CHE 304 (Spring 2007) ______
LAST NAME, FIRST
Quiz #1
Note: Your answers must be correct to 3 significant figures and have the appropriate units.
I. For the gas phase reaction 2A + BC + 3D
The reaction is reversible at constant temperature and pressure. The feed is two moles of A per one mole of B.
1. Write the concentration of A in term of CA0 and X.______
CA =
2. Write the concentration of C in term of CA0 and X.______
CC =
II The irreversible elementary reaction 2A B takes place in the gas phase in an isothermal tubular reactor. The feed is two moles of A per one mole of C, an inert. The entering temperature and pressure are 427oC and 10 atm, respectively. Gas constant R = 0.082 atmL/moloK.
3. Determinethe concentration of A at the entrance to the reactor.______
CA0 = 0.116 mol/L
4. IfCA0 = 1.0 mol/L, the concentration of A at 90% conversion of A is______
CA = 0.143 mol/L
III. (5) Hydrogen gas is fed to a burner, where it is combusted with 300% excess air (21% O2). Moles of nitrogen required for each mole of hydrogen is
______
H2 + 0.5O2 H2O
Moles of nitrogen = 7.52 moles
IV. The chemical species A is known to decompose according to
A(g) = B(g) + C(g)
A rigid container is filled with pure gaseous A at 300oK and 760 mmHg and then heated. Assume ideal-gas behavior and chemical equilibrium.
(6) Ifthe pressure was observed to be 1610 mmHg at 510oK, the mole fraction of A is
yA = 0.605
(7) If the fractional conversion of A is 0.50 at 650oK, determine the pressure of the reactor.
P = 2470 mmHg
V. (8)The irreversible first order reaction AB is carried out in a tubular reactor in which the volumetric flow rate Q is constant. Determine the reactor volume necessary to reduce the exiting concentration to 5% of the entering concentration when the volumetric flow rate is 30 liters/min and the specific rate constant, k, is 0.20 min-1.
V = 449 liters
VI. The exothermic reaction
A B + C
was carried out adiabatically and the following data are given:
The entering molar flow rate of A was 400 mol/min.
9) The volume of a CSTR required for 20% conversion is______
V =4.8 L
10) The volume of a PFR required for 20% conversion is______
V = 6.4 L
CHE 304 (Spring 2007) ______
LAST NAME, FIRST
Quiz #2
Note: Your answers must be correct to 3 significant figures and have the appropriate units.
I. The gas phase reaction A + 4B 2C
which is first-order in A and first-order in B is to be carried out isothermally in a plug flow reactor. The entering volumetric flow rate is 4.0 L/min, and the feed is equimolar in A and B. The entering temperature and pressure are 527oC and 8 atm, respectively. You can neglect pressure drop in the reactor. The specific reaction rate at this temperature is 5 L/molmin and the activation energy is 12,000 cal/mol. Gas constant R = 0.082 atmL/moloK = 1.987 cal/moloK
1) Determinethe volumetric flow rate when the conversion of A is 25%.______
Q = 2.5 L/min
2) Determinethe concentration of A at the entrance to the reactor.______
CA0 = 0.061 mol/L
3) Write the concentration of A in terms of CA0, and X.______
CA =
II. For a gas phase reaction where rA = kCACB
What is the effect on the reaction rate of increasing the reaction pressure by 10% while maintaining constant temperature?
The reactio rate increase by:
A.10%B. 100% C. 121%D.None of the above
III.Dibutyl phthalate (DBP), a plasticizer, is to be produced by reaction of n-butanol phthalate (MBP). The liquid reaction follows an elementary rate law and is catalyzed by H2SO4.
MBP + n-butanol DBP + H2O
A stream containing MBP and butanol is to be mixed with the H2SO4 catalyst immediately before the stream enters the reactor. The concentration of MBP in the stream entering the reactor is 0.4 lbmol/ft3 and the molar feed rate of butanol is five times that of MBP. The specific reaction rate at 100oF is 1.2 ft3/lbmolhr. There is a 1000-gallon CSTR and associated peripheral equipment available for use on this project for 30 day a year (operating 24 h/day).
5) Determine the flow rate in lbmol/hr of DBP leaving the available CSTR to produce 6 million lb/year of DBP (Mw = 278)
______
30 lbmol/hr
6) Determine the exit conversion in the available 1000-gal reactor if the DBP flow rate is 20 lbmol/hr (1 ft3 = 7.48 gal.)
X = 0.814
7) If the MBP feed rate is 60 lbmol/hr and the exit conversion in the CSTR is 0.4, what conversion would be achieved if a second 1000-gal CSTR were placed in series with the first CSTR?
X = 0.786
IV) For the reaction 3A B
The reaction is irreversible at constant temperature and pressure with pure gas A fed to the reactor. Write the concentration of A in terms of CA0, and X.
CA = CA0
V) For the reaction 2A B
The reaction is reversible, non-isothermal with pure gas A fed to the reactor. Write the concentration of A in terms of CA0, T0, T, P0, P, and X.
CA = CA0
VI) Calculate the partial pressure of monatomic hydrogen gas at 1000oK and 1 atm pressure.
For ½H2(g) H(g)
= 120,000 J/mol, gas constant R = 8,314 J/moloK______
PH = 5.3910-7 atm
CHE 304 (Winer 2007) ______
LAST NAME, FIRST
Quiz #3
Note: Your answers must be correct to 3 significant figures and have the appropriate units.
I. We have a mixture with 2 moles of CH4 for every mole of O2 at 10 atm. Estimate the adiabatic reactor temperature if all of the available O2 react to form CO2 and H2O. The feed is at 300oC (HRx = 152 kcal/mol, Cp = 7 cal/moloK.).
T = 3919oC = 4192oK
II. For the gas phase reaction 2A + BC + 3D
The reaction is reversible at constant temperature and pressure. The feed is two moles of A per one mole of B.
2. Write the concentration of A in term of CA0 and X.______
CA = CA0
3. Write the concentration of C in term of CA0 and X.______
CC = CA0
III. Dibutyl phthalate (DBP), a plasticizer, is to be produced by reaction of n-butanol phthalate (MBP). The liquid reaction follows an elementary rate law and is catalyzed by H2SO4.
MBP + n-butanol DBP + H2O
A stream containing MBP and butanol is to be mixed with the H2SO4 catalyst immediately before the stream enters the reactor. The concentration of MBP in the stream entering the reactor is 0.2 lbmol/ft3 and the molar feed rate of butanol is five times that of MBP. The specific reaction rate at 100oF is 1.5 ft3/lbmolhr. There is a 500 ft3 CSTR and associated peripheral equipment available for use on this project for 30 day a year (operating 24 h/day).
4) Determine the exit conversion in the available 500 ft3 reactor if the DBP flow rate is 40 lbmol/hr (1 ft3 = 7.48 gal.)
X = 0.691
5) If the MBP feed rate is 60 lbmol/hr and the exit conversion in the CSTR is 0.4, what conversion would be achieved if a second 500 ft3 CSTR were placed in series with the first CSTR?
X = 0.806
6) What CSTR volume would be necessary to achieve a conversion of 95% for a molar feed rate of MBP of 60 lbmol/hr?
V = 4691 ft3
II. A solute diffuses through a membrane that separates two compartments A and B that have different initial concentrations. The solute concentrations in the two compartments as a function of time, CA and CB are shown below. The volumes of the two compartments are VA and VB.
(A)VAVB(B) Solute diffuses from compartment B to A.
a. A and B are true b.Only A is true c. Only B is true d. A and B are false
IV. For the reaction A(g) + 2B(g) C(g) + D(g,l)
The feed contains only A and B in stoichiometric amounts. The total pressure is 101.3 kPa and species D has a vapor pressure of 30.39 kPa at the isothermal reaction temperature of 300oK. Calculate the conversion at which condensation begins.
X = 0.9/1.3 = 0.692
V. The gas-phase reaction A(g) 3B(g) obeys zeroth-order kinetics with r = 0.25 moles/literhr at 200oC. Gas constant R = 0.082 Latm/moloK.Starting with pure A at 1 atm, calculate the time for 95% of the A to be reacted away in
9) a constant-volume batch reactor______
t = 0.098 hr = 5.88 min = 353 s
10) a constant-pressure batch reactor______
t = 0.0549 hr = 3.29 min = 198 s
CHE 304 (Spring 2007) ______
LAST NAME, FIRST
Quiz #4
Note: Your answers must be correct to 3 significant figures and have the appropriate units.
I. The gas phase reaction A B
has a unimolecular reaction rate constant of 0.0025 min-1 at 90oF. This reaction is to be carried out in parallel tubes 10 ft long and 1 in. inside diameter under a pressure of 150 psia at 260oF. A and B each have molecular weights of 64. Ideal gas constant R = 10.73 psiaft3/lbmoloR = 1.99 Btu/lbmoloR. The conversion of A is 80%.
1) If 1500 lb/hr of B is required, determine the feed flow rate of A in lbmol/min
______
FA0 = 0.488 lbmol/min
2) If the activation energy of the reaction is 35,000 Btu/lbmol, the rate constant at 260oF is
k =4.75 min-1
3) If the reaction rate constant at 260oF is 52.6 min-1 and the feed flow rate of A is 1.0 lbmol/min, the required volume of the reactor is
V = 1.58 ft3
4) If the reaction rate constant at 260oF is 52.6 min-1, the feed flow rate of A is 1.0 lbmol/min, and there is also an inert flow rate of 1.0 lbmol/min, the required volume of the reactor is
V =3.16 ft3
5) If the required volume of the reactor is 1.5 ft3, the number of tubes needed is______
nt = 28
II.The gas phase catalyzed hydrogenation of o-cresol to 2-methylcyclohexanone is given by
o-cresol(A) + 2H2(B) 2-methylcyclohexanone(C)
The reaction rate on a nickel-silica catalyst was found to be
rA = kPB, where k = 1.74 mol of o-cresol/(kg catminatm) at 170oC
The reaction mixture enters the packed-bed reactor at a total pressure of 5 atm. The molar feed consists of 67% H2 and 33% o-cresol at a total molar rate of 40 mol/min.
6) Neglecting pressure drop, write the concentration of CA in term of CA0 and X.
CA = CA0
7) If the pressure drop is not negligible, we need to solve the following ODEs
= 0.435y, and = 0.34, where y = P/P0
The above two ODEs can be solved using the following Matlab statements and function
A) wspan=0:.1:4.8;[w,xy]=ode45('f4d22b',wspan,[0 0]);
function wx = f4d22b(W,xy)
X=xy(1);y=xy(2);
wx(1,1)=0.435*(1-X)*y/(1-2*X/3);
wx(2,1)=-0.34*(1-2*X/3)/(2*y); / B) wspan=0:.1:4.8;
[w,xy]=ode45('f4d22b',wspan,[0 1]);
function wx = f4d22b(W,xy)
X=xy(1);y=xy(2);
wx(1,1)=0.435*(1-X)*y/(1-2*X/3);
wx(2,1)=-0.34*(1-2*X/3)/(2*y);
C) wspan=0:.1:4.8;
[w,xy]=ode45('f4d22b',wspan,[0 1]);
function wx = f4d22(W,xy)
X=xy(1);y=xy(2);
wx(1,1)=0.435*(1-X)*y/(1-2*X/3);
wx(2,1)=-0.34*(1-2*X/3)/(2*y); / D) None of the above
III. A fermentation broth consists of an aqueous solution of nutrients and cells. As the cells grow, they cluster into spherical pellets of radius R(t). On average, the cell density inside a pellet is 0.04 mg of cell mass per cubic millimeter of pellet volume. The dissolved oxygen concentration in the broth is 5 g/cm3. The cells utilize oxygen at a rate of 1.2 mmol of oxygen per hour per gram of cell mass, via a zero-order reaction. The diffusion coefficient DAB of oxygen within the pellet is 1.810-5 cm2/s. The cells and broth have densities close to that of water. There is a finite convective resistance to mass transfer to the surface of the pellet, such that the flux to the surface is given by
molar flux = kc(CBCP)
where CB is the broth oxygen concentration and CP is the (unknown) concentration of oxygen at the pellet surface.
8) Determine the reaction rate, R, per unit volume of the cell in mol/(cm3s)
R = 1.3310-8 mol/(cm3s)
9) If R = 2.510-9 mol/(cm3s),R = 5.010-2 cm and 2kcR/DAB = 4 determine CP (g/cm3)
CP = 3.1510-6 g/cm3
10) If R is the reaction rate per unit cell volume, the differential equation for the concentration of oxygen, CA, in the spherical pellet is
A) + R = 0 / B) R = 0C) R = 0 Ans /
D) None of the above
CHE 304 (Spring 2007) ______
LAST NAME, FIRST
Quiz #5
Note: Your answers must be correct to 3 significant figures and have the appropriate units.
I. A well-mixed sewage lagoon (a shallow pond) is receiving 430 m3/d of sewage out of a sewer pipe. The lagoon has a surface area of 105 m2 and a dept of 1.0 m. The pollutant concentration in the raw sewage discharging into the lagoon is 250 g/m3. The organic matter (pollutant) in the sewage degrades biologically in the lagoon according to first-order kinetics. The reaction rate constant is 0.070 /d. Assuming no other water losses or gains, find the steady state concentration of the pollutant in the lagoon effluent.
CA = 14.5 g/m3
II. An airborne spherical cellular organism, 0.015 cm in diameter (D), utilizes 40.0 mol O2 per hour, per gram of cell mass. Assume Sh = kmD/DAB = 4 (based on DAB in the gas phase.) Assume zero-order kinetics for respiration. The diffusion coefficient for O2 through the cellular material is 10-5 cm2/s and the diffusion coefficient for O2 in air is 0.18 cm2/s at 298oK. The equilibrium concentration (CA) of O2 in the cellular materials is related to the partial O2 pressure (pA) by the relation CA(mol/cm3) = 7.010-6pA(atm). Density of cell is 1 g/cm3. Air is at 1 atm with 21 mole % oxygen. Gas constant Rg = 82.06 cm3atm/moloK
2) At steady state, determine the concentration of oxygen (mol/cm3) in air at the surface of the cellular organism.
km = 8.0110-6 g/cm3
3) If the concentration of oxygen in air at the surface of the cellular organism is 8.510-6 mol/cm3, the concentration of oxygen (mol/cm3) in the cell at the surface of the cellular organism is
______
CAs|cell = 1.45510-6 mol/cm3
III. Hexamethylene tetraamnie, N4(CH2)6, is to be produced in a well-stirred semibatch reactor by adding 20oC aqueous ammonia solution at a constant rate of 25 liters/min to an initial charge of formalin solution:
6HCHO + 4NH3 --> N4(CH2)6 + 6H2O
(A) (B)
The reaction is instantaneous, irreversible, and exothermic. The initial charge of formalin solution is 5000 liters with a formaldehyde concentration, CAi, of 20.0 mol/liter. The concentration of ammonia in the solution is CB = 12.0 mol/liter. Heat capacity of both ammonia and formalin solution is 1000 cal/literoC. Heat of reaction is 74.6 kcal/mol of N4(CH2)6. The initial temperature of formalin solution in the reactor is 25oC.
4) The rate of heat generated by the chemical reaction is______
5595 kcal/min
5) Time required for complete consumption of formaldehyde is______
t = 222 min
IV. The first order reaction A B is carried out in an adiabatic CSTR with CA0 = 2 mol/liter and T0 = 300oK. It is found that 50% conversion is obtained with (= V/Q) = 4 min, and the reactor temperature is 350oK.
6) The reaction rate constant k at 350oK is
______
k = 0.25 min-1
7) The reaction is in water with Cp = 1000 cal/literoK. Find the heat of reaction.
______
Hr = 50 kcal/mol
V. The irreversible, liquid-phase reaction A B is to be carried out in an ideal PFR. The inlet concentration of A, CA0, is 2,500 mol/m3, and the feed temperature is 150oC. The fractional conversion of A in the reactor effluent must be at least 0.90. The reactor will operate isothermally at 150oC. The reaction is second order in A. The rate constant at 150oC is 1.4010-4 m3/(mol As). At 150oC HRx = 165 kJ/mol. The flow rate to the reactor is 0.01 m3/s.
8) Determine the volume of the PFR required for 90% conversion.______
V= 0.257 m3
9) Determine the rate (kJ/min) at which heat is removed from the whole reactor. ______
= 2.23105 kJ/min
VI) (10) The following MATLAB program can evaluate for x = 2
A.x = 2;
sum = 1;
For n=0:10
sum = sum + (1)^n*x^n/factorial(2*n+1);
end / C.
x = 2;
sum = 1; z = x;
For n=1:10
z = z*x/(2*n+1); sum = sum+z
end
B. (Ans.)
x = 2;
sum = 1; z = 1;
For n=1:10
z = z*x/(2*n)/(2*n+1); sum = sum+z
end / D.
None of the above