The Mole by Doris Kolb Illinois Central College How do you know how much material to use in a chemical reaction? "eoeher: Well, ordinarily you want to use amounts that are chemically equivalent, or approximatelyso. Suppose we wanted to react this 10 g sample of aluminum with iodine. How mueh iodine do you think we would need? Xudent: About log? 'eaeher: That would make the reactants equal in mass, hut try to think in terms of atoms. An iodine atom is much bigger than an aluminum atom. It weighs almost five times as much. rtudent: Then I guess we should use five times as much iodine. How about 50 g? 'eacher: That would be about right if each aluminum atom reacted with only one iodine atom, but don't forget that an a h minum atom can combine with three iodine atoms. 'tudent: In that case I guess we would need three times 50grams of iodine. That would he about 150 g. Gosh! That seems like a lot of iodine for only 10 g of aluminum! :tudrn t:
Although the word mole was not used in that dialogue, the ole concept certainly was. The discussion could not have aken place without it. There is probably no concept in the ntire first-year chemistry course more important for students 3 understand than the mole. There are also few things that ive them quite so much trouble. toichiometry
One of the main reasons the mole concept is so essential in le study of chemistry is stoichiometry. That is what the receding conversation was all ahout. Stoichiometry includes I1 the quantitative relationships in chemical reactions. It has do with how much of one substance will react with so much f something else, how much product should he formed, etc. toichiometrv is ordinarv chemical arithmetic. Jeremias ~ i c h t ewas r the first to use the term, based on the reek words stoicheion (element) and metron (measure). His lree volumes on "Foundations of Stoichiometry or the Art
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Doris Kolb Illinois Central College East Peoria. Illinois 61635
"The Mole" is part of a series of substantive reviews of chemical principles taught first in hieh school c h e m ~ t kcourses. Dr. Kolb received a BS degree from the University of Louisville and both MS and PhD degrees from The Ohio State University. She has been emdoved as a chemist at the standard Oil Cam.oanv. and as a television lecturer in a series "Sootlieht on Research."
of Measuring Chemical Elements" (1792-94) represented one of the earliest efforts to provide a mathematical basis for chemistry. Richter was especially interested in the definite proportions in which various substances combined with each other. A thorough discussion of a topic as broad as stoichiometry is not possible here, hut let us a t least consider the question about aluminum and iodine referred to above. The problem is How many grams of iodine will react completely with 10 g of aluminum metal? T o solve it we need first to know the atomic weights of aluminum and iodine, which are 27 and 127, respectively. (Hence, the iodine atom weighs "almost five times as much" as the aluminum atom.) A 27-g quantity of aluminum constitutes one mole, so 10 g of aluminum is 10127 of a mole. The same number of iodine atoms would he present in 10127 of a mole of iodine. Since one mole of iodine weighs 127 g, 10127 mole would weigh 10127 X 127 g = 47 g In order to provide three iodine atoms for each aluminum atom (because the compound formed is AIId, it would he necessary to use three times that much iodine: This is reasonably close to the student's 150 g estimate. A more svstematic a o ~ r o a c hto the oroblem is to start with the halanced equation.for the reaction. The equation in this case is 2Al+312--2AlI~ The 10 g of aluminum given in the problem is best converted to grams of iodine by dimensional analysis, sometimes called the "factor-units" method. Each "factor" is a ratio in which the numerator and denominator are exactly equivalent, and the "units" are set uo so that all of them cancel out excent the unit desired in the answer
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Corning Community College end Bradley University. Since 1967, she has been Professor of Chemistry at Illinois Central College.
Problem: Eouation: or, in terms of mass:
Information from equation:
728 1 Journal of Chemical Education
2 moles
requires requlres
In this case, of aluminum is first converted to moles; moles of aluminum is converted to moles of iodine (in accordance with the balanced equation); and then moles of iodine is converted to grams. Using atomic weights with more significant fieures does not change the value of the answer. but i t does increase its precision.
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Since most atomic weights are very close to whole numbers, "rounded off" atomic weights are satisfactory in many cases and are used here for simplicity. Some students find it helpful to write the balanced equation and then to indicate above it what the problem is and below it what the equation tells them as in the example below.
S mdes
and yields and yields
2 m&s
2(2(27)+ 3(127)(2))
(It is important that the units used below the equation be consistent with those in the problem above.) This equation says that 54 g of Al will react with 762 g of Ip. If we use only 10 zrams of Al. which is 10154 of the amount shown in the equation, then we will need only 10154 as much iodine 10 5dX762g12=141gIz
.. .
Or, since 54 gof Al is seen to be equivalent to 762 g of Ip in this reaction, we can use the method of dimensional analysis.
Or, the problem and the information from the equation can be set UD as a simple algebraic proportion, from which the unknown quantitiis easily determined.
". . . the mass in grams of 6.02 X 102hmoleculesof any substance."
". . . a gram-molecule."
". . . a unit of number equal to Avogadro's number." ". . .one gram formula weight of a substance." ". . . Avogadro's numher of particles."
Etc.
These examples, some of which are clearly in error, are sufficient to show that a mole has sometimes been defined as a weieht or mass. sometimes as a volume of pas. .. . and sometimes as a number, or a number of particles. In the older literature the mole has even been defined as "a weight of material which reacts with 16 grams of oxygen." ~ c c o r d k to g some textbooks agram molecular weight is properly called a mole, but agram atomic weight is not. In modern usage the mole has taken on more generalized meaning. (Elements)
therefore
(Compounds)
There are various ways to solve a given stoichiometric prohlem, but regardless of what approach he chooses, a student must first of all understand what a mole is. What Is a Mole?
Chemistry is the study of matter, hut matter comes in such tiny packages that no one can see them. Since much of what the chemist does is ouantitative. he must be able to count the particles of matter (atoms, ions, and molecules) no matter how infinitesimal thev are. He needs a counting unit sufficiently large so that thiset of particles making ipthe unit is big enough to be seen and handled conveniently. The counting unit he uses is the mole. T h e word mole appears to have been introduced by Wilhelm Ostwald (1896), who took it from a Latin word moles meaning "heap" or "pile." A mole is a very large pile of atoms or molecules that can he described as follows A mole is a certain amount of substance. It contains 6.02 X loz3(Avogadro's number) atoms, malecules, ions, or formula units. Its mass is equal to its formula weight expressed in grams. If in the gaseous state, it occupies about 22.4 I at standard temperature and pressure (STP), which is O°C and 1 atm.
1
gram atomic weight gram atomic mass eram-atom gram molecular weight gram molecular mass gram-molecule gram formula weight gram ionic weight gram-ion
Gas Volume Formula Mass Weight in grams
(SIT)
2 2.4 liters
1
(Ions)
A mole is the amount of substance which contains as man" elemPntw).partirlrsns therearerarhon atom5 i n O O I L kgofrarhon12. Theclemrntaryentity must twspcciiied and may bean atum, a mdcrulr. au iuu, an electron. ctr ur a aprcif;rd g r w p of such particles. A briefer version of the definition is
.
A mole is an amount of substance that contains as many formula units as there are atoms in 12 grams of carbon-12.
or simply A mole is an amount of substance containing Avogadro's number of formula units. The Chemist's Dozen
It is often useful to compare the mole with other collective terms, such as the dozen.
Notice that a mole always contains the same number of formula units (6.02 x 102"), regardless of the particular substance or its comuosition. and a mole of gas a t standard conditions always occupies about the same volume (22.4 l), regardless of the nature or formula of the gas. Perhaps that is why students sometimes mistakenly assume that all substances have the same molar mass (e.p-.. . 1 g, - or 12 p-, or 16 g). The potnt 1s worth emphasizing that the mass of a mile must vary from substance to substance, the molar mass of each substance being its own formula weight expressed in grams. Over the years there has been some confusion as to what the definition of the word mole should be. A mole has been variously defined as
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".. . . t h e weieht of a substance in grams numerically equal to its ~
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Kind of Set
socks. dice egg5 oranges
units
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molecular weight." ".. .22.4 liters of a gas measured at standard conditions."
mole
Then iust what is the best definition for the word mole? In i9fi0fhe Elrvenfh Contwnceun Weightsand Measures met in P m s and driienated the mole as one of the sewn basir units in the ~ ~ s t e m e h t e r n a t i n n(SI), a l a unifying system of units endorsed by both the U S . Bureau of Standards and the IUPAC (~nternationalUnion of Pure and Applied Chemistry). The mole is the SI unit for measuring "amount of substance." The official definition of the mole reads as follows
hems 6.02 x
\
bottles, cans brushes, pencils sheets of paper atoms, molecule^
pair dozen case gross
ream mole
Number in Set 2 12 24 144 500 6.02 X loz3
The mole is then seen to be just another counting unit. It does differ from the others in that the individual items in the set are invisible, and the number making up the set is quite abstruse, but the principle is still the same. The analogy of the mole with the dozen can be especially helpful for students who have difficulty thinking in abstract terms. A dozen lemons and a dozen eraoefruit can orovide a concrete frame of reference for a studeniwho is having trouble comoarina a mole of lithium with a mole of sodium. T h e r e action of; mole of oxygen atoms with 2 moles of hydrogen atoms might be pictured in terms of a dozen tennis balls and two dozen ping pong balls. A mole of aluminum atoms will require exactly three moles of chlorine atoms just as a dozen Volume 55, Number 11, November 1978
/ 729
candelabra (3-place) will require exactly three dozen candles. A dozen blueberries, a dozen plums, and a dozen apples represent a standard quantity (a dozen) of three different kinds of fruit. Obviously they do not all weigh the same. Let us assume that each hatch of fruit is homogeneous with respect to size. If one a o ~ l weighs e four times as much as one plum, then a dozen apples wifweigh four times as much as a dozen olums (and a million apples should weigh four times as much .. as a million plums). A very simple but highly effective visual display is an assortment of flasks each containing exactly one mole of a substance (12 g of carbon, 24.3 g of magnesium, 58.5 g of sodium chloride.,~ 342 " z of sucrose., etc.). olus & a dozen stvrofoam balls in each of several sizes (% in., 1in., and 1'12 in. in diameter). A dozen balls will fill a small beaker or a very large one depending on the size of an individual ball. Likewise, a mole of substance will fit in a small flask (carbon) or will require a large one (sucrose) depending on the size of the individual atom or molecule. What ahout rhestudpnt who understands theduzen and the cross hut still has tn~ul)lewith the mole? It n)uld be that the sheer size of Avogadro's number is part of the problem. ~
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How Big Is Avogadro's Number?
When written in its exponential form, 6.02 X loz3, Avogadro's number looks extremely large, hut to most people it does not appear to he nearly so huge as i t really is. I t may seem somewhat larger when written in the form 602,000,000,000,000,000,00.000
or when recognized as heing equal t o 602,000 X a million X a million X a million, but the number is actually too gigantic for the mind to comprehend. The fact that vou can hold Avoeadro's number of atoms in the palm of you; hand belies the size of the numher because atoms are so incrediblv small. T o convev the magnitude of Avogadro's number weneed to use moretangible;nits. If you had Avogadro's numher of tiny grains of sand, for example, you could spread them out evenly over the entire state of California, and you would end up with a layer of sand as high as a ten-story hnilrlinv
600 miles deep. If Avogadro's number of pennies were distributed equally among all the people on earth (currently around 4 billion), each one would have enough money to spend a million dollars every hour, day and night, throughout his lifetime,and he still would not spend half of it. (Of course, humanity could not actually survive buried under all those pennies. They would be more than 50 miles deep.) Today there are computers that can count about 10 million times per second. For such a computer to make Avogadro's number of counts would require almofit 2 billion years. Avogadro's number is so enormous it defies human comprehension. On the other hand, one need not be able to comnrehend Avoeadro's number in order to use it. There is no reason why 6 k 102"annot he treated the same way we would treat 6 thousand, or 6 hundred, or a dozen. The important thing to remember is that, overwhelming though its size may be, Avogadro's number is still a real and finite number. Students sometimes wonder why Avogadro happened to choose such a strange number. He didn't choose it, of course. No one did. ~voga&o'snumber is the number of atoms in a gram atomic weight of any element. The numher was predetermined when the gram was established as a basic unit of mass. But just where did that number 6.02 X 1023come from? How do we know that really is Avogadro's number? A~
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Determination of Avogadro's Number
Amedeo Avogadro was an Italian physics professor who never knew the numerical value of the constant that bears his name. I t was not measured until after his death. He did conceive the basic idea, however, when he suggested (1811) that eaual volumes of eas contain eaual numbers of molecules (at s a k e conditions) and thereforelthat the weights of individ"al molecules must be proportional to their gas densities. The concept of standard molar gas volume (22.4 1a t STP) and the mole concent itself are direct outerowths of this hvnothesis. ~ l t h o u g hit would later become a cornerstone 6;quantitative chemical relationships, there were few who accepted Avogadro's hypothesis during his lifetime. Ampere (1814) and Dumas (1826) both tried to stir up interest in the idea, but they were as unsuccessful as Avogadro had been. Later Gerhardt (1842) attempted to use it to determine molecular weights of organic compounds (referring to it as "Ampere's hypothesis"), but he did not use it correctly. I t was another Italian scientist. Stanislao Cannizzaro. who finallv succeeded in convincing his fellow chemists of the significance of Avoeadro's hwothesis. This oecurred a t an international conmess of chemists held a t Karlsruhe in 1860. unhappily Avogadro had died in 1856. he idea of thinking of substances in terms of "gram-molecules," their molecular weights expressed in grams, did not occur to chemists right away, but it was clear from Avogadro's hypothesis that such a quantity should always contain the same numher of molecules. he number was assumed to be extremely large, but in order to know just how large one first had to know how small a molecule was. Probably the first attempt a t measuring the size of a molecule was that of Josef Loachmidt (1865),who tried tomeasure the diameter of air molecules by application of the kinetic molecular theorv. He found the diameter to be about a "millionth of a millimeter," or about 10& . (which compares fairly well with todav's value of about 3 A). Loschmidt could have gone on to calchate avalue for ~vogadro'snumber, but (like most of the earlv investieators who were interested in measuring molecula; dimensions) he stopped short of doing that. The Avogadro constant as calculated from Loschmidt's figures was 4.1 X 10z2.There is a related constant called the Loschmidt number which is the number of molecules in 1cm3 of gas a t standard conditions, and which has the current value of 2.70 X 1019 (although in German-speaking countries Loschmidt's number, rather than AvogadGXs,is the name often given to the numher of molecules in a mole). A wide varietv of aonroaches have been used to measure molecular size and/or the Avogadro constant. Over the years Avogadro's numher has been determined bv a t least 20 different methods. During the latter part of thei9th century the techniques tended to be indirect and not verv accurate. but within the first decade or so of the 20th centuiy a number of direct and quite accurate methods were develooed. Avogadro's number is &ally determined by measurinhsome of a unit particle and then comparing that same property a s measured a t the macroscopic level for a mole. Some investigators, for example, have sought by various means to determine Boltzmann's constant, k , which is the gas constant for a single molecule. The molar gas constant R divided by k yields Avogadro's number. A few of the best known methods for measuring Avogadro's numher are the following.
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730 1 Journal of Chemical Education
Electric Charge Method
The determination based on electriccharge was the first reallydirect method for obtaining Avogadro's number. In 1909 Robert Mil-~
It is interesting to note that, just as the standard molar gas volume is 22.4 1, the standard gas volume of an ounce-mole (the formula weight expressed in ounces) is 22.4 ft3. As Linus Pauling has pointed out (J.CHEM. EDUC., 19,494 (1942)), this is pure coincidence. The number of grams in an ounce just happens toequal thenumber of liters in a cubic foot.
likan measured the charge on a single electron by means of his famous oil drop experiment The corrected value for the charge an the electron coulomb. (Millikan's original values were about 0.4% is 1.6022 X low because of a slight error in air viscosity used in the calculation.) The charge on a mole of electrons had been known for some time to be about 96,500 coulombs (one faraday), the amount of electricity needed to plate out one gram equivalent weight of a metal (e.g., 107.87 grams of silver). The currently accepted value for the faraday is 96,485 coulombs. Dividing the charge on a mole of electrons by the charge on a single electron yields the number of electrons in amole, or Avogadro's number.
across the water as a monomolecular film, the carhoxyl groups attaching themselves to the water layer and the hydrocarbon chains remaining in the non-aqueous layer. The area ( A ) of the acid mona1 :-er (which only partially coven the water surface) is measured. Then the height ( L )of the monolaver film is calculated from the density (D) of ;he pure fatty acid and other recorded measurements.
cm. If one Bssumes For oleie acid L is calculated to be about 1.3 X a cubic shape for the fatty acid molecule, then its volume is
L3 = (1.3 X = 6.0220 X
loz3electrons per mole
For many years this was the most accurate method available for determining Avogadro's numher. Radioactive Disintegration Method This technique is based on the fact that as radium undergoes radioactivedecay it gives off alpha particles (He2+ions) which pickup electrons from the environment to become helium atoms. The number of alpha particles given off by a sample of radium per unit time can he measured with a Geiger counter. (This was first accomplished by Ernest Rutherford and Hans Geiger in 1908.) The moles of helium produced over a given time period can be determined by measuring the volume of gas formed. (This was first done in 1910 by Sir James Dewar, who measured the amount of helium produced from a 70 mg sample of radium chloride over a period of 9 months. The total quantity of helium was only about 9 cuhic millimeters.) Careful measurements have shown that alpha decay of a mole of radium-226 yields 0.815 X lor3 disintegrations per second and produces helium gas a t the rate of 1.35 X lo-" mole per second. Avogadro's number is obtained directly from these measurements.
This is a very convincing method for obtaining Avogadro's numher because the principle involved is so simple. X-ray Diffraction Method oer atom in a ervstal can be determined from X-rav The - - volume ~ ~ diffractinn the use of the Braze ........... .. data throneh "~~~ ,... eouation. while volume per mole can brohtmnrd i n m dm+ measurements (Max von L a w llrit demonstrated X-raydiflraction in 1912,and M'. l.awrnre B n g g developed his constructive interference equation, nA = 2d sint, soon after in that same year.) Since density measurement and X-ray diffraction can hoth be carried out with high precision on very pure crystals, this can he an exceptionally accurate method for obtaining Avogadro's number. For example, the silicon crystal is a diamond-like stn~cturewith a cubic unit cell containine 8 silicon atoms. Braea's law calculations hosed ion X-ray diftrartwn measurcmrnts at the National Hurcnu of Standards have shown the unir cell tu be 5 4310lXl X 10-" cn, on s side. This givw rhr wlurnr ppr silinm atom as follows ~
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(5.4310661 X lo-' = 2,0024666 Cm3 8 The molar volume of silicon is obtained bv dividing its molar mass
Dividing the molar volume by the volume per atom yields the number of atoms in B mole.
At preirnt rhr X-ra) method is the must prerisr method available ior detrrmin~ngAwgauru'j numher. Olwiously the accuracy of the d r terminnrwm must drprnd heady cm thr rurrcme purity and flawl~zs condition of the crystals used. Surface Film Method This last method is included here mainly because it is a popular laboratory experiment for chemistry and physics classes. It involves dividing the molar volume of a fatty acid by the volume of a single molecule, determined by floating afatty acid monolayer on water. A small volume (V) of a long chain fatty acid (such as aleic) is dissolved in a solvent (such aspentane) at a certain concentration (C)and delivered from a pipette onto a clean water surface. The acid spreads
~ m= )2.2~X
em3
(This is only a rough approximation of molecular volume because the molecule is not really cubic.) The volume per mole of the fatty acid is calculated by dividing its molar weight by its density. For oleic acid 286 g/mols = 327 cm31mol mol. wt. Molar volume = - 0.873 D glcm Avogadro's number is obtained by dividing this molar volume by the volume of one molecule. 327 cm3/mol = 1.5 X 102bmolecules/mol 2.2 X cm3/molecule More accurate values are obtained when the shape of the molecule is assumed to be rectangular or cylindrical with its length twice as great as its width.
Using the Mole T h e mole (abbreviated mol) is t h e scientific u n i t for "amount of substance," so it is used frequently in chemistry. It is usually represented b y n, which s t a n d s for n u m b e r of moles. Since t h e convenient way t o measure quantity for most substances is to weigh t h e m , i t is often necessary t o convert moles to grams, or grams t o moles. All t h a t is needed to m a k e the conversion is t h e formula weight. Expressed i n grams, it is t h e molar weight.
T h i s relationship is indispensable i n t h e solving of most chemical problems. Solution concentration is normally expressed as molarity (M), t h e n u m h e r of moles of solute p e r liter of solution. molarity =
moles of solute or liters of solution
=
" 1
T h e n it is also t r u e t h a t moles of solute = liters X molarity or n = 1 X M a n d since n is also equal t o g l m . ~ . ,i t follows t h a t l X M = - o r8g = l X M X m . w . m.u.
I n other words, to make u p a solution of compound A, weigh o u t a n a m o u n t of A equal t o its formula weight in grams multiplied by t h e desired molarity of t h e solution a n d t h e n u m b e r of liters being prepared. I n cases involving colligative properties of solutions, it i s usually more convenient to express concentration in terms of molality (m), t h e n u m h e r of moles of solute p e r kilogram of solvent. moles of solute =n(Sdute1 kilograms of solvent k8n(80tveDt~ For example, the depression of freezing point of a solvent by a solute is given b y t h e equation ATl = Kfm, where ATf is t h e change in freezing point, K, is t h e molal freezing point constant, and m is molality. Sometimes it is desirable to have t h e a m o u n t s of h o t h solute a n d solvent expressed i n moles. Concentration c a n t h e n be expressed in terms of mole fraction. number of mdrs c,tX molr irnction of X = total numhrr ot mobs W h e r e gases a r e concerned, t h e n u m h e r of moles is depend e n t o n the pressure, volume, a n d temperature of t h e gas. molality =
Volume 55, Number 11, November 1978 1 731
This is the equation of state for an ideal gas, hut it is approximately true for all real gases. Any units may be used for pressure. volume. and absolute temperature so long as the yalue f o i t h e gas constant, R , is correct for the unitschosen. 3ince n = gramsimol. wt., then it is also true that
Thus, the molar weight of a gas is easify obtained if the mass , f a sample is known as well as its volume a t a certain temperature and pressure. These are only a few examples of how the mole is used in first year chemistry courses. Not to understand the mole concept is obviously a serious handicap for a chemistry student. When the mole is too large or too small to he convenient as 3 counting unit, its size can he modified by an appropriate prefix (e.g., millimole or ton-mole). The mass of the new molar unit still equals the formula weight, but expressed in mass units other than grams. Modified molar quantities can he treated just like gram moles as long as the units are used consistently. If formula weight is e x p r e s s e d in
t h e amount of substance is a
with entities that number
g r a m s (gl milligrams (mg) nanograms (ng) kilograms (kg) pounds tans
m a l e (moi) millimole (mmol) nanomole (nmoll kilomole (kmol) pound-mole ton-mole
6.02 x loz3 6.02 X loz0
A chemical formula represents one molecule of a substance, hut it also represents a mole of it. When thinking about chemical reactions, we tend to think in terms of single molecules, hut when we carry out the reactions we mustuse very large numbers of molecules in order to see what we are doing. So we count out the molecules by moles.
A mole is a oarticular amount
A mole is a specificquantity: Its volume measures twenty-two point four In liters (for a gas at STP). A mole's a counting unit, nothing more. A mole is but a single molecule Rv Avoendro's number multiolied: . . One entity, extremely miniscule, A trillion trillion times intensified. A mole is an expedient amount, For molecules are just too small to count. A
6.46 X lo2'
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- - --- - -- .- .
6.02 X 10" 6.02 X 10'' 2.73 X 10''
Changing the unit of mass simply alters the size of the basic counting unit. The mole concept is useful for counting amounts of elementary entities other than atoms, ions, and molecules. A mole of electrons, for instance, is a faraday, and a mole of photons (energy quanta) is an einstein. Even when speaking of a mole of an element or compound, one should always make it clear what kind of unit he is talking about. "A mole of hromine" can mean 80 g or 160g of hromine. A mole of hromine atoms weighs 80 g, hut a mole of bromine molecules weighs 160 g. T o avoid ambiguity the nature of the elementary entity should he specified.
40 grams of bromine
The molar mass of sulfur is ordinarilv taken to he 32 e, hut sulfur exists as 8-membered rings, a n d a mole of Ss mol&ules would weigh 256 g. There are also compounds for which it is not alwaysclear just what constitutes ;mole. Should mercury(1) chloride he considered as HgCl or Hg2C12?Should aluminum bromide he treated as AIBr3 or as A12Br6?Should the molar weight of acetic acid he based on CH3COOH or (CHXOOH).,. dimer? How do vou . ., , -. the hvdroeen-bonded " decide what formula weight touse for apolymer? And how do vou calculate the formula weieht of a non-stoichiometric
40 g = 0.25 mol "Bra = 160 g/mol
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References Guggenheim. E. A,. "The Mote and Related Quantities." J. CHEM. EDUC.. 38, 86 119611. Hawthorne. R. M., Jr., "Avogadro's Number: Early Valuea by Lmehmidf and Others: J. CHEM.EDUC.,47.751 11970). Hawthorne. R. M., Jr.. "The Mole and Avogadre's Number." J. CHEM. EDUC.. SO. 282 119731. Hildebrand. J. H., and Powell. R. E., "Principles of Chemistry,('7th ad., Chapter 21. The MaemillanCo.,NewYork 1964. Kidfor, W. F.."The Mate Concept in Chemistry: Reinhold. New York, 1962. L. Kine. ". C.. and Nielson. E. K.. "Estimation of Avozadro'r Number: J. CHEM. EDUC.. 35.19811958). Novick, S..snd Menis, J.,"AStudy of StudentPerceptionsof theMoleConeept"J. CHEM. EDUC.. 53.720 119761. Sanders. J. H., "The Fundamental Atomic Constants:' Oxford Uniu. Press, London. 1961. Number by Four Methods: 3. CHEM. EDUC.. 16, 40 Slabaugh, W. H.. ~~Avogadro's 11969). Sunier,A. A,, "Some Methadsol Determining Auogadro'a Number." J. CHEM EDUC.,6. 299 11929).
Chemistry Class Roster II Ms. Spectrum (teacher) "Ox" Alec Acid
Mat Athesis Desi Cator A1 Chemist Vic Dial Ken Etics R. B. Flask
Cloe Form Sol Furic Nan 0.Gram Sis Isomer S. T. Joints Lynn 0.Lenic "Red" Litmus
'For Chemistry Class Roster I, see Felty, W. L., J. CHEM. EDUC., 55,245 (1978).
'32 1 Journal of Chemical Education
Mel T. Point Abe Solute Phil Trait Pete Tridish Rhoda Vaporator I. Wash Kim Wipes Cristol I. Zing Dwight Northfield, W. Chasar Ohio
