lot of variables if each particle was considered independently. A system with a mass of ~1 mg will contain millions of millions of millions of particles to consider. We can take advantage of the large number of particles in a system by taking a statistical approach. The system as a whole should behave as though it consisted of “average” particles. This statistical approach allows us to relate the macroscopic and microscopic states of a system. 7 Entropy, a statistical approach 8 Entropy, a statistical approach 9 Each set of particle locations represents a different microstate. When the volume increases (stopcock opens), the number of microstates is 2n, where n is the number of particles. 10 Entropy, a statistical approach 11 Entropy, a statistical approach Properties of entropy o For any given macroscopic state, there is a fixed number of microscopic states that could apply. Thus, the value for the entropy of a given macroscopic state is fixed. As such, entropy is a state function. It depends only on the macroscopic state of the system. o The change in entropy of a system depends only on the initial and final states – not on the path taken from one to the other. This is true for any state function. o If a system has possible microstates then doubling the size of the system will double the entropy (by increasing the number of possible microstates to 2). Thus, entropy is an extensive property. It depends on sample size. 12 Entropy, a thermodynamic approach The entropy of a perfect crystal approaches zero as the temperature approaches absolute zero. Therefore, we define an absolute entropy scale by defining the entropy of perfect crystal at 0 K as: S = 0 J/mol K We can measure entropies for substances by looking at the relationship between the amount of heat absorbed and the change in T. S dqrev T For an isothermal process, this simplifies to: qrev S T 13 Entropy change during a phase transition In essence, the entropy of a substance is the amount of heat required to increase its temperature by a given amount. Unlike enthalpies (where only changes are measured), entropies are absolute. As reflected in this graph, the entropy, S, of O2 at 298 K is 205.1 J/mol K. Tables of entropies at 298 K for a wide range of materials are available in this fashion as standard entropies, S°. Figure 18.7 The increase in entropy of O2 during phase changes from solid to liquid to gas. 14 The third law of thermodynamics And since entropy is a state function, the entropy change for a process is: r S S( products) S(reac tan ts) Example: Propane (C3H8) is burned near room temperature so that the water produced is liquid rather than vapor. Calculate the entropy change for this reaction. C3H8(g) + 5O2(g) 3CO2(g) + 4H2O(l) J mol K J S(O2(g)) 205.0 mol K J S(CO2(g)) 213.7 mol K J S(H2O(l) ) 69.940 mol K S(C3H8(g)) 269.9 15 Generalities about entropy changes: • the entropy of gases > liquids > solids (reactions in which gases are formed from condensed phases tend to have positive entropy changes) • reactions in solution or in the same phase which produce more product molecules than reactant molecules tend to have positive entropy changes (a matter of stoichiometry) • dissolution of a solid into solution is normally associated with a positive entropy change, but there are exceptions. The third law of thermodynamics Figure 18.8 The entropy of a salt solution is usually greater than the entropy of the solid and the entropy of the water, but it is affected by water molecules becoming organized around each ion. 17 The third law of thermodynamics J mol K J S(Mg 2(aq) ) 138.1 mol K J S(F(aq) ) 13.8 mol K S(MgF2(s) ) 57.24 • The ions organize the solvent due to ion-dipole forces, the water has less entropy with MgF2 dissolved in it. • Powerful ion-ion forces, increase in microstates of MgF2 is not as large as one might suppose. 18