06-607
Physical Chemistry of Colloids & Surfaces
Spring, 2014
Key to Exam #1
1a.) The diffusion of a rigid sphere can be calculated from the Stokes-Einstein equation:
23 J
1.381 10
298K
kT
m2
K
5.04 1014
D
6a
s
9.7 106 m
6 0.893 103 Pa-s
2
1b.) The

06-607
Phys. Chem. of Colloids & Surfaces
Spring, 2014
Homework Set #8
Q
1.) Consider a dipole as two equal but opposite charges (+q
and -q) separated by a distance l. The magnitude of the
dipole moment is ql.
a.
Use Coulomb's law to show that the energy

06-607
Phys. Chem. of Colloids & Surfaces
Spring, 2014
Key to Homework #5
1.) Berg Chapter 2, Prob. 5
Rotating the given ellipse around the
x-axis generates the ellipsoid
2
2
equator
apex
2
x y z
1
a b b
b
The terms apex and equator are
somewhat ambiguou

06-607
Phys. Chem. of Colloids & Surfaces
Spring, 2014
Key to Homework #4
1a.) The pressure inside the larger bubble is
Pa P
2
Ra
while the pressure inside the smaller bubble is
Pb P
2
Rb
The difference between these two pressures is the pressure drop a

06-607
Physical Chemistry of Colloids & Surfaces
Spring, 2014
Key to Exam #2
1a.) The spherical shape has the lowest surface area per unit volume of any geometric shape.
For a given volume of bubble, the spherical shape will minimize the contribution of
s

06-607
Physical Chemistry of Colloids & Surfaces
Spring, 2014
Key to Exam #3
1a.) Hamakers theory simply adds up the pairwise interactions between atoms (one in each
body), ignoring the presence of all other atoms. In sharp contrast, Lifshitz theory treat

06-607
Phys. Chem. of Colloids & Surfaces
Key to Homework #6
1a.)
1b.)
1c.)
Page 1 of 14
Spring, 2014
06-607
Key to Homework #6
Spring, 2014
1d.)
2.) Hiemenz, Chapter 7, Prob. 6
The data is plotted in the graph below.
30
y=2.7864x2 44.216x 140.19
25
20
Su

06-607
Phys. Chem. of Colloids & Surfaces
Spring, 2014
Key to Homework #7
= (8kT/3)-1
1.) Defining
and using a prime (') to denote time differentiation, Smoluchowski's kinetics of
flocculation can be written as:
ck 1
i k 1
ci ck i cck
2
i 1
Expanding th

06-607
Phys. Chem. of Colloids & Surfaces
Key to Homework #9
1.)
Page 1 of 13
Spring, 2014
06-607
Key to Homework #9
= 0.0135 coul/m2
Page 2 of 13
Spring, 2014
06-607
Key to Homework #9
Spring, 2014
Note that 1 coul/V = 1 farad is the SI unit for capacita

06-607
Phys. Chem. of Colloids & Surfaces
Spring, 2014
Key to Homework #11
1.) Berg Chapt. 7, Prob. 4
The potential energy profile between two spheres of radii a is given by (7.80):
A a 64an kT 2
S0 212
exp S0
12 S0
2
(1)
ze
tanh
4kT
where
The c

06-607
Phys. Chem. of Colloids & Surfaces
Spring, 2014
Key to Homework #10
NOTE: Problems #1 - #4 of this assignment were taken from an older one in which the
nonrationalized value of was employed. To convert, in this solution should be
replaced by 4.
1a.

06-607
Phys. Chem. of Colloids & Surfaces
Spring, 2014
Key to Homework #3
1a.) In spherical coordinates, the Laplacian is given by:
2
1 2
1
r
2
sin
r r sin
r 2 r
(1)
The proposed solution to this P.D.E. has the form
(r,) = f(r)cos
After cance

06-607
Phys. Chem. of Colloids & Surfaces
Spring, 2014
Key to Homework #2
1a.) Substituting N = 0, we obtain
N = 0:
1
m m
P m, 0 !
!
2 2
0
if m even
if m odd
From this formula, we can easily deduce that P(0,0) = 1 and P(1,0) = P(-1,0) = 0. Larger
value