From what we know now (i.e, ΔH and ΔS) How do we determine whether a reaction is spontaneous?

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Arnold Shields
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1 pontaneous Rxns A&G-1 From what we know now (i.e, Δ and Δ) ow do we determine whether a reaction is spontaneous? But Δ and Δ are not enough... here is competition between lowering energy and raising entropy! he overall criterion for a spontaneous reaction is: o what are ΔG and ΔA and how do we determine them?

2 pontaneous Rxn at constant and A&G- From nd Law: At constant : From 1 st Law: d w δ d o At constant Or Define a new state function, the elmholtz energy, A: A For a reaction to be spontaneous: (What about equilibrium?)

3 elmholtz Energy and Work A&G-3 ΔA Δ Δ A is a state function so we can choose a path to use to evaluate. If a reversible path is chosen, we know: Δ qrev / ΔA Δ q rev Isothermal, reversible If ΔA < 0, w rev is the max work that can be obtained. If ΔA > 0, w rev is the min work that must be provided to drive rxn.

4 (What about equilibrium?) pontaneous Rxn at constant and A&G-4 From nd Law: If only work d w From 1 st Law: δ d o At constant Or Define a new state function, the Gibbs energy, G: G G For a reaction to be spontaneous:

5 Gibbs Energy and Work G A&G-5 Differentiate: ub: d d δ w rev dg δwrev d d d ub: δ w δw δw d δw rev non non EX-A&G1 dg d δwnon d d d dg δwnon d d Reversible, constant and If ΔG < 0, max non- work that can be obtained. If ΔG > 0, min non- work that must be provided to drive rxn.

6 ummary of elmholtz and Gibbs Energy A&G-6 Ways to Define elmholtz Energy Ways to Define Gibbs Energy A G da d d dg d d ΔA Δ Δ ΔG Δ Δ he Gibbs and elmholtz energy are related by : G A ermann von elmholtz Josiah Willard Gibbs

7 Maxwell Relations A&G-7 hese relations relate thermodynamic properties that can t be measured (i.e.,,,, etc) to thermodynamic properties that can be measured (i.e.,,,, etc). da d d d (general) For reversible process: Compare to formal total derivative of A(,) da d d d d d

8 A&G-8 he Cross Derivative A A Recall: For state functions (i.e., exact differentials), cross derivative are equal (Math Ch ). What are the cross derivatives? o One of many Maxwell relations

9 he use of a Maxwell relation A&G-9 Can we measure all of the thermodynamic properties in this equation? We can use this Maxwell relation to determine how changes with. Integrate at constant Δ 1 d If you know the EO, you can determine Δ. ake the ideal gas EO: Δ nr / nr d nr ln 1 1

10 se ideal as a reference point A&G-10 If you let 1 become very large, the gas behaves ideally Δ (, ) id id d (constant ) Figure. id J mol -1 K -1 Ethane at 400 K (, ) id id d ρ 1/

11 A&G-11 Natural independent variables for d d d d d d If we consider and as independent variables of, the coefficients of Δ and Δ are simple thermodynamic functions. d C d d Compare with and as independent variables: he differential form suggests that and are the natural independent variables of.

12 Differential ummary what to remember d d d A&G-1 You ll need to know the 1 st and nd laws of thermodynamics: Also, you should know the definitions of the other state functions: d d( ) da d( ) dg d( ) From these you can derive: 1. Add d() to both sides: d ( ) d d d d. ubtract d() to both sides: d( ) d d d d 3. Add d() and subtract d() to both sides: d( ) d d d d d d What are natural independent variables?

13 Natural independent variables A&G-13 Function Differential Equation Independent ariables d d d 1 d d d d d d and and and A da d d and G dg d d and

14 A&G-14 Maxwell Relations (ummary) d d d Function Differential Equation Maxwell Relations A G d d d d d da d d dg Can you derive these Maxwell relations?

15 Another use of a Maxwell Relation A&G-15 tarting from the differential equation for the Gibbs energy, find an expression for the dependence of (ee A&G-9 and 10) dg d d 1. Compare to total formal derivative.. Find the cross derivatives and set equal to each other. his gives the Maxwell relation: 3. Integrate at constant to find: Ethane at 400 K Δ 1 d 4. se id as reference. 5. Label graph as in A&G-10. Figure -4 EXA&G-

16 A&G-16 dependence of A A From Maxwell relations on A&G-14, we can relate to data. What if we want to know how other thermodynamic properties vary as a function of,, or? Differentiate A - wrt : id kj mol -1 d id id ), ( isothermal se & Ethane at 400K Figure -3 Integrate from id to : What do you expect for ideal gas? from!

17 A&G-17 dependence of G Differentiate G - wrt and constant ; id kj mol -1 d id id ), ( Recall & Ethane at 400K Figure -5 Integrate from id to : from! how:

18 A&G-18 dependence of G: Method 1 / G Δ Δ Δ G G / G Δ Δ Gibbs-elmholtz Equation Expressions derived on pages For a process: Will be important for equilibrium constants Integrate both sides and assume Δ is temp independent

19 dependence of G: Method A&G-19 We already know how to find () and () individually can could find G() from: G( ) ( ) ( ) sing (0) as the reference for energy, G( ) (0) ( ) (0) ( ) ( ) (0) 0 fus vap fus vap C C C s l g ( ) d ( ) d ( ) d Δ Δ fus vap ( ) 0 fus vap fus vap s C ( ) d l C ( ) d g C ( ) d Δ fus Δ vap From FL-30 From L-5

20 dependence of G: Graphically A&G-0 G decreases with increasing G ( is positive so slope is negative) Figure -7 hase transitions Continuous function phases are in equilibrium and have same G Δ G 0 trs Discontinuous slope (gas) > (liquid)> (solid)

21 dependence of G A&G-1 We have: G (~A&G-15) Integrating at constant : er mole of ideal gas: Δ G ΔG R d 1 1 d R ln 1 1 Let 1 1 bar: G (, ) G o ( ) R ln 1bar he standard molar Gibbs energy. Only depends on. (tandard conditions: one mole of ideal gas at 1 bar.) G increases with the ln of. Is this due to or?

22 What did we learn? A&G- here is a balance between lowering the energy and increasing the entropy for a spontaneous process at constant. he elmholtz and Gibbs energies provide us with thermodynamic state functions representing this balance. elmholtz and Gibbs energies predict the direction of spontaneity and indicate the condition of equilibrium. Maxwell relations allow us to determine thermodynamic state functions ( or G) from data or equations of state. We can translate tabulated values of G at a given (standard) and to any and.

Ch. 19 Entropy and Free Energy: Spontaneous Change

Ch. 19 Entropy and Free Energy: Spontaneous Change 19-1 Spontaneity: The Meaning of Spontaneous Change 19-2 The Concept of Entropy 19-3 Evaluating Entropy and Entropy Changes 19-4 Criteria for Spontaneous