复旦大学物理化学AII 14-5 Temp _ Pressure Effect on equilibrium constants 2015

§5 The effect of temperature aHale Waihona Puke Baidud pressure changes on equilibria
• relation between equilibrium constant and temprature • relation between equilibrium constant and pressure • the effect of inert gases on chemical equilibrium
Temp. & Pressure effect on equilibrium constants
Relation between temp. and equilibrium constants
For condensedphase reaction
r G (T , p) vB (T , p)
k1 ln k 2
k1 sol H 1 1 13000 10 ln R T 293K 8.314 293 303 k2 m02 ,2 0.176, 0.838 m02 ,1
Answer:
The temperature of the downstream water could be roughly estimated as:
0.25(333K-T)=0.75(T-293K) T=303K
According to Henry’s law
pO2 0.21 p k1 m02 ,1 k2 m02 ,2
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Physical Chemistry II
4
Chemical equilibrium
Temp. & Pressure effect on equilibrium constants
Relation between temp. and equilibrium constants
vB B r Gm (T ) (T ) T T T T P B ( T ) v B T T P P
The effect of temp. changes on equilibria
Suppose the temp. does not vary significantly
ln K a (T ) r H m (T ) 2 T RT P
H ln K a r m C RT
* m * B
r G (T , p ) v B (T , p )
0 m 0 B
In the same way, one can deduct:
ln K T
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* a
r H (T , P) 2 RT p
* m
0 0 ln K a rHm (T , p ) 2 T RT p
r H m C p T
' c 2 C a bT cT 2 p T
ln K a (T ) r H m (T ) 2 T RT P
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物理化学II
9
Chemical equilibrium
T2 r Gm (T ) RT ln Ka (T ) substituted into the above equation,
ln K a (T ) r H m (T ) 2 T RT P
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v H B m (T )
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Physical Chemistry II
8
Chemical equilibrium
Temp. & Pressure effect on equilibrium constants
The effect of temp. changes on equilibria
H if r m is related to temp., substitution into the differential equation followed by integration with existing reference Table values, then one can calculate the integration constant.
2015/6/12
Physical Chemistry II
11
Chemical equilibrium
Temp. & Pressure effect on equilibrium constants
Example 6
m02 ,2 m02 ,1
m02 ,2 k1 , ln m0 ,1 k2 2
B
* B

r Gm

0 B
rG
Ka
0 m
* Ka
0 Ka
* r Gm
The standard equilibrium constant is a function of temp. A change in the equilibrium constant can be realized by regulating the reaction temp. Achieving maximum product yield by controlling the reaction tendencies
1
Chemical equilibrium
Temp. & Pressure effect on equilibrium constants
Main objectives of research about chemical equilibrium:


Determine the equilibrium composition
Judging the direction of a reaction Factors affecting an equilibrium shift
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Physical Chemistry II
2
Chemical equilibrium
Temp. & Pressure effect on equilibrium constants
H 1 r m 1 ln K p (T2 ) ln K p (T1 ) ( ) R T1 T2
The above equation is usually employed to calculate the equilibrium constant at a particular temp. from a specified value at known temprature.
2015/6/12
Physical Chemistry II
3
Chemical equilibrium
Temp. & Pressure effect on equilibrium constants
（I）The temp.-dependence of the equilibrium constant
For non-thermal reactions, r H m 0 , the temp. change does not affect K p
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Physical Chemistry II
6
Chemical equilibrium
Temp. & Pressure effect on equilibrium constants
Physical Chemistry II
10
Chemical equilibrium
Temp. & Pressure effect on equilibrium constants
Example 6
The water for cooling a power plant comes from a nearby stream. Assuming that the amount of cooling water accounts for 25% of the total amount of the stream flow. The inlet and outlet water temperatures are 20℃ and 60℃, respectively. Calculate the ratio of water solubility of oxygen between the upstream and downstream of the plant site. Given the average enthalpy change of the oxygen dissolution in water is 13 kJ/mol
Temp. & Pressure effect on equilibrium constants
The effect of temp. changes on equilibria
With a small temp. variation, r H m could be treated as a constant, the following equations can be written :
Chemical equilibrium
Temp. & Pressure effect on equilibrium constants
Physical Chemistry
Temperature &Pressure effect on equilibrium constants
2015/6/12
Physical Chemistry II
ln K a (T ) r H m (T ) 2 T RT P
H For endothermic reaction, r m 0 ,increasing the temp., K p will increase, the forward reaction is favored For exothermic reaction, r H m 0 ,increasing the temp., K p will decrease, the forward reaction is not favored
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Physical Chemistry II
12
Chemical equilibrium
Temp. & Pressure effect on equilibrium constants
(II) Effect of pressure changes on equilibria
Kθ has no relation to pressure, so the system pressure change does not have any effect on the value of Kθ
r H (T ) T
m 2
van’t Hoff equation
Physical Chemistry II
5
Chemical equilibrium
Temp. & Pressure effect on equilibrium constants
The effect of temp. changes on equilibria
What is the meaning of C ?

rGm rHm T rSm

r Gm r H m r Sm ln K a RT RT R
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r S C R
m
Physical Chemistry II
7
Chemical equilibrium