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. '
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2. A ct- B CU-plUAp .
. 3. AB pru.ip
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L/. Wne() A cli.s:1ppears pa.-fh cuts across-Jh!. A6
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MATLS 3C04 Test 5 DM's soluitions
Problem 1 (30 marks)
Use the Ellingham diagram and find:
a. The dissociation pressure of CoO at 1000C 2 1012
b. The equilibrium constant for the reaction of formation of SiO2 at 800C 3 1033
c. The CO/CO2 ratio in equilibr

MATLS 3C04 Test 6 DM's solutions
Problem 1 (5 marks)
Inspect an isothermal section of the ternary system ABC shown in Figure 1. What are possible
numbers of phases?
Solution of Problem 1
Either 1 or 3.
B
B
a
C
A
C
A
Figure 1
Figure 2
Problem 2 (20 marks)

DMs solutions of Test 1 problems
Problem 1
U Mga cos m2 gl sin m1 gl sin Mga cos m gl sin
m2 m1
U g Ma sin ml cos
0
two-sided, becuase
the balance can swing
Since is an independent variation, the following must be satisfied
Ma sin ml cos 0 tan eq
ml
Ma

MATLS 3C04 Test 3
4 regular problems, 1 bonus problem, 2 pages
Problem 1 (20 marks)
A predominance diagram for pure Fe at 105 Pa is given in Figure 1; L designates liquid.
BCC
FCC
1184.80
1667.50
T, K
L
BCC
1811.00
Figure 1
Identify correct and erroneous

MATLS 3C04 Test 4 DM's solutions
Problem 1 (30 marks)
Inspect Figure 1 and Table 1.
Establish a correspondence between the monovariant lines labeled with the letters in
Figure 1 and the reactions labeled with the numbers in Table 1 (you might want to use

MATLS 3C04 Test 1
Problem 1 (40 marks)
A schematic of an unloaded mechanical balance is shown in Figure 1. After the left and right
beams are loaded with masses m2 and m1 , correspondingly, the equilibrium configuration shown
in Figure 2 is eventually att

Dmitri Digitally signed
by Dmitri V.
Malakhov
V.
DN: cn=Dmitri
Malakh V. Malakhov
Date: 2015.09.30
09:00:55 -04'00'
ov
MATLS 3C04 Test 2
4 regular problems, 1 bonus problem, 2 pages
Problem 1 (20 marks)
Is a fragment of a P T diagram of a unary system sho

MATLS 3C04 Test 2
4 regular problems, 1 bonus problem, 2 pages
Problem 1 (20 marks)
Is a fragment of a P T diagram of a unary system shown in Figure 1 thermodynamically
possible? If it is not, then identify an erroneous feature.
P
T
Figure 1
Problem 2 (10

Solutions of Assignment 2 problems
Problem 1 (20 marks)
Consider a gas mixture with the following constituents: H2, H2O, O2, SiO, SiH4 and Si.
1. Decide what the components are and then construct all independent reaction;
2. Construct all independent reac

Chemical potential of a component in a multicomponent
system
Notations
K number of components in the system, K 2
ni number of moles of component i in the system
K
N ni a total number of moles of components. Let us notice that
i 1
N
n1 nK 1, p
n p n p
G n

MATLS 3C04 Thermodynamics of multicomponent systems
Solutions of Assignment 5 problems
Consider a ternary 123 system, in which only the liquid phase exists. The excess Gibbs energy
of the liquid phase is described by the following expression:
G ex 5000 x1

MATLS 3C04 Thermodynamics of multicomponent systems
Test 2
Problem 1 (40 marks)
Inspect Figure 1 and Table 1. Establish a correspondence between the monovariant lines labeled with the
letters and the reactions labeled with the numbers (you might want to u

CHAPTER 10
Ternary Phase Diagrams.
Four-Phase Equilibrium
A maximum of four phases may co-exist in a ternary system. The four-phase equilibria involve
the transformation of one phase or an interaction between two or three phases (p. 119), for
example:
I ‘

MATLS 3C04 Test 3 DMs solutions
Solution of Problem 1 (20 marks)
A predominance diagram for pure Fe at 105 Pa is given in Figure 1; L designates liquid.
BCC
FCC
1184.80
1667.50
T, K
L
BCC
1811.00
Figure 1
Identify correct and erroneous statements below. T

CHAPTER 10
Ternary Phase Diagrams.
Four-Phase Equilibrium
A maximum of four phases may co-exist in a ternary system. The four-phase equilibria involve
the transformation of one phase or an interaction between two or three phases (p. 119), for
example:
1 7

QUIZ 1
Sept 25, 2013
No aids permitted. Use a blank sheet of paper. Use a pen, not pencil. Any calculator is
acceptable, provided you are not communicating or using stored data. Time: 25 min.
_
G = H TS
G = -RT ln K
dG = -SdT + VdP
(dG/dT)P = -S
R = 8.314

It is known that both A and B are oxidized in an oxygen-containing environment.
A (pure) 1 O 2 AO
2
(1)
Since A is oxidized
1
1
G1 G10 RT ln pO1 2 0 RT ln pO2 G10 RT ln pO2 G10
2
2
2
B (pure) 1 O 2 BO
2
Since B is oxidized
1
1
0
0
0
G2 G2 RT ln pO1 2 0 RT

1
M O 2 MO
2
(1)
1
G1 G10 RT ln pO1 2 G10 RT ln pO2
2
2
Metal is not oxidized if the following condition (let us name it condition A) is satisfied
RT ln pO2 2G10
M O MO
(2)
0
0
G2 G2 RT ln pO1 G2 RT ln pO
Metal is not oxidized if following condition (let

How to find independent reactions?
E i i -th element, i 1, , s
B j j -th constituent of the gas phase, j 1, , c
A chemical formula of B j can be presented as E1
1j
E 2
2j
E s where ij is a number of
sj
moles of the component i in one mole of the speci

Oxidation of an alloy leading to the formation
of a mixed oxide
A1 x B x O 2 A1 y B y ABO 2
phase L
(1)
phase
phase L
A value of is unknown, but it is known that
0 min x, y 1
(2)
Let us express , and y through x and .
1 x 1 y
x
, 1 2 , y
x y
1 2
2

How to construct thermochemical cycles?
H 2 O 2 H 2 2H 2 O
(1)
H 2 1 O2 H 2O
2
(2)
H 2 O2 H 2O2
(3)
H 2O 1 O2 H 2O2
2
(4)
Imagine that G0 is unknown. Can standard Gibbs energies of reactions (2)(4) be used to
1
calculate G0 and, if they can be, then how s

Oxidation of silver in AuAg alloy
Au1 x Ag x O 2 Au1 y Ag y Ag 2 O
(1)
is an arbitrarily taken tiny positive number.
Since numbers of moles of gold, silver and oxygen are preserved, we have
1 x 1 y
x y 2
2
(2)
From (2) we find 2 , 1 2 and y x 2 1 2 .

Let elements E1 , E 2 , , E K be old components 1, 2, , K . Chemical potentials of the
components are
G
i
, i 1, , K
ni T , P ,n
i
where ni is a number of moles of the i th old component.
K
dG i dni
(1)
i 1
Let B1 , B2 , , BM be new components. Chemic

Let us consider a ternary system M O S at constant temperature. The gas phase, which is free
of M-containing species, always exists.
f 3 2 5
Since T const
f 4
Four pure substances, namely M, M 2 O, MS and M 2SO 4 , may exist in the system. Let us number
t

Van 't Hoff equation
0
RT ln K GT
ln K
0
GT
RT
0
dGT
0
T GT 1
0
0
0
0
0
T ST GT GT T ST
d ln K
1 d GT
1 dT
dT
R dT T
R
T2
RT 2
RT 2
0
0
0
0
0
0
GT H T T ST H T GT T ST
0
d ln K H T
dT
RT 2
0
T 2 d ln K H T
R
dT
0
d ln K H T
dT
R
2
T
0
d ln K
H T
R
d

lb
410 [xva‘ 1
ASSOCIATED SOLUTIONS
containing molecules which have considerable electric charges near the
surface of the molecule, such as in molecules containing the groups
NHZ, OH, ; we call solutions of molecules of this kind associated
solutions.
2.

Pressure inside a spherical droplet
This is a system we are interested in. The system contains one component only.
Since we have a feeling that pressures in phases and may be different, we dont want to use
the Gibbs energy in the Gibbs criterion of equili