4-9. A three component liquid mixture flows in a pipe with a mass averaged velocity of 0.9 m/s.
The density of the mixture is = 850 Kg/m3. The components of the mixture and their mixture
and their molar fractions are: n-pentane, xP = 0.2, benzene, xB = 0.
4-23. A complex mixture of aromatic compounds leaves a chemical reactor and is fed to a
distillation column. The mass fractions and flow rates of distillate and bottoms streams are given
in Table 4.23. Compute the molar flow rate and composition, in molar
4-14. Derive Eq. 4-81 given that either v n or A is constant over the area of the exit.
4-14. It was suggested in the text that Eq. 4-81
B= N
A = m A
(1)
mB
B =1
was valid when either v n or A is constant over the area of an exit (or an entrance).
To exp
4-13. Use Eq. 4-77 to prove Eq.4-78.
4-13. Given Eq. 4-77
MA
= xA M
(1)
we sum over all N species to obtain
A= N
MA
= x A M + xB M + xC M + . + xN M
A=1
(2)
=
[ xA
+ xB + xC + . + xN ] M
At any point, the mole fractions are constrained by
x A + xB + xC +
4-12. Show that Eq. 4-77 results from Eq. 4-76 when either cv n or x A is constant over the area
of the exit.
4-12. We begin this problem with Eq. 4-77
MA
=
x A c v n dA
(1)
Aexit
and consider the case for which c A v n is a constant. For this case, Eq. 1
4-11. A flash unit is used to separate vapor and liquid streams from a liquid stream by lowering its
pressure before it enters the flash unit. The feed stream is pure liquid water and its mass flow rate
is 1000 kg/hr. Twenty percent (by weight) of the fee
4-7.Develop a representation for the mole fraction of species A in an N-component system in
terms of the mass fractions and molecular masses of the species. Use the result to prove that the
mass fractions and mole fractions in a binary system are equal wh
4-3. A gas mixture contains the following quantities per cubic meter of carbon monoxide, carbon dioxide and hydrogen: carbon monoxide, 0.5 moles/m3, carbon dioxide, 0.5 moles/m3, and hydrogen, 0.6 moles/m3. Determine the species mass density and mass frac
4-1. Determine the mass density, , for the mixing process illustrated in Figure 4-1.
4-1. The mixing process illustrated in Figure 4-1 is a batch process in which the mass of each species is conserved. We express this idea as o V A A = AV , o VB B = BV ,
Problem 2-17
Given the following 33 matrices i -3 5 -4 j j j 1 9 A= j 6 j j k 4 -3 2 y z z z z z z cfw_ i 2 -1 3 y j z j z j 2 5z z B= j 1 j z j z k -3 -5 2 cfw_
determine A+B and A-3B
Solution
If Aij is the element in the ith row and jth column of A , a
2-11. In the literature you have found an empirical equation for the pressure drop in a column packed with a particular type of particle. The pressure drop is given by the dimensionally incorrect equation
0.15 H 0.85 v1.85 p = 4.7 d 1.2 p
which requires
2-9. A liquid has a specific gravity of 0.865. What is the density of the liquid at 20 C in the following units: (a) kg/m3 (b) lbm/ft3 (c) g/cm3 (d) kg/lt
2-9. Specific gravity is the ratio of the density of the liquid with respect to the density of water
2-9. A liquid has a specific gravity of 0.865. What is the density of the liquid at 20 C in the following units: (a) kg/m3 (b) lbm/ft3 (c) g/cm3 (d) kg/lt
2-9. Specific gravity is the ratio of the density of the liquid with respect to the density of water
2-3. The density of a gas mixture is = 1.3 kg/m3. Calculate the density of the gas mixture in the following list of units: (a) lbm/ft3 (b) g/cm3 (c) g/lt (d) lbm/in3
2-3. Parts (a) and (b) can be determined directly in terms of the conversion factors list
2-1. Convert the following quantities as indicated: a) 5000 cal to Btu b) 5000 cal to watt-sec c) 5000 cal to newton-meter
2-1. The solution requires the simple use of conversion factors that are contained in
5000 cal = 5000 cal cfw_1 1 Btu = 5000 cal 252
4-15. Prove Eq.4-84.
4-15. In order to prove the relation
A= N
xA b
=1
(1)
A=1
we begin with the definition of the bulk mole fraction at an exit which is given by
xA b
=
x A v n dA
Aexit
(2)
v n dA
Aexit
Since the volumetric flow rate is given by
Q=
v n
5-1. Show that the mole fraction in an ideal gas mixture can be expressed as y A = p A p .
5-1. The equation of state for an ideal gas mixture is given by
pA V
= n A RT ,
A = 1, 2, .N
(1)
for the individual species and by
pV
= nRT
(2)
If we divide Eq. 1 b
5-4. Determine the vapor pressure, in Pascal, of ethyl ether at 25 C and at 30 C. Estimate the heat
of vaporization of ethyl ether using these two vapor pressures and the Clausius-Clapeyron
equation.
5-4. The vapor pressure is given by the Antoines equati
6-11. The production of alumina, NaAlO 2 , from bauxite, Al ( OH )3 , requires sodium hydroxide
as a reactant and yields water as product. For this system, determine the ratio of reaction rates
given by
RAl(OH)3
RNaAlO2
RH 2O
RNaOH
,
RNaAlO2
,
RNaAlO2
6-1
6-10. Methanol can be synthesized by reacting carbon mono xide and hydrogen over a catalyst.
The r ate of production of methanol at 400 K is of rCH3OH = 0.035 kg/m3s . D etermine th e r ate of
production in mo l/m3s for all componen ts of th e synth esis
6-9. Use the chemical composition matrix determined in Pro blem 6-2 and the r eaction rates found
in Problem 6-8a, to prove th at atomic sp ecies are n either cr eated nor destroyed by th is ch emical
reaction .
6-9. A visual illustration of the chemical
3-7. According to the problem, the volume of the horizontal cylindrical tank is given by:
V = L R2 L R2 ( sin ) 2
(1)
where is a function of time. If we try to calculate the value of h (high) with this definition of variables, we have:
h = R + R cos( ) 2
4-5. A mixture of gases contains one kilogram of each of the following species: methane, ethane, propane, carbon dioxide, nitrogen. Calculate the following: 1. The mole fraction of each species in the mixture 2. The average molecular mass of the mixture
4
2-19. Write an expression for the volume per unit mass, V , as a function of the molar volume, V , (that is the volume per mole) and the molecular weight, MW. Write an expression for the molar volume, V , as a function of the density of the component, ,
2-14. Energy is sometimes expressed as v 2 / 2 g although this term does not have the units of energy. What are the units of this term and why would it be used to represent energy? Think about the fact that gh represents the gravitational potential energy
2-5. A revolution represents 360 or 2 radians, thus the conversion factor that we need can be expressed as
1 rev = 360
o
o
= 2 radians
Use of this result leads to
1 rev/min = rev min 2 rad min = 0.1047 rad/s 60 s rev
2-4. The cgs system of units is commonly used in science. What is the unit of force in the cgs system? Find the conversion factor from this unit and a Newton. Find the conversion factor between this unit and a lbf.
2-4. The letters c-g-s represent centime
Problem 7-11
Metallic silver may be obtained from sulfide ores by roasting to sulfates, leaching with water, and precipitating the
silver with copper. It is this latter process, involving the chemical reaction
Ag2 SO4 + Cu2Ag + CuS04
that we wish to cons
Problem 7-3 . Carbon is burned in air with all the carbon oxidized to CO2 . Calculate the flue gas composition
when the percent of excess air is 0.50, 100. The percent of excess air (PEA) is defined as
molar flow rate
molar flow rate of consumption
J
N-J