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Relationship between
Δ
r
Gº,
Δ
r
G, Q, and K
Fill in the blanks and boxes!!
At constant P and T and w
e
=0, dG is a criterion of spontaneity and dG =
(
Eqn 1
)
μ
ii
i
N
dn
=
∑
1
and for calculating
Δ
G or dG, we take G =
.
μ
i
N
n
=
∑
1
Consider the balanced chemical reaction at some arbitrary composition
a
A
+
b
B
⇔
cC +
dD
initial # of moles
n
A
n
B
n
C
n
D
infinitesimal change dn
A
dn
B
dn
C
dn
D
(if all dn
i
are positive)
d
ξ
=
dn
a
A
=
dn
b
B
=
dn
c
C
=
From
Eqn 1
, initial G = G
i
=
Final G = G
f
=
μ
A
(n
A
ad
ξ
) +
μ
B
(n
B
bd
ξ
)
+
μ
C
(n
C
+cd
ξ
) +
μ
D
(n
D
+dd
ξ
)
From the previous two equations
dG = G
f
 G
i
=
= d
ξ
(a
μ
A
b
μ
B
+ c
μ
C
+
d
μ
D
)
We can rewrite the equation above as
Δ
r
G =
∂
∂ξ
G
TP
⎛
⎝
⎜
⎞
⎠
⎟
,
= (a
μ
A
b
μ
B
+ c
μ
C
+
d
μ
D
)
=
(
c
μ
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 Spring '08
 OHRN
 Physical chemistry, pH

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