Lecture 3.pdf-Thermochemistry State func...
Lecture_3.pdf-Thermochemistry State functions & exact differentials
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Lecture 3.pdf-Thermochemistry State functions & ex...
Lecture_3.pdf-Thermochemistry State functions & exact differentials
Lecture 3.pdf-Thermochemistry State...
Lecture_3.pdf-Thermochemistry State functions & exact differentials
Page 18
Temperature dependence of reaction enthalpies
(Kirchoff’s Law)
Seen before :
H = C
p
T
(at constant p)
Thus if a substance is heated from T
1
to T
2
:
H(T
2
) = H(T
1
)
Assuming no phase transition takes place in the T range of interest
As this equation applies to each substance in the reaction, we may
write it in terms of the reaction enthalpy
r
H
o
(T
2
)=
r
H
o
(T
1
)
Where


Page 19
Example with Kirchoff’s Law
H
2
(g) +
½
O
2
(g)
H
2
O (g)
f
H
o
for H
2
O (g) at 298 K is -241.83 kJ mol
-1
Estimate its values at
100
°
C, given the following values of the molar heat capacities
at
constant p:
H
2
O(g): 33.85 JK-1mol-1
H
2
(g) : 28,82 JK
-1
mol-1
O
2
(g) : 29.36 JK
-1
mol-1
Assuming the C
p
’s are independent of T, the integral
becomes simply
And thus
:
r
H
o
(T
2
) =
r
H
o
(T
1
)
+


Page 20
State functions & exact differentials
U and H are state functions
Value depends only on current state,
independent of history
Heating and work done in preparing a state
are path functions
Amount of q and w needed to prepare a state
are path dependent


Page 21
Exact & inexact differentials
In going from state i to state f, change in U is :
Where dU is an exact differential, an infinitesimal quantity that,
when integrated, gives a result that is independent of the path
taken to go between i and f
Considering the heat used to go from i to f, we write :
Note : we write q and not
q, since q is not a property of the
system; in some textbook, the inexact differential is shown as
dq


Page 22
Changes in internal energy (U)
For a closed system of fixed composition
U is a function of p, V and T; because it is a
function of state, stating the values of 2 of the
variables fixes the value of the third variable
Expressing U as a function of V and T, we may
write:
We recognize the term
as C
V
The other term
(called internal pressure)
Thus dU =


Page 23
Road map
(previous edition only)
Error : w = +C
v
T


Page 24
Suggested exercises & problems
9
th
Edition:
Exercises : 2.19(a); 2.24(a); 2.27(a)
Problems : 2.11; 2.17; 2.44
10
th
Edition:
Exercises : 2C.3(a); 2C.7(a); 2C.8(a)
Problems : 2C.6; 2C.9; 2D.1


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