Reaction Equilibrium in Ideal Gas Mixtures

1
Chapter 6
Physical Chemistry
Chapter 6

• Reaction Equilibrium in Ideal Gas Mixtures

2
Chemical Potentials in an Ideal Gas Mixture
Physical Chemistry
Chapter 6
Chemical Potential of a Pure Ideal Gas
(4.36)
isothermal, pure ideal gas
isothermal, pure ideal gas
(6.1)
pure ideal gas, Po?1 bar
(6.2)
3
Chemical Potentials in an Ideal Gas Mixture
Physical Chemistry
Chapter 6
For a pure ideal gas
Fig. 6.1 T is fixed
4
Chemical Potentials in an Ideal Gas Mixture
Physical Chemistry
Chapter 6
An ideal gas mixture
(1)
(2) The mixture is separated by thermally
conducting rigid membrane permeable to gas i
only, and
ideal gas mixture
Fig. 6.2
(6.3)
5
Chemical Potentials in an Ideal Gas Mixture
Physical Chemistry
Chapter 6
ideal gas mixture
(6.3)
Fig. 6.2
The fundamental thermodynamic equation
6
Chemical Potentials in an Ideal Gas Mixture
Physical Chemistry
Chapter 6
For an ideal gas mixture
Fig. 6.1 (modified)
7
Ideal Gas Reaction Equilibrium
Physical Chemistry
Chapter 6
For the ideal-gas reaction
(4.36)
the equilibrium condition
8
Ideal Gas Reaction Equilibrium
Physical Chemistry
Chapter 6
(6.5)
the equilibrium condition
9
Ideal Gas Reaction Equilibrium
Physical Chemistry
Chapter 6
(6.6)
(6.7)
10
Ideal Gas Reaction Equilibrium
Physical Chemistry
Chapter 6
the equilibrium condition
(6.8)
11
Ideal Gas Reaction Equilibrium
Physical Chemistry
Chapter 6
(6.9)
(6.10)
(6.11)
12
Ideal Gas Reaction Equilibrium
Physical Chemistry
Chapter 6
(6.12)
(6.13)
(6.14)
(6.15)
13
Ideal Gas Reaction Equilibrium
Physical Chemistry
Chapter 6
the standard equilibrium constant the standard
pressure equilibrium constant
14
Ideal Gas Reaction Equilibrium
Physical Chemistry
Chapter 6
the equilibrium constant the pressure
equilibrium constant
15
Ideal Gas Reaction Equilibrium
Physical Chemistry
Chapter 6
(6.23)
16
Ideal Gas Reaction Equilibrium
Physical Chemistry
Chapter 6
?n/mol
same dimension as Po
17
Ideal Gas Reaction Equilibrium
Physical Chemistry
Chapter 6
18
Ideal Gas Reaction Equilibrium
Physical Chemistry
Chapter 6
(6.25)
(6.26)
(6.27)
19
vant Hoff Equation
Physical Chemistry
Chapter 6
From (6.14)
20
vant Hoff Equation
Physical Chemistry
Chapter 6
From
21
vant Hoff Equation
Physical Chemistry
Chapter 6
22
Gibbs-Helmholtz Equation
Physical Chemistry
Chapter 6
23
Gibbs-Helmholtz Equation
Physical Chemistry
Chapter 6
When it is applied to changes
24
vant Hoff Equation
Physical Chemistry
Chapter 6
From (6.14)
Differentiation of lnKPo with respect to
temperature gives
The differentials are complete because K and G
depend only on temperature, not on pressure.
Using Gibbs-Helmholtz equation
(6.36)
25
vant Hoff Equation
Physical Chemistry
Chapter 6
26
vant Hoff Equation
Physical Chemistry
Chapter 6
The vant Hoff equation is an expression for the
slope of a graph of the equilibrium constant
(specially, lnK) plotted against the temperature.
It may be expressed in either of two ways
27
Ideal Gas Reaction Equilibrium
Physical Chemistry
Chapter 6
The equilibrium extent of reaction
The extent of reaction
The reaction goes to right
The reaction reaches equilibrium
The reaction goes to left
28
Simultaneous Equilibria
Physical Chemistry
Chapter 6
A system with several simultaneous reactions that
have species in common.
(6.47)
(6.48)
29
Simultaneous Equilibria
Physical Chemistry
Chapter 6
At 600 K, CH3Cl(g) and H2O(g) react to form
CH3OH, and then form (CH3)2O with a simultaneous
equilibrium shown
(1)
(2)
Starting with equal amount of CH3Cl and H2O, find
the equilibrium amounts of all species.
30
Simultaneous Equilibria
Physical Chemistry
Chapter 6
Suppose that a system initially contains 1 mole
of CH3Cl(g) and H2O(g), x moles of HCl and y
moles of (CH3)2O are formed at equilibrium.
(1)
1-x
1-xy
x-2y
x
(2)
x-2y
y
1-xy
31
Simultaneous Equilibria
Physical Chemistry
Chapter 6
Suppose that a system initially contains 1 mole
of CH3Cl(g) and H2O(g), x moles of HCl and y
moles of (CH3)2O are formed at equilibrium.
32
Simultaneous Equilibria
Physical Chemistry
Chapter 6
The equilibrium amounts of all species are
(1)
0.952
0.961
0.03
0.048
(2)
0.03
0.009
0.961