Chemical Equilibrium Notes

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Physical Chemistry

Transcript of Chemical Equilibrium Notes

  • Chemical Chemical EquilibriumEquilibrium

    Part 1Part 1

    Week Topic Topic Outcomes3-4 Chemical equilibrium

    The Gibbs energy & Helmholtzenergy

    The Gibbs energy of a gas in a mixture

    The thermodynamic equilibrium constant, Kp for a mixture of ideal gases

    The dependence of eq on to T & P

    It is expected that students are able to:

    Interpret the spontaneity of a gas mixture.

    Calculate the Gibbs energy and the equilibrium partial pressure of mixing for ideal gases.

    Topic Outcomes

  • (3)

    How fast we get the product How much we get the product

    Introduction

    In each phase of the closed system, the number of molesof each substance present remains constant in time.

    Reaction equilibrium:Is equilibrium with respect to

    conversion of 1 set of chemical species to another set.

    Phase equilibrium:Is equilibrium with respect to transport of matter between

    phases of the system without conversion of 1 species to

    another.

    Definition

  • Reaction Equilibrium:Involves different chemical species, which may or may not be present in the same phase.

    E.g.: CaCO3 (s) CaO (s) + CO2 (g)

    N2 (g) + 3H2 (g) 2NH3 (g)

    Phase equilibrium:Involves the same chemical species present in different phases

    E.g.: C6H12O6 (s) C6H12O6 (aq)

    Example

    Entropy & Equilibrium

    Consider an isolated system that is not at material equilibrium;

    The spontaneous chemical rxn / transport / matter btw phases in this system are irreversible processes that increase the entropy (S).

    The processes continue until the S is maximized once the S is maximized, further processes can only decrease S, i.e., violating the 2nd Law.

    Criteria for equilibrium in an isolated system is the maximization of the systems entropy, S.

  • Material equilibrium in Closed System

    Ordinarily not isolated: can exchange heat and work with its surroundings.

    By considering the system itself plus the surroundings with which it interacts to constitute an isolated system

    Then, the condition for material equilibrium in the system is maximization of the total entropy of the system plus its surroundings:

    a maximum at equilibriumgsurroundinsystem SS +

    Reaction Equilibrium

    1. Rxn that involve gases Chemicals put in container of fixed V,

    System is allowed to reach equilib. at const. T & V in a const.-T bath.

    2. Rxn in liquid solutions E.g.: The system is usually held at atm P

    Allowed to reach equilib. at constant T & P.

  • The Gibbs The Gibbs Energy and Energy and HelmholtzHelmholtz

    EnergyEnergy

    (10)

    New State Functions

    Spontaneity is discussed in context of the approach to equilibrium of a reactive mixture of gas.

    2 new state functions are introduced that express spontaneity in terms of the properties of the systemonly.

    Previously: the direction for an arbitrary process in predicted by Ssys + Ssurr > 0.

  • Reactant Product

    Systems at const. V & T Systems at const. P & T

    Criterion for determining if the reaction mixture will evolve toward reactants or products:

    Kp derived Predict equilibrium conc.

    The Helmholtz Energy, AMaterial equilib. in a system held at const. T &V (dV= 0, dT= 0)

    dU TdS + SdT SdT + dw

    dU d(TS) SdT + dw

    d(U TS) SdT + dw

    at equilibriumdU TdS + dw

    Add & subtract SdT:

    Since d(TS) = SdT + SdS

  • d(U TS) SdT PdV

    d(U TS) 0Const. T & V, dT=0, dV=0, closed syst.In therm. & mech. Equilib.,P-V work only

    At const. T & V, dT=0, dV=0

    Since dw = P dV

    State function

    Helmholtz free energy

    A U - TS

    The Gibbs EnergyConsider for const.T & P, dw = PdV into dU TdS + dw

    dU d(TS) SdT d(PV) + VdP

    d(H TS) SdT VdPd(U + PV TS) SdT + VdP

    dU TdS + SdT SdT - PdV - VdP + VdP

    d(H TS) 0At const. T and P, dT=0, dP=0

    G H TS U + PV TSGibbs free energy,

  • dAT,V 0 dGT,P 0

    Equilibrium reached

    Const. T, P

    Time

    G

    Equilibrium State

    G decreasesSuniv increase

    In a closed system capable of doing only P-V work,

    Const. T & V material-equilibrium condition is the minimization of the A,

    Const. T & P material-equilibrium condition is the minimization of the G.

    dA = 0

    dG = 0

    at equilib., const. T, V

    at equilib., const. T, P

  • Relationship Gequilib & SunivConsider a system in mechanical & thermal equilib.which undergoes an irreversible chemical reaction / phase change at const. T & P.

    / TG / TSTH S/ THSSSsystsystsyst

    systsystsystsurruni v

    ==+=+=

    / TGS systuni v = Closed syst., const. T, V, P-V work onlyGsyst as the system proceeds to equilib. at const. T&P corresponds to a proportional Suniv.The occurrence of rxn is favored by +ve Ssyst and +veSsurr

    Work Function: A

    at const. T( ) dwSdTTSUd +dwdAwA

    dwSdTdA +

    wwby =Awby Const. T, closed syst.

    Closed system in thermal & mechanical equilibrium

    Finite isothermal process

    Work done by the system on its surroundings

    A carries a greater significance than being simply a signpost of spontaneous change:

    Awmax =Change in the Helmholtz energy is equal to the max. work the system can do:

    Equality sign reversible proc. wby can be greater or less than U (int. energy of syst.)

    wby = U + q (E.g. Carnotcycle, U = 0 & wby>0)

  • Work Function: G

    TSPVUTSH G +PVAPVTSU G ++ VdPPdVdAdG ++=

    VdPPdVdwSdTdG +++

    ( ) dwSdTTSUd +dwSdTdA +

    PdVdwdG + const. T & P, closed syst.

    From

    and H=U+PV

    d(PV)=PdV+VdP

    VPnondwPdVdw +=

    VPnondwdG VPnonby,VPnonwwG

    =

    VPnondwdG Gw VPnonby, const. T & P, closed syst.

    If the P-V work is done in a mechanically reversible

    PdVdwdG +Note:

    Awby Earlier for A;

    From dw

    wA Compare A

    Compare A

  • Gw maxV,Pnon =

    ( )PVddwdqdH ++=

    ( ) ( )PVddwTdSPVddwTdSdG rev +=++=

    dwdqdU +=

    ( ) VdPdwVdPPdVdwPdVdG VPnonVPnon +=+++=

    revdwdw=TdSdqdq rev ==

    The max. non-expansion work from a process at cont. P & T is given by the value of G

    (const. T, P)Reversible change, equality sign holds & wby,non-P-V= G

    From dU

    dH=dU+d(PV)

    dS=dQ/T

    dG=dH-TdS

    dH

    What G means: +G : not spontaneous Zero G : at equilibrium G : spontaneous

    What A means: +A : not spontaneous Zero A : at equilibrium A : spontaneous

    Second law of thermodynamics:

    Entropy must always increase!

    Summary

    Gibbs Free Energy Helmholtz Free EnergySTHG =

    STUA =

    Initial & final states of system at the same values of

    P & T

    Initial & final states of system at the same values of

    V & T

  • Working Session

    For a phase change on vaporization of 1.0 mol water at 1 atm and 100C, calculate G and A.

    Given: molar volume of H2O (l) at 100C is 18.8 cm3/mol, R=8.314 J/mol.K=82.06 cm3.atm/mol.K

    Example 1You wish to construct a fuel cell based on the oxidation of hydrocarbon fuel. The 2 choices for a fuel are methane & octane.The reactions are,

    Methane: CH4 (g) + 2O2 (g) CO2 (g) + 2H2O (l)Octane: C8H18 (l) + 25/2 O2 (g) 8CO2 (g) + 9H2O (l)

    Calculate the maximum work and non-expansion work available through the combustion of these 2 hydrocarbons, on a per mole and a per gram basis at 298.15 K and 1 bar pressure.

    Given at 298.15K: Hcombustions(CH4,g)=891kJ/mol;Hcombustions(C8H8,l)=5471 kJ/mol; Sm(CH4,g)=186.3 J/mol.K; Sm(C8H8,l)=361.1 J/mol.K; Sm(O2,g)=205.2 J/mol.K; Sm(CO2,g)=213.1 J/mol.K; Sm(H2O,l)=70 J/mol.K

  • Differential Differential Forms of Forms of UU, , HH, ,

    AA and and GG

    All thermodynamic state-function relations can be derived from six basic equations,

    1st basic equation it combines the 1st & 2nd Laws

    Next 3 basic equations are the definitions of H, A, and G

    Finally, the 2 equations are for the CP and CV equations

    PdVTdSdU = Closed syst., P-V work onlyPVUH += TSUA = TSHG =

    Closed syst., in equilib., P-V work only

    VV T

    UC

    =

    PP T

    HC

    =

    Closed syst., in equilib., P-V work only

  • The Gibbs Equations

    Closed syst., rev. proc., P-V work only

    VdPTdSdH +=

    PdVTdSdU =

    SdTPdVdA =SdTVdPdG =

    Equivalent Expressions

    VPHandTS

    HSP =

    =

    PV

    U and TSU

    SV =

    =

    VPG and ST

    GSP =

    =

    PV

    A and SSA

    TV =

    =

  • VT TP

    VS

    =

    PT TV

    P S

    =

    PS SV

    PT

    =

    SV VT

    S P

    =

    The last two are extremely valuable.

    Maxwell Relations

    The first two are little used.

    The equations relate the isothermal P & V variations of entropy to measurable properties.

    Dependence of G & A on P, V, T

    Most reactions of interest to chemist are carried out under const. P rather than const. V conditions.

    VPG and ST

    GSP =

    =

    G, T

    G ,P

    Macroscopic change in P & T, 2nd expression integrate

    ( ) ( ) ==P

    P

    P

    PVdP'PT,GPT,GdG

    oo

    oo Initial P, P = 1 bar

    This equation takes on different form for liq. & solids & for gaseous.

  • Liquids & Solids

    Independent of P over a limited range in P,

    ( ) ( ) ( ) ( )oooooo

    PPVPT,GVdP'PT,GPT,G PP

    ++=

    Systems changes appreciably with P

    ( ) ( ) ( ) ( )