Chemical Engineering Calculations 1
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MCKAY, KRISTIEN KATE S. BSChE
CHE 413 July 17,2017
CHEMICAL ENGINEERING CALCULATIONS 1 – SOLVED PROBLEMS
1. If 1 L of ethyl alcohol is mixed with 1 L of water at 20°C, how many kilograms of solution result? How many liters?
Required: mass of P (in (in kg) volume of P (in L) Solution:
ρE at 20°C=0.789 g⁄mol ρ at 20°C 20°C = 0.998 0.998 g⁄mol mF1 = 1 L EtOH mF2 = 1 L
H O
0.789 g
1000 mL
1 kg
mL 0.998 g
1L 1000 mL
1000 g 1 kg
mL
1L
1000 g
OMB: mP = mF1
= 0.789 kg EtOH = 0.998 kg EtOH
+m
F2
mP = 0.789 kg + 0.998 kg mP = 1.787 kg solution
ρ = xρ + xρ . 0.998 kg⁄L 0.789 + ρ = . 0.998 =0.906 . . V = mρ
P
P
. . / =
= 1.972 L
MCKAY, KRISTIEN KATE S. BSChE
CHE 413 July 17,2017
2. A liquid adhesive, which is used to make laminated boards, consists of a polymer dissolved in a solvent. The amount of polymer in the solution must be carefully controlled for this application. When the supplier of the adhesive receives an order for 3000 kg of an adhesive solution containing 13 wt% polymer, all it has on hand is (1) 500 kg of a 10 wt% solution, (2) a very large quantity of a 20 wt% solution, and (3) pure solvent. Calculate the weight of each of the three stocks that must be blended together to fill the order. Use all the 10 wt% solution.
Required: mass of F2 and F3 Solution: mP = mF1 mF2 mF3 OMB: 3000 = 500 + mF2 + mF3 2500 = mF2 + mF3
+ +
Polymer Balance: mF1 xF1 + mF2 xF2 + mF3 xF3 = mP xP 500 0.10 + mF2 0.20 + mF3 0 = 3000 0.13 mF2 = 1700 kg mF3 = 800 kg
( ) ( ) ( )
MCKAY, KRISTIEN KATE S. BSChE
CHE 413 July 17,2017
3. You are asked to measure the rate at which waste gases are being discharged from a stack. The gases entering contain 2.1% carbon dioxide. Pure carbon dioxide is introduced into the bottom of the stack at a measured rate of 4.0 lb per minute. You measure the discharge of gases leaving the stack, and find the concentration of carbon dioxide is 3.2%. Calculate the rate of flow, in lb mol/minute, of the entering waste gases.
Required: flowrate of F1 (in lbmol/min) Solution: 4 lb CO2 1 lbmol ɳ F = = 2 min 44.01 lb
OMB:
ɳ P = ɳ F
1
0.091
lb mol min
+ ɳ
F2
ɳ P = ɳ F + 0.091 1
( ) ( ) ɳ 0.021 + 0.0911= ɳ 0.032
CO2 Balance: ɳ F xF1 + ɳ F xF2 = ɳ P xP 1
2
F1
ɳ F = 8.008 lbmol/min 1
ɳ P = 8.009 lbmol/min
P
MCKAY, KRISTIEN KATE S. BSChE
CHE 413 July 17,2017
4. The waste acid from a nitration operation contains 23% wt HNO 3, 57% H2SO4 and 20% H2O. It is specified that the concentrated acid products should contain 27% HNO 3, 60% H2SO4, and 13% H2O. If the H2SO4 available contains 7% H2O and HNO3 contains 10% H 2O, how many pounds of each must be added to produce 10000 lbs of product?
Required: mass of F1, F2, and F3 Solution: OMB:
F +F +F = P F + F + F =1000 HNO Bal: 0.23F +0.90F =10000.27 H SO Bal: 0.57F +0.93F =10000.60 3
2
4
F1 = 416.894 lbs F2 = 389.646 lbs F3 = 193.460 lbs
MCKAY, KRISTIEN KATE S. BSChE
CHE 413 July 17,2017
5. Pure oxygen is mixed with air to produce an a n “enriched air” containing 50% m O 2. What ratio of oxygen to air should be used?
Required: F1 to F2 ratio Solution: Basis of 100 lbs of enriched air OMB:
F +F =P F + F =100 O Bal: F +0.21F =0.50100 F +0.21F = 50 2
F1 = 36.709 lbs F2 = 63.291 lbs
= . = 1.724 .
MCKAY, KRISTIEN KATE S. BSChE
CHE 413 July 17,2017
6. A mixture of NaOH, NaCl, and MgCl 2 contains 34.6% w chloride and 20.0% w hydroxide, i.e., 34.6% Cl and 20.0% OH. What are the weight and mole fractions of NaOH, NaCl, and MgCl2 in the mixture? Solution:
1 mol OH 1 mol Na 22.99 g Na = 27.03 g Na 20 g OH 17.01 g OH 1 mol OH 1 mol Na
wt NaOH = 20 + 27.03 = 47.03 g NaOH = 47.03% NaOH – 34.6 wt Na + wt Mg = 100 – 100 – 47.03 47.03 – 34.6 = 18.37 g wt Cl in NaCl = wt Na
. = 1.542 wt Na . . = 2.916 wt Mg .
wt Cl in MgCl 2 = wt Mg
1.542 wt Na + 2.916 wt Mg = 34.6 wt Na = 13.804 g wt Mg = 4.566 g
wt Cl in NaCl = 21.286 g wt Cl in MgCl2 = 13.314 g
wt NaCl = 13.804 + 21.286 = 35.09 g NaCl = 35.09% NaCl wt MgCl2 = 4.566 + 13.314 = 17.88 g MgCl 2 = 17.88% MgCl2
MCKAY, KRISTIEN KATE S. BSChE
CHE 413 July 17,2017
7. It is desired to make 100 kg of a solution containing 40% salt by mixing solution A containing 25% salt and solution B containing 50% salt. Determine the mass in kg of solution A.
Required: mass of F1 in kg Solution: OMB:
F +F =P F + F =100 40100 00 Salt Bal: 0.25F +0.50F = 0.401 F = 40 kg F = 60 kg
MCKAY, KRISTIEN KATE S. BSChE
8. D 9. D 10. D 11. D
CHE 413 July 17,2017
MCKAY, KRISTIEN KATE S. BSChE
CHE 413 July 17,2017
12. Calculate the weight flowrate in lb/hr of NH 3, through a pipe from the following data: A stream of pure oxygen is admitted to the NH3 line at a rate of 40 ft 3/min and the resulting mixture is sampled farther along the pipe and found to contain 10%v O2. The entering oxygen is metered at 18 psia and 85°F. 85°F . Solution: PV = nRT
/) ps ps ( f = 0.1231 lbmol/min = − R RT = .− R
nO2
mNH3 =
0.1231 lbmol O2 90 lbmol NH3 17 lb NH3 60 min min 10 lbmol O2 lbmol NH3 1 hr
mNH3 = 1130.26 lb/hr
13. In testing filter media for a proposed installation, a laboratory technician suspends 50 grams of a slightly soluble salt in 100 grams of water. By filtration he obtains a wet filter cake (precipitate) weighing 53.9 grams and a clear filtrate solution. He dries the cake and finds that it weighs 49.0485 g. Calculate the solubility of the salt in g/100 g of water. The concentration of the salt in the filtrate is the same as that in the liquid which adheres to the solid precipitate.
Solution:
Suy = 50 – 49.0485 50 – 49.0485 . S Solubility =
MCKAY, KRISTIEN KATE S. BSChE
CHE 413 July 17,2017
14. A mixture of phenol and water, under certain conditions of temperature and compositions forms two separate liquid phases, one rich in phenol and the other rich in water. At 30°C the composition of the upper and lower layers are 70 and 9%w phenol, respectively. If 40 lbs of phenol and 60 lbs of water are mixed and the layers allowed to separate at 30°C, what will be the weights of the two layers? Solution:
Solution: Phenol Bal: H2O Bal:
0.7+0.09=40 0.3+0.91=60 X = 50.82 lbs Y = 49.18 lbs
MCKAY, KRISTIEN KATE S. BSChE
CHE 413 July 17,2017
15. A gas mixture is known to consist of CO 2, N2, and H2O. It is analyzed by first passing it through a drying train where all the water is removed. The remaining gases are placed in a 1 L flask and weighed. In one analysis 0.0843 g of water is removed in the train. The remaining gases weigh 1.5550 g at 30°C and 1 atm. What is the % composition of H2O?
Solution: OMB:
=+ =0.0843+1.5550 = 1.6393
H2O Bal:
1.6393 6393 = 0.0843 0843100 = 5.14%
16. CaCO3 contains __________ percent of Ca by weight. Solution:
1 mol CaCO3 1 mol Ca 40.08 g Ca 100 g CaCO 100.09 g CaCO3 1 mol CaCO3 1 mol Ca = 40.04 g Ca = 40.04% Ca
17. Equal masses of CH 4 and H2 are mixed in an empty container. The partial pressure of hydrogen in this container expressed as the fraction of total pressure is Solution:
= . = . = × . = = . . .
+ = . .
MCKAY, KRISTIEN KATE S. BSChE
CHE 413 July 17,2017
18. N2 content in a urea sample was found to be only 42%. What is the actual urea content of the sample? Solution:
C42 40.08 g C42 42 g 128molg NN22 1 mol 1 mol N2 1 mol C42 = 90 g
C = 90% C
19. A solution is made by dissolving 1 kilo mole of solute in 2000 kg of solvent. The molality of the solution is Solution:
= = 0.5 M= 20.
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