NAME:
SID:
Chem 135, Spring 2015, Problem Set 6
Due in class, Tuesday, April 7, 2015
Problem Set 6
Question 1. Provide a detailed, arrowpushing mechanism for the following transformations. These
concepts should be review from organic chemistry and are de
Chem 120B Spring 2013
Problem Set 7 Solutions
1. (a) The temperature of coexistence is a function of both p and x, T (p, x) = T0 (p) + T (p, x) where
T0 (p) is the coexisting temperature for pure liquid water. Use a Taylor series to express T as a
linear
Chemistry 120B Problem Set 4
due March 1, 2013
1. Einstein crystal. Albert Einstein pictured a low temperature crystal as if each atom was vibrating
independently of all the others, so that the net energy of a N atom microstate is
N
N
(x + y + z ) +
[x n
Chem 120B
Problem Set 7
Due: October 30, 2013
1. Salt water is plentiful on earth; natural supplies of fresh water, on the other hand, are dwindling while
mankinds demands grow. One appealing solution to this imbalance is to remove the salt from ocean
wat
CV\ew>
0
laOW
K T l
SWu"W*vis
IO/D^/XOIH
c ^
4 ^
o p*fc
'
R _ j V ^ e
^
CB")
"
q a .
l . 
AB
A</>
wUeve
TT
( 1 4 .
v

n
"X i s i U e .
e^sie.
lre&<juct^ov\ fay c o u u n t f * ^
S * .
i j v

2 f H 3
i
c
s i n e i
ts.
2C M
f
t
.
'
*
I
>

i 2
f i
l
Chem 120B Problem Set 11 Solutions
Chenlu Xie
November 30th, 2015
Problem 1
(i)
For a dilute solution, the osmotic pressure should be
= , = , =
M is the molecular weight of the enzyme, and is the solute mass density
=
And if the solution is an ideal d
Chem 120B Spring 2012
Problem Set 6 Solutions
1. Chemical potentials and particle density uctuations: the grand canonical ensemble.
(a) We can derive the probability either from the microcanonical (N, V, E ) or the canonical (N, V, T )
enssemble.
Microcan
YOUR NAME HERE
October 7, 2014
Chem 120B Midterm #1
Denitions and Useful Formulas:
Inverse temperature: = 1/kB T , kB = 1.38 1023 J/K
Boltzmann distribution and canonical partition functions:
eE
,
Q
P () =
Q=
PA
QA
=
PB
QB
eE ,
Equilibrium averages:
E =
Chem 120B
Problem Set 4
Due: October 2, 2013
1. In lecture, we considered the rotational and vibrational partition functions for an oxygen molecule at
room temperature. We considered the nature of the partition function to count accessible states.
(i) At
Chem120B
Problem Set 5
Due: October 2, 2015
1. Rotations about a covalent bond, such as the carboncarbon bond in ethane, are hindered by forces
between other chemical groups attached to the bonded atoms. The potential energy U due to these
forces typical
Chemistry 120B Problem Set 8
due April 17, 2013
k1
k2
k1
k2
1. Consider a threestate kinetic scheme 1 2 3. That is to say,
dc1
= k1 c1 + k1 c2
dt
dc2
= k1 c1 k1 c2 + k2 c3 k2 c2
dt
dc3
= k2 c3 + k2 c2
dt
where the net probability is normalized, c1 + c2 +
Chem 120B Problem Set 9 Solutions
Jon Weisberg
Nov 6, 2015
Problem 1
i)
We want to plot (0) = (0) (water) (0) (octanol) as a function of T for the six peptide solutes, as
well as (0) /T versus 1/T . Lets nd an expression for (0) that makes use of the give
Chem 120B Spring 2012
Problem Set 4 Solutions
1. Einstein Crystal
(a) Determine the average energy of the Einstein crystal as a function of N , temperature T , and the
fundamental frequencies x , y , and z .
Q = exp
N
(x + y + z )
2
nx1 =0
N
exp
nxN =0
Chemistry 120B Problem Set 7
due April 3, 2013
1. In this problem you will derive an expression for the eect of solute concentration on the temperature of
phase equilibrium, and then use what you have derived to predict the freezing temperature and boilin
Chem 120B Spring 2013
Problem Set 3 Solutions
1. Ideal Polymer Chain
Since M is xed through the entire process, note that the energy depends only on temperature. Because the equilibrated system starts and ends at the same temperature, we therefore know th
Problem Set 1 Solutions
Chem 120B, UC Berkeley
September 12, 2013
1. NL particles on the left side of the box, N particles total.
i
ii
iii
The number of particles is the same as the number of times each student ips his or her coin (like
we did in class),
#2
#3
#4
iii) In summary, the feature of a probability distribution that leads to large values of S is that the probability is spread out over a large range of values. This is consistent with the result from the next problem set, where it is deter
Chem120B
Problem Set 4
Due: February 22, 2008
1. Problems 1837, and 1839 in Simon and McQuarrie's Physical Chemistry. 2. Rotations about a covalent bond, such as the carboncarbon bond in ethane, are hindered by forces between other chemical gro
Chem 120B
1.
Problem Set 4 Solutions
Due: October 2, 2013
(i) At what temperature does the vibrational transition energy of O2 , 1580 cm1 , equal
kB T ? Wavenumbers (cm1 ) are used as a unit of energy, with conversion factor cm1 =
2 1023 J . Using this co
Chem 120B
Problem Set 1
Due: February 1, 2008
1. (i) Problem 166 in McQuarrie & Simon's Physical Chemistry textbook. (ii) Let N be the number of molecules contained in the ultrahigh vacuum chamber of Problem 166. How large are typical fluctuati
Chem 120B
PSET 1 solutions
1. (a) Knowing that the square of number is positive, so that hA2 i 0, we see that
hA2 i hAi2 0
= hA2 i hAi2
(b) More generally,
hABi = h(A hAi)(B hBi)i
= hABi hAihBi
(c) If A and B are statistically independent, then hABi = hAi
Chem 120B: Problem Set 9 Solutions
Layne Frechette
November 5, 2016
Problem 1
i) By definition,
sol (oct)
Nsol (oct)/Voct
Nsol (oct) Vwat
=
=
sol (wat)
Nsol (wat)/Vwat
Nsol (wat) Vcot
Also, we can rewrite the partition coefficient as:
Nsol (oct)/(Nsol (oc
Chem 120B
PSET 7 solutions
1. (a) When we push the membrane through the solution, we are reducing the volume available
to each particle. Thus there are less microstates available, and consequently the entropy
of the system decreases. This requires that we
Chem 120B
PSET 10 solutions
1. (a) Performing the Taylor expansion on ,
(T, p + p) (T, p) +
= (T, p) +
p
p
T
V
p
N
(b) The change in chemical potential relative to kB T , the thermal energy scale, is
V
p
N
1
18cm3
1m3
=
9atm 105 Pa/atm
NA kB 298K
mol
(
Problem Set 2 Solutions
Luning(Chris) Zhao
(Dated: September 9, 2016)
I.
QUESTION 1
(i)From Boltzmann distribution, we know that:
pup = e~B/2 ,
pdown = e~B/2
thus,
B
pup /pdown = eB = e kB T
(ii) With the two equations below,
B
pup /pdown = e kB T
pup + p
Chem 120B
PSET 4 solutions
1. (a) Here we just plug in appropriate values to evaluate the energy constant:
(6.626x1034 kg m2 /s)2
h2
=
8mL2
kB (298K)8(1m2 )(4x103 kg/mol)NA1
2x1021
The spacing between states is extremely small.
(b) See table below.
n
1
2
Chem 120B: Problem Set 8 Solutions
Luning(Chris) Zhao
(Dated: October 22, 2016)
I.
PROBLEM 1
(i) The Boltzmanns definition of entropy is
S = kB lnW
Since at 0K, the multiplicity of system is 1 (ground state) provided that the ground state is
not degenerat
Chem 120B: Problem Set 5 Solutions
Luning(Chris) Zhao
(Dated: October 1, 2016)
I.
PROBLEM 1
(i) For every molecule, there are 6 translational degrees of freedom: x, y, x, vx , vy , vz .
Molecules with no specific symmetry have 3 rotational degrees of free