9C.2.1.2.4 Moles & STEM Interactions
Demonstrate how unit consistency and dimensional analysis can guide the calculation of quantitative solutions and verification of results.
Use significant figures and an understanding of accuracy and precision in scientific measurements to determine and express the uncertainty of a result.
Determine the molar mass of a compound from its chemical formula and a table of atomic masses; convert the mass of a molecular substance to moles, number of particles, or volume of gas at standard temperature and pressure.
Determine percent composition, empirical formulas and molecular formulas of simple compounds.
Overview
MN Standard in Lay Terms
1. Abstract concepts such as modern atomic theory can be visualized with the use of models. Models are representations NOT actual theories.
2. Atoms are held together by chemical bonds which involve the interaction of an atoms' electrons. Atoms in a compound have properties such as mass and percentage composition. Atoms and molecules are "counted" in packages of moles, a unit fundamental to chemistry calculations.
3. Science requires the application of mathematics and the use of technology and engineering. All of these are interrelated and utilized with each other.
Big Idea
1. Physical, mathematical, and conceptual models are tools for learning about the things they are meant to resemble. Physical models are by far the most obvious so they should be used to introduce the idea of models. Mathematical modeling shows the nature and power of models and provides a context for integrating knowledge from many different domains. The main goal should be getting students to learn how to create and use models in many different contexts, not simply to recite generalizations about models. Students should understand that there may be no "true" model at all. (Benchmarks of Science Literacy)
2. The microscopic properties of atoms and molecules can be made macroscopic by the use of the chemical mole. The mole allows chemists to organize atoms and molecules into packages that are measurable and quantifiable. Ratios of moles are equivalent to ratios of atoms which allows for measurement and prediction on a macroscopic level. The properties of one atom are the properties of a mole of atoms.
3. Scientific inquiry is driven by the desire to understand the natural world, and technological design is driven by the need to meet human needs and solve human problems. Technology has a more direct effect on society than science because its purpose is to solve human problems, help humans adapt, and fulfill human inspirations. Technological solutions may create new problems. Science answers questions that may or may not directly influence humans.
MN Standard Benchmarks
9.1.3.4.5 Demonstrate how unit consistency and dimensional analysis can guide the calculation of quantitative solutions and verification of results.
9C.1.3.4.1 Use significant figures and an understanding of accuracy and precision in scientific measurements to determine and express the uncertainty of a result.
9C.2.1.2.4 Determine the molar mass of a compound from its chemical formula and a table of atomic masses; convert the mass of a molecular substance to moles, number of particles, or volume of gas at standard temperature and pressure.
9C.2.1.2.5 Determine percent composition, empirical formulas and molecular formulas of simple compounds.
The Essentials
Structure and properties of matter
12BPS2.1 Atoms interact with one another by transferring or sharing electrons that are furthest from the nucleus. These outer electrons govern the chemical properties of the element.
12BPS2.2 An element is composed of a single type of atom. When elements are listed in order according to the number of protons (called the atomic number), repeating patterns of physical and chemical properties identify families of elements with similar properties. This "Periodic Table" is a consequence of the repeating pattern of outermost electrons and their permitted energies.
12BPS2.3 Bonds between atoms are created when electrons are paired up by being transferred or shared. A substance composed of a single kind of atom is called an element. The atoms may be bonded together into molecules or crystalline solids. A compound is formed when two or more kinds of atoms bind together chemically.
12BPS2.4 The physical properties of compounds reflect the nature of the interactions among its molecules. These interactions are determined by the structure of the molecule, including the constituent atoms and the distances and angles between them.
Understandings about science and technology
12EST2.1 Scientists in different disciplines ask different questions, use different methods of investigation, and accept different types of evidence to support their explanations. Many scientific investigations require the contributions of individuals from different disciplines, including engineering. New disciplines of science, such as geophysics and biochemistry often emerge at the interface of two older disciplines.
12EST2.2 Science often advances with the introduction of new technologies. Solving technological problems often results in new scientific knowledge. New technologies often extend the current levels of scientific understanding and introduce new areas of research.
12EST2.3 Creativity, imagination, and a good knowledge base are all required in the work of science and engineering.
12EST2.4 Science and technology are pursued for different purposes. Scientific inquiry is driven by the desire to understand the natural world, and technological design is driven by the need to meet human needs and solve human problems. Technology, by its nature, has a more direct effect on society than science because its purpose is to solve human problems, help humans adapt, and fulfill human inspirations. Technological solutions may create new problems. Science, by its nature, answers questions that may or may not directly influence humans. Sometimes scientific advances challenge people's beliefs and practical explanations concerning various aspects of the world.
12EST2.5 Technological knowledge is often not made public because of patents and the financial potential of the idea or invention. Scientific knowledge is made public through presentations at professional meetings and publications in scientific journals.
Physical Setting: Structure of Matter
Atoms often join with one another in various combinations in distinct molecules or in repeating three-dimensional crystal patterns. 4D/H7a
Mathematics, Science and Technology
Mathematics and science as enterprises share many values and features: belief in order, ideals of honesty and openness, the importance of criticism by colleagues, and the essential role played by imagination. 2B/H2
Mathematics provides a precise language to describe objects and events and the relationships among them. In addition, mathematics provides tools for solving problems, analyzing data, and making logical arguments. 2B/H3*
Developments in science or technology often stimulate innovations in mathematics by presenting new kinds of problems to be solved. 2B/H4a
Developments in mathematics often stimulate innovations in science and technology. 2B/H5
A mathematical model uses rules and relationships to describe and predict objects and events in the real world. 11B/H1a*
A mathematical model may give insight about how something really works or may fit observations very well without any intuitive meaning. 11B/H1b
Computers have greatly improved the power and use of mathematical models by performing computations that are very long, very complicated, or repetitive. Therefore, computers can reveal the consequences of applying complex rules or of changing the rules. The graphic capabilities of computers make them useful in the design and simulated testing of devices and structures and in the simulation of complicated processes. 11B/H2*
The usefulness of a model can be tested by comparing its predictions to actual observations in the real world. But a close match does not necessarily mean that other models would not work equally well or better. 11B/H3*
Often, a mathematical model may fit a phenomenon over a small range of conditions (such as temperature or time), but it may not fit well over a wider range. 11B/H4** (SFAA)
The behavior of a physical model cannot ever be expected to represent the full-scale phenomenon with complete accuracy, not even in the limited set of characteristics being studied. The inappropriateness of a model may be related to differences between the model and what is being modeled. 11B/H5** (SFAA)
Technological problems and advances often create a demand for new scientific knowledge, and new technologies make it possible for scientists to extend their research in new ways or to undertake entirely new lines of research. The very availability of new technology itself often sparks scientific advances. 3A/H1*
Mathematics, creativity, logic, and originality are all needed to improve technology. 3A/H2
Technology usually affects society more directly than science does because technology solves practical problems and serves human needs (and also creates new problems and needs). 3A/H3a*
One way science affects society is by stimulating and satisfying people's curiosity and enlarging or challenging their views of what the world is like. 3A/H3b*
Engineers use knowledge of science and technology, together with strategies of design, to solve practical problems. Scientific knowledge provides a means of estimating what the behavior of things will be even before they are made. Moreover, science often suggests new kinds of behavior that had not even been imagined before, and so leads to new technologies. 3A/H4** (SFAA)
NAEP
Common Core Standards
2010 Literacy Standards - Reading Benchmarks: Literacy in Science and Technical Subjects 6-12
Integration of Knowledge and Ideas Benchmark 11.13.7.7 Integrate and evaluate multiple sources of information presented in diverse formats and media (e.g., quantitative data, video, multimedia) in order to address a question or solve a problem.
Common Core Language Arts Standards: Students can write a laboratory report in the proper form and using their knowledge of technical writing skills. Common Core Standards addresses
RST.9-10-1. Cite specific textual evidence to support analysis of science and technical texts, attending to the precise details of explanations or directions.
RST.9-10-2. Determine the central ideas or conclusions of a text; trace the text's explanation or description of a complex process, phenomena or concept; provide an accurate summary of the text.
RST.9-10.3. Follow precisely a complex multistep procedure when carrying out experiments; taking measurements or performing technical tasks, attending to special cases or exceptions defined in the texts.
Misconceptions
- Students sometimes confuse atomic mass and molar mass. The atomic mass is the mass of one atom expressed in atomic mass units (a.m.u.), the molar mass is the mass of one mole of atoms expressed in grams.
- Students are challenged when asked the number of atoms in a mole of an element such as chlorine. Because chlorine consist of diatomic molecules one mole of chlorine will have two moles of chlorine atoms.
- When determining empirical formulas for compounds students struggle with the concept that one mole of a compound such as water H2O has one mole of oxygen atoms and two moles of hydrogen atoms.
- Students sometimes misunderstand that one mole of a element has a mass in grams equal to the atomic mass of the element by thinking one mole of an elements is the mass in grams, for example one mole of carbon has a mass of 12.0 grams.
- Some research suggests that students can understand and use the engineering model before they can the scientific model-that is, that students inevitably will think about producing desirable outcomes before they are able to do the more analytic form of thinking involved in scientific inquiry (Schauble et al., 1991). High-school students do not distinguish between the roles of science and technology unless explicitly asked to do so (Fleming, 1987). This is evidenced, for example, by students' view that science serves the public interest. More generally, some students believe science affects society in more positive ways than does technology. That is partly because students associate science with medical research but associate technology with pollution or weapons. Students appear to understand the impact of science on technology but they do not always appreciate the impact of technology on science (benchmarks of scientific literacy research base).
- Middle-school and high-school students typically think of models as physical copies of reality, not as conceptual representations (Grosslight et al., 1991).
Vignette
The mole concept and its applications are fundamental to the study of chemistry. Students struggle with the mole concept because "packaging" atoms in such a large quantity (Avogadro's number) is foreign to them. As Ms. Apple introduces the mole concept she works to relate the student's experiences with other package units (such as the dozen or pair) to the mole concept.
Ms. Apple begins the unit with an inquiry challenge which allows students to engage in and explore the concept of "counting by massing." Each lab group is given a film canister filled with pellets, lead shot or plastic beads. (Make sure that the pellets are uniform and of a small enough size that it would be difficult to "count" the pellets.) Ms. Apple tells the student groups that they are to determine the number of pellets in the container without counting them. The students may use any lab equipment and may open the container but they may not count the pellets. She offers a prize to the group that comes closest to the number that she has determined. (Perhaps a "Mole Dollar" Flinn Scientific Mole Dollar.)
Students are puzzled at first. Then many begin to recognize that the number of pellets in the container is related to a property of the pellets such as their mass (some students try to use volume). If the mass of one pellet is known and the mass of all of the pellets is known, the number of pellets will equal the total mass divided by the mass of one. However, if the pellets are small (like lead shot) students will recognize that the mass of one pellet can't be determined very precisely. Some groups mass ten pellets and find the average mass of one pellet. In this way students determine the number of pellets in the container.
After giving students time to work the challenge and turn in their answers Ms. Apple selects the winner and asks that group to explain the process they used. She then asks the students to determine the mass of a dozen pellets. She tells them they are to use only this number (a dozen have a mass of ___grams) to determine the number of pellets in some quantities she gives them, like 152.8 grams. Students use the factor label method with the masses to determine how many dozens of pellets there are then how many individual pellets there are. Students are also asked how many grams of pellets would be needed for one 100,000 pellets.
Next Ms. Apple asks students to discuss how they might determine the number of atoms that would be in a 63.5 gram sample of the element copper. Students are encouraged to share their method with the class. The class discussion leads to the idea that if the mass of one atom is known it can be used to determine the number of atoms. Students can be lead to realize that the mass of an atom is known which is the atom's atomic mass in atomic mass units. Using the mass in grams of 1 atomic mass unit (1.66 x 10-24 g) students can determine that the number of atomic mass units in 1.0 grams is 6.02 x 1023 (Avogadro's number). So an Avogadro's number of copper atoms would have a mass of 63.5 amu / 1gram/ amu = 63.5 grams. Ms. Apple then goes on to explain that an Avogadro's number of atoms is called a mole and is the method by which chemists "package" atoms. This phase of the "learning cycle" (see Best Practices below) introduces the appropriate terms and provides explanations which the students will use in their applications.
Ms. Apple shows students how to convert units such as grams to other units such as moles using "dimensional analysis" (see assessment examples below). She encourages students to show their work using dimensional analysis. Lesson Plans and Practice Problems For Dimensional Analysis
(Benchmark: 9.1.3.4.5 Demonstrate how unit consistency and dimensional analysis can guide the calculation of quantitative solutions and verification of results.)
Ms. Apple continues the unit with students by providing students a number of activities and assignments which reinforce the basics of the mole and its applications. Students should become comfortable determining the molecular or formula mass of a compound, converting grams to moles or moles to grams. Students should also be able to determine the number of atoms in a given number of moles of an element or number of molecules in a given mass of a compound. One application to the mole concept with gases is to determine the volume of a given number of moles of a gas at standard pressure and temperature using molar volume. (Benchmark: 9C.2.1.2.4 Determine the molar mass of a compound from its chemical formula and a table of atomic masses; convert the mass of a molecular substance to moles, number of particles, or volume of gas at standard temperature and pressure.)
There are a number of lab activities that can be done to show students applications of the mole concept. One standard lab activity is to determine the formula of a chemical hydrate. Students heat a sample of a hydrate and by measuring the mass of the hydrate before and after heating the mass of water can be determined. Students use this data to determine the moles of water and dehydrated crystals. The mole ratio of water to crystals gives the formula of the hydrate.
After students are comfortable with the mole concept Ms. Apple provides activities which enable students to determine the percentage by mass of the elements in a compound and empirical formulas (simplest mole ratios of the elements in a formula) and molecular formulas. One lab activity which encompasses several tasks is to find the empirical formula of a compound of copper (II) chloride. This activity involves percentage composition, gram to mole conversions and empirical formulas. Another similar lab is to find the empirical formula of magnesium oxide. (Benchmark: 9C.2.1.2.5 Determine percent composition, empirical formulas and molecular formulas of simple compounds.)
Ms. Apple completes the unit with a performance based assessment. Students are given a sample of a hydrate and asked to determine the percentage of water in the hydrate and its empirical formula in the lab by dehydrating the compound. (Benchmark: 9C.2.1.2.5 Determine percent composition, empirical formulas and molecular formulas of simple compounds.)
Resources
Instructional Suggestions/Options
Encourage students to "show their work" for all calculations. Students should label all measurements when doing various mole calculations. Constantly remind them to show their work and units. If they leave out their units write N3 next to their number, the N3 is an abbreviation for No Naked Numbers! We tell them that in science numbers must "wear" units unlike numbers in math which can "be naked."
Chemical Information Sources For Teaching and Studying Chemistry
It is sometimes the case that a chemist is asked to teach a course with little or no guidance or preparation. Likewise, students could often benefit from consulting supplemental materials to assist in understanding certain aspects of chemistry. This site will lead you to materials and resources that will be useful for both teaching and studying chemistry.
The "Best Practices" of Science Teaching
Many of the best practices are summarized and examples are given in the chapter "Guided inquiry in the science classroom" by Minstrell, J. & Kraus, P. found in How Students Learn: History, Mathematics, and Science in the Classroom. (M. Suzanne Donovan and John D. Bransford, Editors) Washington, DC: National Research Council (2005).
Other best practices are to be found in Robert Marzano's Classroom Instruction that Works. (2001) ASCD
Here are some applications of best practices for the mole benchmarks.
1. The traditional approach is to 1) verbally introduce students to the content to be learned; 2) have students verify what they have just been told through a "recipe" hands-on activity; and 3) complete the lesson with a teacher-led discussion, the assignment of related problems and/or having students apply what they have learned through another structured activity.
Implement the learning cycle by 1) using the materials and/or laboratory first (Exploration); 2) discussing and helping students summarize what they have learned from the laboratory experience and then introducing the appropriate terms (Term Identification); and 3) having students apply what they have learned through another exploration activity or a student generated experiment or a report or a field trip or a class debate/role play or...(Concept Application).
then introducing the appropriate terms (Term Identification); and 3) having students apply what they have learned through another exploration activity or a student generated experiment or a report or a field trip or a class debate/role play or...(Concept Application). From the 1998 SciMath Framework.
2. Employ "active learning" going from the "concrete" to the "abstract." The use of activities such as the one introducing counting by massing pellets will assist students in developing an abstract concept like the mole.
Use of manipulatives such as model kits can assist students during the explanation part of the learning cycle in moving from the concrete to the abstract. For example, when discussing the mole ratio of chlorine to carbon in the formula of carbon tetrachloride you might make a model of CCl4 and break it apart to show that there are four chlorine atoms for each atom of carbon in the molecule of CCl4. Students will then better understand that the empirical formula of carbon tetrachloride has 4 moles of chlorine to each mole of carbon. If you were to make a dozen models of the molecule they would see that the number of molecules does not change the ratio of the atoms.
Suggested Labs and Activities
1. Lesson plans and activities which use the 5 E Learning Cycle to Introduce the Mole Concept.
(9.1.3.4.5 Demonstrate how unit consistency and dimensional analysis can guide the calculation of quantitative solutions and verification of results).
"Apple Jacks" Mole Introduction Activity
2. Empirical Formula for Copper (II) Chloride - (Benchmark 9C.2.1.2.4 & 9C.2.1.2.5)
Students are given a 2.00 gram sample of anhydrous copper (II) chloride which they dissolve in 50 ml of hot distilled water. If a more reactive metal like aluminum (Al strips may be obtained from science supply companies) the metal will displace the copper ions in solution and copper metal will precipitate. This can be filtered, dried and massed. Knowing the mass of the copper obtained students can determine the mass of the chloride (chlorine). They can then determine the mass percentage of each element in the compound, the moles of each element and the empirical formula. This activity provides an excellent opportunity to compile class data by using various samples sizes of the copper (II) chloride for different groups and comparing results. Students will see that the empirical formula is constant. They will also encounter applications of the use of significant digits as they determine what whole number should be used to represent their mole ratio of chlorine to copper. For example is 1.8 a 2:1 ratio or a 3:2 ratio?
3. Empirical Formula of magnesium oxide. (Benchmark 9C.2.1.2.4 & 9C.2.1.2.5)
Students heat a sample of magnesium ribbon in a crucible with a cover. The sample is massed before and after heating to determine the mass of oxygen gained. After initial combustion of the magnesium students add water to the ash (enough to wet the ash) and heat until dry. This ensures the conversion of magnesium to magnesium oxide and not magnesium nitride. From the data students can determine the mass percentage of each element in the final product and the moles of each. The mole ratio gives the empirical formula of magnesium oxide.
4. Empirical Formula of Copper Oxide - (Benchmark 9C.2.1.2.4 & 9C.2.1.2.5)
The Journal of Chemical Education online has two procedures for determining the formula of copper (II) oxide. One involves the use of methane gas to reduce the copper oxide to copper metal. The other involves dissolving the copper oxide in acid then using a single displacement reaction with a more active metal to precipitate the copper. See Journal of Chemical Education
5. Empirical Formula of a Hydrate (Benchmarks: 9C.2.1.2.4 & 9C.2.1.2.5)
This is a standard lab activity that can be used as an introductory application of the mole concept or as a "performance based" assessment. It is easy to do, can be done in one class period and the equipment and chemicals are commonly found in most high school chemistry labs. Students are given a hydrate which they "dehydrate" by heating in an evaporating dish. Commonly used hydrates include barium chloride dihydrate (BaCl2 ● 2H20) or copper (II) sulfate pentahydrate (CuSO4 ● 5H2O). Students usually use a mass of about two grams and heat this in an evaporating dish. They must record the mass before and after heating. The laboratory technique of heating to a constant mass can be explained and applied. From the mass difference before and after heating the students can determine the mass of water lost, mass of dehydrated crystals, mass percentage of water, moles of water, moles of dehydrated crystals and the empirical formula for the compound.
Additional Resources
1. Additional Mole Cartoons by Flinn Scientific
2. National Mole Day Celebration occurs on October 23 at 6:02 in honor of Avogadro's number and the chemical mole unit.
3. "Mole Day" jokes such as:
What did Avogadro have on his pancakes? (Molasses).
What does Avogadro do when he wants to go to town? (He jumps in his automobile.)
What do you call 6.02 x 1023 avocados mashed with equal amounts of chili peppers and tomatoes? (Guacamole)
How did Avogadro die? (Molaria)
What did Avogadro cry out when someone stepped on his foot in church? (Holy Moley!)
How hot does Avogadro like his coffee? (Molten!)
What is Avogadro's favorite type of candy (carmole).
What kind of music does Avogadro like? (Moletown and Rock & Mole)
4. World of Chemistry Video Series: The Mole World of Chemistry and video guide questions :
World of Chemistry Video Guide Questions
Students learn about material balances, a fundamental concept of chemical engineering. They use stoichiometry to predict the mass of carbon dioxide that escapes after reacting measured quantities of sodium bicarbonate with dilute acetic acid. Students then react the chemicals in a small reactor made from a plastic water bottle and balloon.
Vocabulary/Glossary
- Mole A chemical unit of matter composed of Avogadro's number (6.02 x 1023) of particles (atoms or molecules) having a mass equal to the atomic mass of an element or formula mass of a compound.
- Molar Mass The sum of the atomic masses of all atoms of elements in a chemical formula.
- Avogadro's number The number of particles in a chemical mole (6.02 x 1023) much like a dozen contains twelve.
- Percentage composition The percentage by mass of the atoms of all elements in a compound.
- Empirical Formula The simplest whole number ratio of atoms in a compound which corresponds to the simplest whole number ratio of moles of each element in a compound.
- Molecular Formula The whole number ratio of atoms in a compound which will be a whole number multiple of the empirical formula of a compound.
From the Minnesota Mathematics Standards:
Math standards can be easily incorporated into this topic:
9.3.1.5 Make reasonable estimates and judgments about the accuracy of values resulting from calculations involving measurements.
9.4.1.3 Use scatter plots to analyze patterns and describe relationships between two variables. Using technology, determine regression lines and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.
9.4.2.3 Design simple experiments and explain the impact of sampling methods, bias and the phrasing of questions asked during data collection.
6.1.2.2 Understand the concept of ratio and its relationship to fractions and to the multiplication and division of whole numbers. Use ratios to solve real-world and mathematical problems. Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations.
6.3.3.1 Choose appropriate units of measurement and use ratios to convert within measurement systems to solve real-world and mathematical problems. Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units.
Assessment
Assessment of Students
1. Calculate the empirical formula and molecular formulas of a compound that contains 80.0% and 20.0% H with a molar mass of 30.0 g/mole. Taxonomic level: application.
Answer:
80.0 g C x 1 mol C = 6.7 mol C
12.0 g C 6.7 = 1
6.7
20.0 g H x 1 mol H = 20 mol H
1.0 g H 20 = 3
6.7
Empirical Formula = CH3
CH3 = 12 + 3(1) = 15 g/mol = empirical mass
Molecular mass 30 = 2 2 (CH3) = C2H6 Which is the molecular formula
Empirical Mass 15
2. What is the molar mass of fluorapatite (Ca5(PO4)3F)? Taxonomic Level: Application
A. 314 g/mol B. 344 g/mol C. 442 g/mol D. 504 g/mol E. 524 g/mol
Answer: D
3. How many atoms are in 0.625 moles of Ge (atomic mass = 72.5) Taxonomic level: Application
A. 2.73 x 1025 B. 6.99 x 1025 C. 3.76 x 1023 D. 9.63 x 1023
Answer: C
4. What is the percentage by mass of nitrogen in the compound ammonium nitrate (NH4NO3)? Taxonomic level - application
A. 17.5 % B. 21 % C. 3.5 % D. 35 % E. 60 %
Answer: D
5. A 5.00 gram sample of hydrated nickel (II) chloride is heated to constant mass in an evaporating dish of mass 35.82 g. After heating to a constant mass the dish and dehydrated crystals have a mass of 38.55 grams. Find the mass of water lost and formula for this hydrate. Taxonomic level: synthesis
Answer: Total mass of sample and dish before heating is 40.82 g - the mass of the dish and dehydrated crystals after heating = 2.27 g. This is the mass of the water. Converting it to moles = 0.126. The mass of the remaining dehydrated crystals are 2.73 g. This is the nickel (II) chloride which equal 0.0211 moles. The ratio of moles of water to moles of nickel (II) chloride is 6. So the formula is NiCl2 ● 6H20.
6. How can 12.0 grams of carbon and 63.5 grams of copper have the same number of atoms when the mass of the copper is much greater than the mass of the carbon? Taxonomic level: synthesis.
Answer: The individual copper atoms have a greater mass but 63.5 grams are one mole which contains an Avogadro's number of atoms. The 12.0 grams of carbon are also one mole which also contains Avogadro's number of atoms. This would be like a dozen golf balls and a dozen bowling balls each contain 12 balls but the dozen bowling balls would be much heavier.
Assessment of Teachers
As a teacher how would you help students understand why the mass of one mole of an element equals the element's atomic mass but in grams?
One method is to use an analogy. Suppose one has a dozen new pencils and each pencil has a mass of 8.5 grams. The total mass would be 8.5 x 12 = 102 grams. Likewise a dozen golf balls each having a mass of 25.6 grams would have a total mass of 25.6 x 12 = 307.2 grams.
Now consider a mole of carbon. It has Avogadro's number (6.02 x 1023) atoms of carbon. Each carbon atom has a mass of 12.0 atomic mass units. An atomic mass unit in grams equals 1.66 x 10-24 grams. So the mass of a mole of carbon atoms is 12.0 amu x 6.02 x 1023 x 1.66 x 10-24 g/amu = 12.0 grams. So for all elements one mole of the element has a mass in grams equal to the element's atomic mass in amu.
As a teacher how would you help students understand that one mole of carbon tetrachloride (CCl4) has four times Avogadro's number of chlorine atoms?
Answer: You might use an analogy like this: Dogs have one tail and four legs. If I had one dog how many tails are there (one) but how many legs ? (4) So a mole of CCl4 has Avogadro's (6.02 x 1023 ) number of C atoms but 4 x 6.02 x 1023 Cl atoms.
How can you as a teacher help students from being confused whether to divide or multiply by the atomic mass when converting grams to moles or moles to grams?
Answer, if students have practiced and are comfortable with the "factor label" method or dimensional analysis those techniques will help avoid confusion when converting with moles.
Set up the conversion factor and insist that students show their work when making mole conversions.
Differentiation
Struggling and At-Risk
Struggling / At-Risk students often find it challenging to understand the order needed to solve complex problems like finding the empirical formula of a compound. In The Journal of Chemical Eduction, 1988 Joel S. Thompson wrote a rhyme that can used to determine a simple chemical formula. It goes like this: Percent to mass, mass to mole, divide by small, multiply 'til whole.
Give students the percent composition of a compound like 43.6 % phosphorus and 56.4 % oxygen. Have students write each line of the rhyme and show how each line is used to determine the empirical formula of this compound.
Percent to mass: 43.6 % = 43.6 grams P, 56.4 % = 56.4 grams O.
Mass to moles: 43.6 grams P = 1.41 moles, 56.4 g O = 3.52 moles.
Divide by small: 1.41 mole P / 1.41 = 1 3.52 moles O / 1.41 = 2.5
Multiply 'til whole: 2 (1) P = 2, 2 (2.5 O) = 5 The formula is P2O5.
The Sourcebook for Teaching Science - Strategies, Activities, and Instructional Resources
The science classroom is often a frustrating place for English language learners. Science has a complex vocabulary that is difficult even for native English speakers to learn. Difficulty learning English should not be confused with an inability to think scientifically. Many of the strategies that are useful for English language learners are effective for differentiating instruction for others. For example:
Model laboratory activities - Demonstrate activities in front of class to ensure that English language learners can see the procedures before engaging in an activity. This can be done as a "pre-lab" activity the day before doing the activity or by setting up a " lab station" which illustrates the laboratory activity. Another method for helping English Language Learners is to make sure they have a lab partner who understands the procedure. The Synthesis of Magnesium Oxide is a lab that could be modeled.
Teaching Science to English Language Learners: Building on Students' Strengths - Can a student's cultural background support learning in science? Or is concentrating on the specialized vocabulary of science the best way to help English language learners learn science? This book addresses these and other pressing questions you face when working with students whose linguistic and cultural backgrounds, as well as their languages, are different from your own.
Give students four or five samples of an element such copper. Students are to mass each sample and determine the number of moles in each sample. Have students graph these two variables (they should determine which variable goes on each axis) so that the graph will illustrate the atomic mass of copper in grams per mole. How does the graph illustrate this? (Answer a graph of the mass of the sample vs the number of moles should be linear with the slope of the line equal to the atomic mass of copper in g/mole.)
Have students research Amadeo Avogadro's life and what it would be like to live in Italy in the early 1800's when he lived and proposed "Avogadro's hypothesis." Here is an excellent short video to introduce the idea.
The Mole- Amedeo Avogradro's number. Shows the historical development of the mole and background of Avogadro.
Have students make a "Foldable" to help them organize information about conversion factors. Collect three sheets of paper and fold each in half. Measure and draw a line about 3 cm from the left edge. Cut along the line to the fold. Repeat for each sheet of paper. Then have students label each top sheet with a description of the conversion factor as these are gone over in class. Staple the sheets together along the outer edge of the narrow flaps. The students could be allowed to use this on their tests.
Parents/Admin
Administrators
Administrators should see teachers engaging students with meaningful applications of the mole concept in the laboratory and solving various problems.
You can support your student's understanding of the mole concept by reinforcing "package units" at home. Ask your student what makes the difference between a dozen large eggs and a dozen small eggs. Twelve similar eggs are put into a carton for a dozen then the total mass determines whether the eggs are considered "large" or "small."
Give your student other examples of "package" units at home and ask your student to calculate the number of individual items in a given number of packages such as the number of cans of pop in 7 'six packs.'