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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

#

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%%

&

'

((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

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\$%

&

'(

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)