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April 7, 2010
Chem 120B Midterm #2
Defnitions and UseFul ±ormulas:
Inverse temperature:
β
=
1
k
B
T
,k
B
=1
.
38
×
10

23
J
/
K
±irst law oF thermodynamics:
dE
=
TdS

pdV
+
±
i
μ
i
dN
i
Entropy and the second law:
S
=
k
B
ln
W,
S
=

k
B
±
ν
P
(
ν
)ln
P
(
ν
)
,d
S
=
¯
dq
rev
T
≥
¯
dq
T
(Δ
S
)
E,V,N
≥
0
,
(Δ
A
)
T,V,N
≤
0
,
(Δ
G
)
T,p,N
≤
0
±unctions oF state:
H
=
E
+
pV,
A
=
E

TS,
G
=
H

TS
ClausiusClapeyron equation:
dp
dT
=
Δ
s
Δ
v
Intensive variables:
sdT

vdp
+
±
i
x
i
dμ
i
=0
,x
i
=
N
j
N
Chemical potential:
μ
i
=
μ
(0)
i
(
T,p
)+
k
B
T
ln
x
i
Colligative properties:
Δ
T
b
=
k
B
T
*
b
Δ
s
x
sol
,β
π
=
x
sol
ρ
=
ρ
sol
1
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View Full DocumentQuestions on this exam concern dilute amphiphilic moleculesin(andatthe
surface of) aqueous solutions. One such molecule (denoted “A” for “amphiphile”),
consisting of a polar head and a nonpolar tail, is sketched below.
polar head
nonpolar tail
A =
1. These amphiphilic solutes can shield their hydrophobic tails from solvent by forming
micelles, roughly spherical clusters of solutes whose head groups point outward
toward solvent.
micelle (cross section)
A
n
=
Each micelle (denoted A
n
)ismadeupo
f
n
amphiphile molecules. We will not
specify a value for
n
,excepttosaythatitismuchgreaterthanone
.
Let
μ
1
be the chemical potential of an individual amphiphile A that is well
separated from other solutes. Let
μ
n
be the chemical potential of an entire micelle
A
n
.S
im
i
l
a
r
ly
,w
ew
i
l
ld
en
o
t
eth
enumb
e
ro
fun
a
s
s
o
c
i
a
t
edamph
iphiles per unit
volume as
ρ
1
,andthenumbero
fm
ice
l
lesperun
itvo
lumeas
ρ
n
.F
ina
l
,l
e
t
N
be
the total number of amphiphiles (including those in micelles), so that
c
=
N/V
=
ρ
1
+
nρ
n
is their total concentration.
Temperature
T
and pressure
p
will be ±xed throughout this problem.
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 Spring '09
 JAMESAMES
 Physical chemistry, Thermodynamics, pH, Entropy, pts, chemical potential

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