CBE 102B
Problem Set 1
Due: Monday, April 16, 2012
1. (60 pts.)
[ABET]
Consider a fluid that obeys the van der Waals equation of state
RT
1
p=
a 2 ,
Vm b
Vm
where Vm is the molar volume. For this fluid, U m , CVm , H m , S m , Am and Gm can be expressed
i
PP1
CBE 102B
Practice Problems 1
Do Not Submit
A generalized homogeneous function has the following property:
1.
(
)
f p1 x1 , p2 x2 , , pn xn = m f ( x1 , x2 , , xn )
Show that Eulers theorem is
n
p
j =1
j
xj
f
= m f ( x1 , x2 , , xn ) .
x j
One mole of
PP3
CBE 102B
Do Not Submit
Practice Problems 3
1.
The thermal expansion coefficient of a condensed phase is usually expressed as a power
series in temperature:
p =
1 Vm
= 0 + 1T + 2 T 2 +
Vm T p
Show that the molar volume can be expressed as a function o
PP4
CBE 102B
Practice Problems 4
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One mole of an ideal gas with constant heat capacities undergoes an adiabatic and reversible
process. This process can be described by the following equations:
pVmx = const.
T Vmy = const.
T p z = const. Find
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CBE 102B
1.
Do Not Submit
Practice Problems 2
Consider the function z = z ( x, y ) . The differential of z is given by
z
z
dz = dx + dy = f ( x, y )dx + g ( x, y ) dy .
x y
y x
Show that
( z, w )
( , )
=f
( x, w )
( , )
+g
( y, w )
( , )
w
PP5
CBE 102B
Do Not Submit
Practice Problems 5
Consider the functions H, A, G, J, and Y of a pure-component system. Derive the Euler
form of these functions. Using the Euler form of U ( U = T S p V + n ), show that the Euler
form of these functions is con
PP6
CBE 102B
Practice Problems 6
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For the ideal-gas reaction 2 A(g) + B(g)
C(g) + D(g) , K p = 6.51 at
T = 800 K . The initial mixture contains 3 moles of A, 1 mole of B, and 4 moles of C in a
container of volume V = 8000 cm3 . Find the mixtu
PP8
CBE 102B
Practice Problems 8
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For the following cases, find the number of independent intensive variables, f,
required to describe the state of the system and suggest an appropriate set:
(a)
Aqueous solution of H3PO4.
(b)
Aqueous solution
PP7
CBE 102B
Practice Problems 7
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A mixture initially consists of 2 mole of CH 4 ( g ) and 3 mole of H 2 O ( g ) . When
equilibrium is established at 1000 K and 1 bar, the mixture is found to contain CH 4 ( g ) ,
H 2 O ( g ) , CO ( g ) , CO 2
PP9
CBE 102B
Practice Problems 9
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1.
B(g) . The standard state chemical
Consider the ideal gas reaction A(g)
0
potentials of pure A and B are [A(g)] = 50 kJ/mole and 0 [ B(g) ] = 45 kJ/mole at
298.15 K. For a reaction starting with 1 mole of
PP10
CBE 102B
Practice Problems 10
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Let A=benzene and B=toluene. At T = 20 o C , the vapor pressures of benzene
and toluene are p = 74.7 torr and pB = 22.3 torr . Find the partial pressures of benzene
A
and toluene above a liquid solution of
PP12
CBE 102B
Practice Problems 12
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Let A=chloroform and B=ethanol. At T = 35 o C , the vapor pressures of the pure
liquids are p = 295.1 torr and pB = 102.8 torr . The vapor pressure of a liquid solution
A
of chloroform and ethanol with xB =
PP13
CBE 102B
Practice Problems 13
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For the reaction Fe3O 4 (s) + CO(g)
3 FeO(s) + CO 2 (g) K a = 1.15 at
o
T = 600 C . The initial numbers of moles are:
n(Fe3O 4 ) = 2 n(CO) = 3 n(FeO) = 4 n(CO 2 ) = 5 .
Find the number of moles at equilibri
PP11
CBE 102B
Practice Problems 11
Do Not Submit
The colligative molality in a typical biological cell is mB = 0.3 mole/kg H 2 O .
Estimate the osmotic pressure in a biological cell at T = 37 o C . The density of water at
T = 37 o C is = 0.9933 g/cm3 .
1.
CBE 102B
Problem Set 2
Due: Monday, April 23, 2012
1. (35 pts.)
For a closed system (n=fixed) use the differential expressions for Um, Hm, Am, and
Gm, Maxwell relations, and derivative reduction calculus, to prove the following relations:
U
(a) m = C pm
CBE 102B
Problem Set 3
Due: Monday, April 30, 2012
1. (30 pts.) A function f = f ( x, y ) is concave when the eigenvalues 1 and 2 of the matrix
of 2nd derivatives are both negative. Use this result to show that the necessary and sufficient
conditions for
CBE 1028 Problem Set 2 Due: Friday, April 16, 2010
1. (12 pts.) [ABET] Consider a uid that obeys the van der Waals equation of state
* RT _a1
p Vnb V
where Vm is the molar volume. For this uid, Am, Jm, G
m, and Ym can be expressed in the
following f
CBE 102B Problem Set 6 [ABET] Due: Wednesday, May 19, 2010
For a uid that obeys the van der Waals equation of state
RT 1
_a 7
V b V;
m
p:
7
we found the following expressions for the functions Um , H m , Sm , Am, and ,u = Gm
l
Um (VmaT)=Ufn(T) 7
CBE 102B Problem Set 3 Due: Friday, April 23, 2010
1. (15 pts.) A function f = f (x, y) is concave when the eigenvalues 21 and 32 of the matrix
of 2nd derivatives are both negative. Use this result to Show that the necessary and sufcient
conditions for
CBE 102B Problem Set 5 Due: Friday, May 7 2010
1. (15 pts.) A system contains C, C0, C02, H2, and H20 in chemical equilibrium. Find the
number of independent reactions, R, and suggest stoichiometric coefficients vj.
2. (15 pts.) According to the Debye t
CBE 102B Problem Set 8 [ABET] Due: Friday, June 4, 2010
1. (14 pts.) One mole of liquid benzene is mixed with two moles of liquid toluene. At 20 0C,
the vapor pressures of benzene and toluene are 51.3 and 18.5 kPa, respectively. As the pressure
is reduc
CBE 102B Problem Set 7 Due: Wednesday, May 26, 2010
1. (30 pts.) Consider a liquid solution of water (A) and methanol (B) at T=25C and
atmospheric pressure. The following data are available for the mean molar volume
V m3 / mole) of the solution as a lncti
CBE 102B Problem Set 1 [ABET] Due: Friday, April 9, 2010
W
1. (40 pts.) Consider a uid that obeys the van der Waals equation of state
RT 1
Vin b VIII-1
where V is the molar volume. For this uid, U
m m 9
the following form
Usz (V T)=U<)(T)+(V,T)
m m 3 m
CBE 102B SPRING 2012
NAME:
1. (12 pts.) At 1 atm, liquid water has its maximum density at 4 °C. Using this information,
deduce as to how the molar entropy, Sm = Sm (p, T), of liquid water varies with pressure at xed
temperature T = 3 °C, 4 °C, an