mass
'no magic to the mole'
amount
molar mass
concentration
solution volume
gas volume
molar gas volume
Avogadro
constant, L
number of
entities, N
Now try the following question.
X3. AVOID AVOGADRO'S CONSTANT ON FIRST TEACHING OF AMOUNT
In the unnecessary and misguided quest to explain to pupils at the outset what a mole actually is, a majority of instructors perhaps - across all levels of experience - choose to introduce the Avogadro number in an attempt to clarify matters.
From the pupils' viewpoint, it achieves no such thing: immediately one is placing demands on them to conflate the relationships n = m / M with N = n L, typically in an effort to solve a problem like:
The most capable candidates, probably working two or more years ahead of their class or grade level, might embrace this degree of complexity early in the proceedings. But, in the vast majority of cases, it is too much too soon, before the use of the SI unit symbol mol has been firmly established. Logical sequencing will have gone out the window as the macroscopic observational picture and nanoscopic particle model are muddled early and simultaneously.
Professor A. H. Johnstone (1930-2017) - of the University of Glasgow and D fame - 'realised that the novice learners cannot handle macroscopic, nanoscopic and symbolic levels at the same time due to the limitations in the capacity of the working memory. He argued that, in the early stages in learning chemistry, we must be very careful not to attempt to bring in explanations and representations until the descriptive aspects are well established.' See
'A tribute to Professor Alex H Johnstone (1930–2017) His unique contribution to chemistry education research'
by Norman Reid. From the journal Chemistry Teacher International. doi: org/10.1515/cti-2018-0016
In fact, for calculations that require use of the Avogadro constant, there are very good reasons for leaving the topic until after stoichiometry has been dealt with. After all, an apparently simple calculation of the type:
is a de facto stoichiometry problem, since the dissociation of the ionic lattice must be contemplated. This is a far from simple task for a near beginner, however.
It is worth pointing out here the distinction between the Avogadro number and Avogadro constant: the latter is a physical quantity with dimensions reciprocal mole, / mol; the former is a pure number.
So the relation N = n L where N represents the number of elementary chemical entities, is only dimensionally homogeneous when L has units / mol, those belonging to the Avogadro constant, rather than the dimensionless Avogadro number.
Pupils are normally far better served if the first time they come across Avogadro in the context of introductory chemical calculations, it is in seeing the Avogadro postulate (aka hypothesis, principle, theory, law) and the approximately constant nature of molar gas volume for dilute gases, i.e., those existing at low pressure.
This provides the opportunity to solve successfully problems of the type:
In using the relationship
however, the corresponding units of molar volume should be addressed:
In all likelihood, the audience should have met derived units for density, molar mass, and perhaps concentration, before they come across the likes of L / mol. It should not be too difficult to see that the dimensions of molar gas volume are those of reciprocal concentration, in the same manner that the units for time (s) and frequency (/ s or Hz) bear a resemblance, as would be made clear from physics. If pupils have already met Avogadro in the shape of the derived unit for molar gas volume then, when the time comes, they are far less likely to feel intimidated by the unit associated with his constant, L or NA.
When discussing gas volume, inevitably the temperature and pressure under which measurements are taken will likely arise. While the loose 'RTP' specified for elementary courses like i/GCSE generally elicits a molar gas volume of 24 L / mol, the picture varies considerably with curriculum. In turn this affects numerical values generated in answers to problems requiring calculation of a gas volume.
For reference purposes, the table below should contain sufficient necessary detail.
The strong recommendation of this author, therefore, is to deal with simple calculations that require use of molar gas volume - underpinned by the Avogadro postulate - some time before attempting any calculations relying on the Avogadro constant. Getting pedagogical delivery of the Avogadro constant and N = n L out of logical sequence creates conceptual problems for pupils that might last years, not weeks. At the pre-16 level, the effect of such a blunder might well be to convince otherwise perfectly able candidates that they are not capable of tackling an advanced chemistry course. Instead, they select other options: politics, history, art, history of art, geography, business studies or economics; you know the score. Instructors' inability to deliver the quantitative components competently is the major contributor to any haemorrhaging of uptake in chemistry at IB / AP / A level, etc.
Historically, the Avogadro postulate (1811) was published nearly 100 years before J-B. Perrin's famous work (1908) - based on Einstein’s Brownian motion paper (1905) - managed to determine experimentally how many molecules are present in a volume containing 1 g-molecule
of gas: 6.8 x 10 from his data. Since the ideal gas law (1834) - of
which Avogadro's law is a special case - and the kinetic theory of gases
(1738-1908), gave that equal volumes of dilute gases under the identical conditions of temperature and pressure should contain the same number of molecules, Perrin coined the term Avogadro number.
23
Avogadro had died four years before the Karlsruhe Congress (1860) where Stanislao Cannizzaro FRS (1826-1910) finally had the scientific community appreciate the great importance of his theory of diatomic molecules that had been ignored for half a century. The theory paved the way for his own publication (1858) in the journal Nuovo Cimento:
“Sunto de un corso di filosofia chimica” ('Summary of a chemical philosophy course'), in which he clearly explained how to determine the atomic and molecular weights of elements and compounds respectively. Confusion about these weights and the fundamental structure of chemical compounds were the order of the day in the late 1850s. Cannizzaro's recognition of true atomic weights allowed Meyer (1864 & 1870) and Mendeleev (1869) to articulate the famous periodic law within a decade.
In modern science, the purpose of the physical quantity amount of substance and its SI unit mole is to operate at the bulk - macroscopic - level while avoiding being concerned with a direct count of the likes of molecules and atoms, as would be the case on a nanoscopic level. It is surprising, therefore, that early on in the chemical calculations' arena, many educators demand that their charges fixate on the nanoscopic, viz 'Calculate the number of atoms...'. While likely coerced by examiners enthusiasm particularly for multiple choice questions of this type, approaching such questions should not be made a priority in the early stages.
To begin with, the unit mol need only be used for comparing chemical amounts of different substances. Indeed, if one intends later to teach stoichiometry using the method of stoichiometric masses rather than stoichiometric amounts, the need for a more sophisticated understanding of the mole will likely not be required.
Where pupils are unlikely to continue with chemistry at 16+, the method of stoichiometric masses has much to recommend it. The chief disadvantage is that it can be a difficult routine to jettison for those who do continue, where a far wider range of calculations must be tackled.
In mixed ability settings at the GCSE or equivalent level, therefore, skilled practitioners should be giving serious thought to delivering a dual-channelled programme: higher-ability pupils embrace the ideas of amount of substance; others would focus on the proportionality that stoichiometric masses offer to obtain the correct answer with a minimum of fuss.
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