The mole - unit and concept

Featured paper

Fang, S.C., Hart, C. and Clarke, D. (2014) 'Unpacking the meaning of the mole concept for secondary school teachers and students', Journal of Chemical Education, 91, pp. 351-356.

This paper reports the findings of an in-depth content analysis relating to the concept of the mole. This content analysis was used by the authors to form of a concept map. 

Unlike other SI units such as the gram and the second, the mole is often described as the "mole concept". The concept map provides a visualisation of the interconnected sub-concepts that are needed to understand the wider mole concept. The authors suggest that the concept map could be a useful tool for teachers in thinking about how they could meaningfully teach the mole concept to students.

Please note that the authors used the  IUPAC definition of a mole that was valid at the time of publication  rather than the most recent version.

A mole is the amount of substance which contains as many elementary entities as there are in carbon atoms in 0.012kg of carbon-12.  When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particle or specified groups of such particles.

The authors created a concept map (illustrated below) to show how specific sub-concepts connect to enable an overall understanding of the mole concept. 

The authors describe the idea of the amount of substance (in moles) as being the bridge that links the number of elementary entities to the mass of a substance.

The concept map includes some sub-concepts that are linked to understanding of atoms, molecules and relative atomic and molecular mass as well as sub-concepts linked specifically to the mole concept. Identification of the importance of the atomic-molecular concept in understanding the mole concept was a key outcome of the content analysis. 

The atomic-molecular sub-concepts link to the mole concept in two different ways.

Link 1 - connecting the sub-concept of atoms and molecules to the number aspect of the mole concept

This idea connects the concept of a single atom or molecule (or other elementary entity) with the idea of thinking about a ‘standard pack’ of atoms or molecules called the mole.
This idea of aggregating atoms or molecules into a “standard pack” does not explain to students why the number 6.02x10^23 was chosen as the number in this “standard pack.” This number is not mentioned in the original definition of the mole.
The authors suggest that students are taught that the number of atoms in 12g of carbon-12 was experimentally determined to be 6.02x10^23.

Link 2 - connecting the sub-concept of relative atomic or molecular mass to the mass aspect of the mole concept

By definition, one mole of any substance always has the same number of elementary entities as 12g of carbon-12. If the number of elementary entities of different elements are the same, then the ratio of their masses will be the same as the ratio of their atomic or molecular masses.
Due to the choice of 12g of carbon-12 being the measure of one mole, the relative atomic mass of any other element in g will also contain one mole of atoms.

The authors alert teachers that this understanding requires students to use proportional reasoning. 

Consequences for teaching

The authors recommend that in order to meaningfully teacher students about the mole they should guide students to make the connection between the atomic-molecular concept to both the number and mass aspects of the mole concept. 

BEST Diagnostic Question

Relative atomic mass

Every element has a relative atomic mass.
You can find the relative atomic mass of an element in the Periodic Table.
Which answer best states the relative atomic mass of helium?

A 4g
B 4mg
C 4
D 4x10^-9g

The correct answer is A. Relative atomic mass does not have a unit.
A student who chooses option A may hold the misconception that relative atomic mass is the same as the molar mass, which is measured in g.
Selection of option B or D may suggest that a student thinks that relative atomic mass is the mass of an actual atom (which is smaller than a gram).

Reflective questions

How do you first introduce the mole? 

What connections do you make with earlier understanding?

To what extent does the current definition make the mole concept easier or more difficult to understand?

The current IUPAC definition of a mole is:
The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.02214075x1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in mol^-1, and is called the Avogadro number.

Useful links

BEST Topic 6 Key Concept 1: Amount of substance

Diagnostic questions to check for student misconceptions about the atomic model as part of a five-part progression (and including response activities)

University of York Science Education Group

Welcome to the SciEd Distillery

 

Being “research informed” is considered essential for anyone working in education but a huge swathe of the research literature is inaccessible to anyone who does not work in a university setting.

During the four years that I worked for the University of York Science Education Group as the chemistry lead on the Best Evidence Science Teaching project I searched out chemistry education research papers that identified misconceptions of students aged 11-16.

More recently I have been working for the Centre for Industry Education Collaboration trawling the science education literature relating to the misconceptions of primary children (aged 5-11).

Many of these papers related to small studies and individually do not draw conclusions that are significant enough to have a direct impact on changing practice in the classroom. However, some of the papers made me stop and think about the curriculum and how science is taught. These are the papers that I am planning to feature in the SciEd Distillery. 

This blog uses the metaphor of a distillery to encapsulate the process by which I shall be distilling these thought-provoking ideas from more lengthy research papers.   

These ideas will not tell you what the research advises you to do but my intention is that they will support you to reflect on your own practice.

Having had the time and opportunity to explore the research literature I am now looking forward to sharing more widely the essence of some fascinating research relating to science education.

 

Atomic models in the curriculum

Featured paper

Taber , K. S. (2003) 'The atom in the chemistry curriculum: Fundamental concept, teaching model or epistemological obstacle?', Foundations of Chemistry, 5, pp. 43-84.

It is no surprise that students in school hold alternative conceptions about ‘the atom'. This paper by Keith Taber discusses why students may acquire ideas about the atom that differ from modern scientific understanding. The key argument made in this paper is that these alternative ideas stem, in part, from the way atoms are presented in the school curriculum. The paper discusses how the concept of the atom met in the curriculum is not coherent and is based on historical models. 

For the full argument it is important to read the original paper as expressed by the author but a few key points that have influenced my work are summarised here. These relate to how the atom is described at different points in a typical chemistry curriculum and how the word 'atom' is used in teaching different age groups. The fact that these are not always the same is a reason that this paper is one I return to repeatedly. 

The concept of the atom that is often first presented to students is of atoms being the indivisible and forming the constituent particles of all substances. Elements are defined as being made up of ‘one type of atom’ in contrast with compounds which are made up of ‘two or more types of atom’. Chemical reactions are described as the ‘rearrangement of atoms’. The idea of an atom as indivisible is clearly a much older model of the atom than even more recent historical models. 

The paper suggests that students may continue to attribute to atoms the property of being indivisible and of forming the constituent particles of all substances even when a later model of the atom has been introduced. However this earlier indivisible model of the atom may still be referred to in teaching older students.  At age 14 to 16 students should understand that an atom is not indivisible because it is made up of sub-atomic particles but the term 'atom' may still be used to mean the more simple model when convenient. As students learn about structure and bonding, they should recognise that substances may be made up of ions or molecules rather than complete atoms. This concept is essential for further understanding for example to understand the concept of a mole. One mole of the substance oxygen is not one mole of oxygen atoms it is one mole of oxygen molecules.

In this paper Keith Taber coins the term ‘atomic core’ to refer to the nucleus of an atom plus the inner electrons and argues that very often, when the word ‘atom’ is used in the curriculum, it is actually an atomic core that is referred to. 

This idea of an 'atomic' core prompted to me to reflect on exactly what is meant when the term atom is used in teaching in a variety of scenarios. The questions below were inspired by this thinking.
 

Developing Understanding question

This question for the RSC’s Developing Understanding series asks students to think about what is represented in a diagram of the structure of diamond.

Diamond has a three-dimensional giant molecular structure.
The diagram below shows a representation of the structure of diamond.

a.    Which part of a carbon atom is represented by a line on the diagram?

A nucleus    
B shared pair of outer electrons
C nucleus and inner electrons
D inner electrons

b.    Which part of a carbon atom is represented by a circle?

A nucleus    
B shared pair of outer electrons
C nucleus and inner electrons
D inner electrons

Even though the circles in this sort of diagram would commonly be called atoms, they actually represent just the nucleus and inner electrons of each atom, or what Keith Taber referred to as the ‘atomic core.’
 

BEST Diagnostic Question

Comparing models

The diagnostic question checks whether students are able to compare the particle model and the atomic model.

 
A helium atom may be represented using the particle model and the atomic model.

Some students compare the two different models.
Who do you agree with, and why?

A student who agrees with Aaron is demonstrating an understanding that a model is not a direct reflection of reality. Agreement with Arush shows recognition that a model has a purpose and that in some cases a simpler model may provide a clearer explanation.

Reflective questions

How and when do you use the term ‘atom’ in your teaching?

What do you actually mean each time use use the term 'atom'?

Does your use of the term change with different phases of the curriculum?

Useful links

Developing Understanding: Carbon allotropes

A ramped student worksheet that aims to help students to deepen their understanding of carbon allotropes and to strengthen their mental models. 

Royal Society of Chemistry

 
BEST Topic 6 Key concept 1: Atomic model

Diagnostic questions to check for student misconceptions about the atomic model as part of a five-part progression (and including response activities)

University of York Science Education Group

Metallic bonding representations

 

Featured paper

de Posada, J. E. M. (1999). The presentation of metallic bonding in high school science textbooks during three decades: Science educational reforms and substantive changes of tendencies. Science Education, 83, 423-447.

In this study the authors analysed 58 Spanish high school chemistry textbooks from 1974-1998 in relation to their treatment of metallic bonding

The authors found that every textbook explained that metals are made up of metal cations (positive ions) and free electrons, but very few explicitly acknowledged that this is a theoretical model. Unsurprisingly at the level of textbook being examined, very few mentioned the band theory of metals.

Graphical representations

The graphics used to represent the metallic bonding model varied. Some diagrams represented electrons as particles, but others showed the delocalised electrons as a cloud. A student who is operating only in terms of the surface features of the diagrams would observe lines, circles, symbols and shading. The authors suggest that the diversity of these diagrams is confusing for students.

Language

The authors noted that the language used to describe metallic bonding uses metaphors, for example a ‘sea’ of electrons and a metallic ‘lattice’. Students use these words in everyday life and may therefore bring their own existing ideas with them to the chemistry classroom. The authors suggest that textbooks should make clear which attribute of the metaphor is linked to metallic bonding.

Reflective questions

How could you support students to interpret the range of metallic bonding diagrams that they may encounter?

How could you clarify the metaphorical language used so that students understand which attributes apply to metallic bonding and which do not?

BEST Diagnostic question

Metallic structure diagrams

This question was devised to show four students that are thinking in different ways about representations of metallic structure and bonding. Exploring your own students' views may help you to understand if their thinking is similar to any of the students in the question. 

Some students have drawn diagrams to show how they think about the structure of a metal.

1. Whose thinking do you most agree with?

2. Whose thinking do you disagree with?

Explain your answers

The diagram by student A has a balance of positive and negative charge and pictures the electrons in particle form which is consistent with the model of the atom commonly taught to the 14 to 16 age group.

Student C’s thinking does not include any negative charge at all. Agreement with this way of thinking could suggest a literal interpretation of the idea that metallic structure is made up of positive metal ions surrounded by a ‘sea of electrons'.

A student who most agrees with student B’s thinking may also have been influenced by references to a ‘sea of electrons. The student may be taking the metaphor more literally than it is intended by representing the structure with a vast number of electrons.

Agreement with the thinking of student D may also indicate misunderstanding about a ‘sea of electrons’ as it could be representing the electrons as being in the sea. Alternatively, it may be indicating a continuous area of negative charge. This is inconsistent with the model of the atom commonly taught at this age which treats electrons as being particles. 

Useful resources

BEST Topic 7 Key Concept1: Metallic structure model

Diagnostic questions to check for student misconceptions about metallic bonding as part of a five-part progression (and including response activities)

University of York Science Education Group

Developing Understanding: Metallic bonding

A ramped student worksheet that aims to help students to deepen their understanding of metallic bonding and to strengthen their mental models.

Royal Society of Chemistry

Metallic bonding models

Featured paper

Cheng, M. M. W. and Oon, P.T. (2016). Understanding metallic bonding: Structure, process and interaction by Rasch analysis. International Journal of Science Education, 38(12), 1923-1944.

 

The authors categorise three ways in which students think about metallic bonding.

1.      As a structure – a lattice arrangement of cations (positive ions) and delocalised electrons

2.       As a process – metal atoms losing outer electrons to form a ‘sea of electrons’

3.       As an interaction – a lattice arrangement of cations held together by electrostatic attractions between    these positive ions and the free electrons

The study aimed to test if structure, process and interactions were at increased levels of understanding. 3006 year 10-12 students in Hong Kong took part in the research survey.

The research study supported an order of difficulty where thinking of metallic bonding as an interaction was the model that was the most difficult:

interaction > process > structure

In Year 7-9 in Hong Kong a ‘particle model’ was used. This describes metals as being made of particles with each metal being made of one kind of particle. Changes of state were explained as a change in arrangement of these particles, but forces of attraction are not considered.

From Year 10 a ‘free electron’ model was used in which metals are made of a lattice of positive metal ions with delocalised electrons moving around them. This structure is held together by an all-directional electrostatic force.

When students are taught the initial particle model in this curriculum the focus of thinking is on structure. Later, to fully understand the ‘free electron model’ students must move to thinking in terms of interactions. The authors suggest that this shift is a challenge for students. Some students may remain thinking in terms only of structure. Consequently, they may not fully gain an understanding of metallic bonding as a form of electrostatic interaction.

Reflective questions

In your curriculum, does the initial particle taught at age 11-14 include the idea of forces of attraction between particles? What are the benefits and drawbacks of including this concept from the outset?

Are your students able to select and justify their choice of the most appropriate model to explain different properties of metals such as malleability and electrical conductivity?

Useful resources

Developing Understanding: Metallic bonding  

A ramped student worksheet that aims to help students to deepen their understanding of metallic bonding and to strengthen their mental models.

Royal Society of Chemistry

BEST Topic 7 Key Concept 1: Metallic structure model

Diagnostic questions to check for student misconceptions about metallic bonding as part of a five-part progression with additional response activities.

University of York Science Education Group