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# Physical Chemistry II CH 433

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This 23 page Class Notes was uploaded by Sienna Shields on Thursday October 15, 2015. The Class Notes belongs to CH 433 at North Carolina State University taught by Staff in Fall. Since its upload, it has received 28 views. For similar materials see /class/224005/ch-433-north-carolina-state-university in Chemistry at North Carolina State University.

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Date Created: 10/15/15

Chemistry 433 Lecture 13 Free Energy Functions NC State University System and surroundings both play in role in the entropy In an isolated system the criterion dS gt 0 indicates that a process is spontaneous In general we must consider dSsys for the system and dSsurr for surroundings Since we can think of the entire universe as an isolated system dStotal gt 0 The entropy tends to increase for the universe as a whole If we decompose dStotal into the entropy change for the system and that for the surroundings we have a criterion for spontaneity for the system that also requires consideration of the entropy change in the surroundings The free energy functions will allow us to eliminate consideration of the surroundings and to ex ress a criterion for s ontaneit solel in terms of parameters that depend on the system Free Energy at Constant T and V Starting with the First Law dU 8w Sq At constant temperature and volume we have SW O and dU Sq Recall that d8 2 SqT so we have dU s TdS which leads to dU TdS s 0 Since T and V are constant we can write this as dU T8 3 O The quantity in parentheses is a measure of the spontaneity of the system that depends on known state functions Definition of Helmholtz Free Energy We define a new state function A U TS such that dA s 0 We call Athe Helmholtz free energy At constant T and V the Helmholtz free energy will decrease until all possible spontaneous processes have occurred m that point the system will be in equilibrium The condition for equilibrium is dA 0 time Question The statement dA s 0 means A The condition for equilibrium is dA 0 B Processes are not spontaneous if dA lt 0 C dA cannot be greater than 0 D All of the above time Question The statement dA s 0 means A The condition for equilibrium is dA 0 B Processes are not spontaneous if dA lt 0 C dA cannot be greater than 0 D All of the above time Definition of Helmholtz Free Energy Expressing the change in the Helmholtz free energy we have AA AU TAS for an isothermal hange from one s anther The condition for spontaneous change is that AA is less than zero and the condition for equilibrium is that AA 0 we write AA AU TAS s O at constant T and V lfAA is greater than zero a process is not spontaneous It can occur if work is done on the system however The Helmholtz free energy has an important physical interpretation Noting the qrev TAS we have AA AU Clrev According to the first law AU qrev wrev so AA wrev reversible isothermal A represents the maximum amount of reversible work that can be extracted from the system Question AA wrev means that the Helmholtz free energy is equal to the maximum amount of reversible work that can be extracted from the system This follows from the fact that A The reversible heat is equal to TAS B A is a state function C The reversible work is the maximum work D All of the above Question AA wrev means that the Helmholtz free energy is equal to the maximum amount of reversible work that can be extracted from the system This follows from the fact that A The reversible heat is equal to TAS B A is a state function C The reversible work is the maximum work D All of the above Definition of Gibbs Free Energy Most reactions occur at constant pressure rather than constant volume Using the facts that Sqrev s TdS and Swrev PdV we have dU s TdS PdV which can be written dU TdS PdV s O The sign applies to an equilibrium condition and the lt sign means that the process is spontaneous Therefore dU TS PV 3 O at constant T and P We define a state function G U PV T8 H TS Thus dG s O at constant T and P The quantity G is called the Gibb39s free energy In a system at constant T and P the Gibb39s energy will decrease as the result of s ontaneous I rocesses until the system reaches equilibrium where dG 0 Comparing Gibbs and Helmholtz The quantity G is called the Gibb39s free energy In a system at constant T and P the Gibb39s energy will decrease as the result of spontaneous puocesses unu the system leaches equilibrium where dG 0 Comparing the Helmholtz and Gibb39s free energies we see that AVT and GPT are completely analogous except thatA is valid at constant V and G is valid at constant P We can see that G A PV which is exactly analogous to the relationship between enthalpy and internal energy For chemical processes we see that AG AH TAS s 0 at constant T and P AA AU TAS s O at constant T and V Conditions for Spontaneity We will not use the Helmholtz free energy to describe chemical processes It is an important concept in the derivation Ul Lllc UlbUD CllClgy Huvvevcl IIUIII LIIID JUIIIL we will consider the implications of the Gibbs energy for physical and chemical processes There are four possible combinations of the sign of AH and AS in the Gibbs free energy change AH A8 of gt0 gt0 for T gt AHAS lt0 lt0 for T lt AHAS lt0 gt0 for all T gt0 lt Question For a given reaction we have AH gt O and AS lt 0 When will the reaction will be spontaneous A never B when T gt AHAS C always D when T lt AHAS Question For a given reaction we have AH gt O and AS lt 0 When will the reaction will be spontaneous A never B when T gt AHAS C always D when T lt AHAS AS gt0 for T gt AHAS lt0 for T lt AHAS gt0 for all T lt Gibbs energy for a phase change For a phase transition the two phases are in equilibrium Therefore AG O for a phase transition For example for water liquid and vapor are in equilibrium at 37315 K at 1 atm of pressure We can write Avaime where we have expressed G as a molar free energy From the definition of free energy we have A Gm A H TA 8 vap vap m vap m The magnitude of the molar enthalpy of vaporization s 407 kJmol and that of the entropy is 1089 JmolK Thus AWE 4065 k mar1 37315 K1089 1 K marl 0 Question Which statement is true for a phase transition AAGOandAo u BAGOandAHO CAGOandAS O DASOandAH O Question Which statement is true for a phase transition AAGOandAo u BAGOandAHO CAGOandAS O DASOandAH O Gibbs energy for a phase change However if we were to calculate the free energy of vaporization at 36315 K we would find that it is 11 kJmol SO vaporizcuiun ID IIUL DIJUIILGIIUUUD a mat LGIIIpcraLUIc If we consider the free energy of vaporization at 38315 K it is 108 kJmol and so the process is spontaneous AG lt 0 State Function Summary At this point we summarize the state functions that we have developed U internal energy H U PV enthalpy S entropy A U TS Helmholtz free energy G U PV T8 H TS Gibbs free energy Please note that we can express each of these in a differential form This sim l refers to the 7 ossible chanes in each function expressed in terms of its dependent variables dH dU PdVVdP dA dU TdS SdT dG dH TdS SdT Question We have shown the dU TdS PdV This means that the natural variables of internal energy are entropy and volume What are the natural variables of the enthalpy A dH TdS VdP entropy and pressure u uo PdV entropy and volume C dH SdT VdP temperature and pressure D dH SdT PdV temperature and volume Question We have shown the dU TdS PdV This means that the natural variables of internal energy are entropy and volume What are the natural variables of the enthalpy A dH TdS VdP entropy and pressure u uo PdV entropy and volume C dH SdT VdP temperature and pressure D dH SdT PdV temperature and volume Question We have shown the dU TdS PdV This means that the natural variables of internal energy are entropy and volume What are the natural variables of the Gibbs free energy A dG TdS VdP entropy and pressure av uo PdV entropy and volume C dG SdT VdP temperature and pressure D dG SdT PdV temperature and volume Question We have shown the dU TdS PdV This means that the natural variables of internal energy are entropy and volume What are the natural variables of the Gibbs free energy A dG TdS VdP entropy and pressure av uo PdV entropy and volume C dG SdT VdP temperature and pressure D dG SdT PdV temperature and volume

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