Calculating Equilibrium Composition

1
Calculating Equilibrium Composition

• Example
• Cl2 (g) ? 2Cl (g)

2
Calculating Equilibrium Composition

• Example
• Cl2 (g) ? 2Cl (g)
• Initially, n0 moles of Cl2 gas is placed in a
  closed reaction vessel.
• The molecule partially dissociates into atoms.

3
Calculating Equilibrium Composition

• Example
• Cl2 (g) ? 2Cl (g)
• Both are gasses, so use partial pressures rather
  than concentrations.
• We know that at equilibrium we have a definite
  mixture (i.e., the composition of the mixture is
  not arbitrary), as the reactants and products are
  related.

4
Calculating Equilibrium Composition

• What is the expression for the equilibrium
  quotient?

5
Calculating Equilibrium Composition

• What is the expression for the equilibrium
  quotient?
• We need expressions for the partial pressures at
  equilibrium.

6
Calculating Equilibrium Composition

• Initial No. of moles Cl2 ?

7
Calculating Equilibrium Composition

• Initial No. of moles Cl2 n0 2Cl ?

8
Calculating Equilibrium Composition

• Initial No. of moles Cl2 n0 2Cl 0

9
Calculating Equilibrium Composition

• Initial No. of moles Cl2 n0 2Cl 0
• No. of moles at eq. Cl2 ?

10
Calculating Equilibrium Composition

• Initial No. of moles Cl2 n0 2Cl 0
• No. of moles at eq. Cl2 n0 a

11
Calculating Equilibrium Composition

• Initial No. of moles Cl2 n0 2Cl 0
• No. of moles at eq. Cl2 n0 a 2Cl ?

12
Calculating Equilibrium Composition

• Initial No. of moles Cl2 n0 2Cl 0
• No. of moles at eq. Cl2 n0 a 2Cl 2a

13
Calculating Equilibrium Composition

• Initial No. of moles Cl2 n0 2Cl 0
• No. of moles at eq. Cl2 n0 a 2Cl 2a
• Mole fractions at eq. Cl2 ?

14
Calculating Equilibrium Composition

• Initial No. of moles Cl2 n0 2Cl 0
• No. of moles at eq. Cl2 n0 a 2Cl 2a
• Mole fractions at eq. Cl2 n0 a/ n0a 2 Cl
  2a/n0a

15
Calculating Equilibrium Composition

• Initial No. of moles Cl2 n0 2Cl 0
• No. of moles at eq. Cl2 n0 a 2Cl 2a
• Mole fractions at eq. Cl2 n0 a/ n0a 2 Cl
  2a/n0a
• Partial pressures at eq. Cl2 ?

16
Calculating Equilibrium Composition

• Initial No. of moles Cl2 n0 2Cl 0
• No. of moles at eq. Cl2 n0 a 2Cl 2a
• Mole fractions at eq. Cl2 n0 a/ n0a 2 Cl
  2a/n0a
• Partial pressures at eq. Cl2 (n0 a/ n0a )p
• 2Cl (2a/n0a)p

17
Calculating Equilibrium Composition

• Initial No. of moles Cl2 n0 2Cl 0
• No. of moles at eq. Cl2 n0 a 2Cl 2a
• Mole fractions at eq. Cl2 n0 a/ n0a 2 Cl
  2a/n0a
• Partial pressures at eq. Cl2 (n0 a/ n0a )p
• 2Cl (2a/n0a)p
• Now express Kp in terms of what we have.

18
Calculating Equilibrium Composition

• Partial pressures at eq. Cl2 (n0 a/ n0a )p
• 2Cl (2a/n0a)p
• Now express Kp in terms of what we have.
• In terms of partial pressures. Which, in terms of
  a and n0 is

19
Calculating Equilibrium Composition

• Partial pressures at eq. Cl2 (n0 a/ n0a )p
• 2Cl (2a/n0a)p
• Now express Kp in terms of what we have.
• Which in terms of a and the total pressure is

20
Calculating Equilibrium Composition

• Partial pressures at eq. Cl2 (n0 a/ n0a )p
• 2Cl (2a/n0a)p
• Now express Kp in terms of what we have.
• This can now be expresses in terms of a and p only

21
Calculating Equilibrium Composition
Thus, knowing Kp and the total pressure, we can
calculate the equilibrium composition of the
mixture.
22
Relative stability of Gases, Liquids, and Solids
23

• Common experience
• Low T favours solids
• High T favours gases
• Similarly for high and low pressure.
• Hear we study the conditions under which two (or
  even three) phases co-exist in equilibrium, at a
  given p and T.

24

• Phases Solid, liquid, gases.
• Gases exist in only one phase..

25

• Phases Solid, liquid, gases.
• Gases exist in only one phase..
• Liquids primarily also exist in only one phase..

26

• Phases Solid, liquid, gases.
• Gases exist in only one phase..
• Liquids primarily also exist in only one phase..
• Exception supercritical liquids

27

• Phases Solid, liquid, gases.
• Gases exist in only one phase..
• Liquids primarily also exist in only one phase..
• Exception supercritical liquids.
• Solids can exist in several phases.
• E.g., crystal structures..

28

• Water in a beaker, exists as a single phase.
• Water and ice in a beaker mixture of two
  distinct phases.

29
Conditions under which substances spontaneously
form S, L, or G

• Common experience
• T reduces from 300 to 250 K.
• Water (liquid) turns to ice (solid)
• T increases from 300 to 400 K
• Water turns to steam (gas)

30
Conditions under which substances spontaneously
form S, L, or G

• Solid CO2 at room temperature.
• Sublimes Turns from solid to gas, with out going
  through a liquid phase.

31
Conditions under which substances spontaneously
form S, L, or G

• What determines which phase is favoured (most
  thermodynamically stable) at a given p and T?
• What is the criterion for stability?

32
Conditions under which substances spontaneously
form S, L, or G

• The minimising of the Gibbs energy.
• For a pure substance,
• m chemical potential, n mole fraction,

33
Conditions under which substances spontaneously
form S, L, or G

• The minimising of the Gibbs energy.
• For a pure substance,

34
Conditions under which substances spontaneously
form S, L, or G

• As dm dGm,

35
Conditions under which substances spontaneously
form S, L, or G

• Thus, the variation of m with p and T can be
  determined.

36
Conditions under which substances spontaneously
form S, L, or G

• Sm and Vm are always positive, thus
• m decreases as T increases, and
• Increases with increasing p.

37
Conditions under which substances spontaneously
form S, L, or G

• The entropy varies slowly with T ( as ln T),
• Thus, over a limited T range,
• a plot of m v. T at const. p is a straight line
  of negative slope.

38
Conditions under which substances spontaneously
form S, L, or G

• We know from experience that melting and boiling
  are endothermic.
• Thus, DS DH/T is positive for both of these
  constant T processes.
• We also know that Gasses, liquids and solids all
  have positive heat capacities.

39
Conditions under which substances spontaneously
form S, L, or G

• Therefore,

40
Conditions under which substances spontaneously
form S, L, or G

• The entropy of a phase is the magnitude of the
  slope of
• m versus T.
• Recall

41
Conditions under which substances spontaneously
form S, L, or G

Thus, the functional relationship between m and T
for solids, liquids, and gasses (at a given p)
can be expressed graphically. The stable state
at any given T is the phase with the lowest m.
42
Conditions under which substances spontaneously
form S, L, or G

Start in the solid phase and increase
temperature. As T increases, m decreases with a
certain slope.. Note the slopes for liquid and
gas are greater. Therefore, they intersect. The
points of intersection of the solid/liquid and
the liquid/gas are the melting and boiling
temperatures, respectively.
43
Conditions under which substances spontaneously
form S, L, or G

At the melting point (solid/liquid intersection)
both phases exist in equilibrium. However, a
further, but small increase in T results in
complete melting. Why?
44
Conditions under which substances spontaneously
form S, L, or G

At the melting point (solid/liquid intersection)
both phases exist in equilibrium. However, a
further, but small increase in T results in
complete melting. Why? The Liquid phase has a
lower m at Tm dT than the solid phase.
45
Conditions under which substances spontaneously
form S, L, or G

At the melting point (solid/liquid intersection)
both phases exist in equilibrium. However, a
further, but small increase in T results in
complete melting. Why? The Liquid phase has a
lower m at Tm dT than the solid phase.
46
Conditions under which substances spontaneously
form S, L, or G

Similarly, at Tb both liquid and gas coexist at
eq. The system is a gas at T gt Tb.
47
Conditions under which substances spontaneously
form S, L, or G

Note the progression from solid to liquid to gas
cam be fully explained only by
and
48
Conditions under which substances spontaneously
form S, L, or G

What is we increase the temperature fast (too
fast)?.
49
Conditions under which substances spontaneously
form S, L, or G

What is we increase the temperature fast (too
fast)?. At a phase change, the system does not
reach equilibrium, leading to super heating.
50
Conditions under which substances spontaneously
form S, L, or G

What is we increase the temperature fast (too
fast)?. At a phase change, the system does not
reach equilibrium, leading to super heating
(bumping). Similarly, rapid cooling leads to
supercooling (e.g., glass formation).
51
Conditions under which substances spontaneously
form S, L, or G

What happens as a function of p at constant
T?
52
Conditions under which substances spontaneously
form S, L, or G

What happens as a function of p at constant
T?
53
Conditions under which substances spontaneously
form S, L, or G

What happens as a function of p at constant
T? Mostly, VmSolid lt VmLiquid ltlt VmGas
54
Conditions under which substances spontaneously
form S, L, or G

What happens as a function of p at constant
T? Mostly, VmSolid lt VmLiquid ltlt VmGas
Therefore, m versus T changes more rapidly.
55
Conditions under which substances spontaneously
form S, L, or G

Note Vmgas gtgt Vmliquid gtgt 0. Therefore,
increasing p leads to an increase in the boiling
point.
56
Conditions under which substances spontaneously
form S, L, or G

Note if Vmliquid gt Vmsolid Increasing p leads to
melting point elevation if Vmliquid lt
Vmsolid Increasing p leads to melting point
supression.