ENGLISH UNIT CALCULATIONS in GENERAL CHEMISTRY GILBERT FORD KINNEY Pratt Institute, Brooklyn, New York
Chemical engineers need to be familiar w'th both metric and English systems of measurement. Computations in English units, though usually avoided in chemistry courses, are not dificult, and chemistry problems stated in these
units require f e u more conversion factors than metric system problems. Introduced into firstyear chemistry, these computations are of decided advantage to the beginning chemical engineer and to other students as well; they
1 cubic foot of water weighs 62.3 pounds (all a t help lay the foundation fur engineering cukulations later, 20°C.) and they help the student connect his chemistry with meryahy life. (3) Simple Boyle's law computation using English Sareral types of problems may be used. A classifica- units of pressure can easily be included along with tion, illustrative problems with answers, and a table of other gas law problems. By including pressure values conversion factors are included. in "gage" readings (above atmospheric pressure) as well as absolute values, the problems-are made no more diicult, for the conception of absolute pressure is apparently an easy one to grasp. Such a procedure NGLISH units are used in practically all engineer- helps materially with the apparently more difficult coning work in the United States, and practice in cept of an absolute temperature. Necessary factors for this type of problem are these calculations is an essential part of the 1 atmosphere = 760 mm. of mercury training of an engineer. Computations of this sort can 14.7 pounds per square inch and should be included even in a beginning course in 29.92 inches of mercury general chemistry, but, unfortunately for the student (4) Problems including Fahrenheit temperature engineer, mention of chemical engineering units is usually omitted. This omission probably results from should be included with other gas law problems. Using two things. (1) Most available chemistry texts do not absolute scales in both Fahrenheit and Centigrade include English unit calculations. (2) Practically all units (degrees K or Kelvin, Centigrade plus 273; and laboratory work in chemistry, because of the obvious degrees R or Rankine, Fahrenheit plus 460) avoids advantages of the metric units, is conducted in the conversions, and gas law computations remain essentially a straightforward process. Since Centigrade C.O.S. system. The fact remains, however, that all engineers use the temperatures are used in some chemical processes English system, and that the chemical engineer must (practically the only exception to the almost universal learn to deal in pounds, gallons, and cubic feet as well use of English units in engineering practice), it is all as in the chemist's grams and cubic centimeters. the more necessary that the chemical engineer be able Chemistry problems stated in the engineering units of to think freely in either scale, avoiding bothersome, pounds, gallons, and cubic feet involve but little more unnecessary conversions. The necessary temperature factors are than just substitution of pounds for grams in .the more Absolute zero = -273°C. = -460°F. customary type of chemistry problem, and familiarity (5) Prohlems using the pound molecular volume with these essentially simple calculations gives much helpful introductory training with the chemical calcu- are important. The pound molecular volume, three hundred fifty-nine cubic.fe&, is strictly comparable to lations of chemical engineering. Altogether there are five types of English unit prob- the gram molecular volume, 22.4 liters. It is extremely lems that really belong in a first-year chemistry course. useful for computing gas densities, and in stoichiometric (1) The most important type of problem is that in- relations when a gas is involved. volving simple stoichiometric relationships, and probThese problems, some of which are illustrated, are lems dealing with materials actually used in commercial not intended to displace the a,bsolutely necessary work processes can be made a helpful part of the descriptive in metric units, but are suppkmentary to this. The work of the course. Some calculations should be made chemical engineer must be able to use either system with yields less than perfect and purities less than one of measurements; it happens that the English system is the one commonly neglected in first-year chemistry. hundred per cent. (2) Prohlems involving volumes of materials are often While these calculations are primarily for the engifound confusing, probably because the student fails to neer, they have decided value for any beginning studistinguish sharply in his own mind between two proper- dent. Working problems about real things helps disties of matter, "mass" and "volume." To a large .pel any impression, too often gained, that chemistry extent this confusion is avoided in the English system deals with something in a watertight compartment because conversion factors are always necessary, and and with no relation to anything else. Regardless of by using specific gravities (avoiding "densities") less pedantic views, chemistry has an objective field of inconfusion results even with problems in the metric quiry into the real things of ordinary life. Chemical system. The conversion factors necessary for prob- calculations about ordinary things in ordinary units lems of this sort must, of course, be given to the stu- make chemistry more nearly real and living to the ordents, who in general know at least part of them al- dinary student. Surely this should not he beneath ready. It should be emphasized that it is not necessary the dignity of even the most formalized presentation. for the student to memorize tables and that conversion SAMPLE PROBLEMS factors will always be available. The factors necessary for problems involving spe(1) How much dry ice can be recovered per ton of coal that cific gravities are, to slide d e precision, analyses 78.5 per cent. carbon, 4.3 per cent. hydrogen, 1.2 per 1gallon of water weighs 8.33 pounds cent. nitrogen, and 2.5 per cent. sulfur, if the scrubbers remove 31 per cent. of available CO*? 1cc. of water weighs 1 gram
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(2) A fire extinguisher holds one pound of bicarbonate of soda. How many cubic feet of carhan dioxide, measured a t standard conditions, can this much soda generate? (3) The gas capacity of the Hindenburg was approximately seven million cubic feet. How many pounds of hydrogen and how many pounds of helium (bath a t standard conditions) would be required t o fill it? What would have been the loss in lifting power if helium had been need? (4) A plane that required 1000 pounds of fuel would need how many gallons of gasoline, specific gravity 0.661 What would be the capacity of its fuel tanks in cubic feet? (5) One hundred cubic feet of air a t a gage pressure of 20 pounds is equivalent t o how many cubic feet a t 1 atmosphere pressure? (6) What is the weight of air (dry, a t 7 5 T . and 750 mm.) in a room that measures 20 X 30 X 10 feet? (7) A tank of chlorine holds 1W pounds of the liquified material. What volume of gas would be produced if this were liberated a t 75-F. and 1atmosphere? How many gallons of water would this chlorinate if one-half part per million of chlorine were used? (8) A ton of salt will furnish how many cubic feet of chlorine, at standard conditionss assuming 95 per cent' >...A,.....measured .L Y ' L L J , (9) What weight of sulfuric acid, specific gravity 1.72, 79 per cent. hydrogen sulfate, can be obtained from 1 ton of sulfur, 98 per cent. pure? How many gallons is this? (10) Heats of combustion of &el gases are often measured with the gases a t 609P.. 30 inches of mercury, and saturated with water vapor. What volume would one cubic foot a t these conditions become a t standard conditions? FACTORS
1 gallon of water weighs 8.33 pounds 1 &.of water weighs~lgram 1cubic foot of water weighs 62.3 pounds (at 20°C.) 1atmosphere = 760 mm. of mercury 14.7 pounds per square inch 29.92 inches of mercury absolute zero = -273' Centigrade -460' Fahrenheit 1 pound mole of a gas occupies 359 cubic feet (std. cond.) 1 gram mole of a gas occupies 22.4 liters (std. cond.) 453.6 grams = 1 pound
2.54 centimeters = 1inch 0°C. = 32'F. ANSWERS TO PROBLEMS
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(1) From the equation. 1atom of carbon gives 1mole of CO, 12 lbs. carbon give 44 lbs. CO, 2000 X .785 = 1570 lbs. carbon give 5770 lbs. C02 a t 31 per cent. recovery .31 X 5770 = 1780 lbr. Ans. (2) From the equation, 1 mole N ~ H C O Igives 1 mole CO, 84 lbs. NaHCOa give 359 cu. ft. CO, 1lb. gives 4 . 2 8 cubic J u l A m . (3) 7,000,000 cubic feet a t standard conditions is 7,W0,000/359 = 19,500 pound moles 19,500 lb. moles of HI 19.500 X 2 39,000 p a n & A m . 19,500 ib. moles of He 78,000 pounds Ans. 19,500 X 4 Loss in lifting power 78.000 - 39,000 39,000 pounds A m . (4) 1 gallon of gasoline weighs 8.33 X .66 = 5.5 lbs. 1000 lbs. = 1000/5.5 = 180 gallons Ans. 1cubic foot of gasoline weighs 62.3 X .66 = 41 Ibs. 1000 Ibs. = 1000/41 = 24 cubic feel A m . (5) 100 X (14.7 20)/14.7 236 cubic feet A m . (6) Volume of room 20 X 30 X 10 = 6000 cu. ft., equivalent
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6000 X (32 460)/(75 f 460) X (750/760) = 5450cu. ft. atstd. cond. 5450 cu. ft. = 5450/359 = 15.2 moles 15.2 X 29 (apparent M.W. of air) = 442 16s. A m . (7) One hundred pounds of chlorine = 100/71 = 1.41 pound moles 1.41 X 359 = 506 cubic feet Anr. One hundred pounds of chlorine a t one-half part per million will chlorinate 200,000,OW pounds of water ~00,000,000/8.33 24 million gallons Ans. (8) From the equation, 2 mdes salt give 1mole chlorine 117 pounds salt give 359 cubic feet chlorine 2000 pounds salt give 6130 cubic feet chlorine a t 95 per cent. recovery 6130 X .95 = 5820 cubic feet Ans. (9) From the equation, 1 sulfur atom gives 1mole hydrogen sulfate 32 pounds sulfur give 98 pounds hydrogen sulfate 1960 pounds gives 6000 pounds hydrogen sulfate 7600 pounds acid A m . 6000/.79 = Each gallon weighs 8.33 X 1.72 = 14.3 pounds 7600 pounds is 7600/14.3 = 530 gallons A m . (10) From the tables, the vapor pressure of water a t 60°F. is .52 inches 1 X (30 00 - .52)/29.92 X (460 f 32)/(460 4-60) 0.935 cu. Jt. Ans.
