Statistical Molecular Thermodynamics - The Cramer · PDF fileSelf-assessment Explained Is the...

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Transcript of Statistical Molecular Thermodynamics - The Cramer · PDF fileSelf-assessment Explained Is the...

  • Statistical Molecular Thermodynamics

    Christopher J. Cramer

    Video 12.6

    Temperature Dependence of K

  • Dependence of K on T

    We can apply the Gibbs-Helmholtz equation (cf. video 8.7)

    G! /TT

    #

    $

    %%

    &

    '

    ((P

    = H!

    T 2

    ( ) ( )TKRTTG Plnr = !And substitute

    lnKP T( )T

    "

    #$

    %

    &'P

    =d lnKP T( )

    dT=rH!

    RT 2vant Hoff Equation

    Another manifestation of Le Chteliers principle

    Endothermic: 0r >!H KP(T) increases with T.

    Exothermic: 0r

  • Integrating the vant Hoff Equation d lnKP T( )

    dT=rH!

    RT 2lnKP T2( )KP T1( )

    =rH! T( )

    RT 2T1

    T2

    dTintegrate

    Over small T ranges we can consider rHo constant (T independent):

    lnKP T2( )KP T1( )

    = rH!

    R1T21T1

    #

    $%

    &

    '(

    600oC

    900oC slope =

    RH !r

    ( ) ( ) ( ) ( )gOHgCOgCOgH 222 ++

    Clausius-Clapeyron analog

    ln P2P1=

    vapHR

    1T21T1

    #

    $%

    &

    '(

    (cf. video 9.6)

    ( ) ( )lXgX

  • Self-assessment Is the water gas shift reaction as written below

    exothermic or endothermic?

    600oC

    900oC slope =

    RH !r

    ( ) ( ) ( ) ( )gOHgCOgCOgH 222 ++

  • Self-assessment Explained Is the water gas shift reaction as written below

    exothermic or endothermic?

    600oC

    900oC slope =

    RH !r

    ( ) ( ) ( ) ( )gOHgCOgCOgH 222 ++

    Endothermic. One can see this either by noting that KP is larger at higher temperature, or by noting that the slope being negative implies rHo must be positive.

  • Integrating the vant Hoff Equation

    lnKP T2( )KP T1( )

    =rH! T( )

    RT 2T1

    T2

    dT lnKP T( ) = lnKP T1( )+rH! "T( )

    R "T 2T1

    T

    d "T

    If we cannot consider rH(T) constant over the T range,

    rH! T2( ) = rH! T1( )+ CP! T( )T1

    T2 dT

    We do know how to calculate the T dependence of H,

    where CP(T) is often reported as a series in T from an experimental fit,

    CP! T( ) = A+BT +CT 2 +"( ) ( ) ( )gNHgN2

    1gH23

    322 +

    the vant Hoff plot is no longer linear

  • Next: Determining K from Q (the other Q)