Concept Development Studies | Atomic Molecular Theory

Why Concept Development Studies? The body of knowledge called Science consists primarily of models and concepts, based on observations and deduced from careful reasoning. Viewed in this way, Science is a creative human endeavor. The models, concepts, and theories we use to describe nature are accomplishments equal in creativity to any artistic, musical, or literary work. Unfortunately, textbooks in Chemistry traditionally present these models and concepts essentially as established facts, stripped of the clever experiments and logical analyses which give them their human essence. As a consequence, students are typically trained to memorize and apply these models, rather than to analyze and understanding them. As a result, creative, analytical students are inclined to feel that they cannot "do" Chemistry that they cannot understanding the concepts, or that Chemistry is dull and uninteresting. This collection of Concept Development Studies in Chemistry is presented to redirect the focus of learning. In each concept development study, a major chemical concept is developed and learned by analysis of experimental observations and careful reasoning. So in this series of Concept development studies I will try to clarify some topics conceptually. These were originally written by John H. Hutchinson of Rice University. Remember that after reading the topics from here you will never raise any question about how, why and what of that topic. This is my First Lecture so follow me if you want to be a part of this.

INTRODUCTION In this study, our goal is to develop the concept of the Atomic Molecular Theory. This is the theory at the foundation of everything we understanding about Chemistry, as it states that all matter is made up of individual particles called atoms, which combine in ways that are both simple and complex to form larger particles called molecules. When we understand these atoms and molecules, it changes the way that we look at the world around us. We can understanding the properties of the substances we interact with, we can make predictions about the changes and reactions that these substances will undergo, and we can design materials with properties that would be useful to us. The idea that everything is made of atoms is something we are told at a very early age, and for many students, it is hard then to imagine a world in which we don’t know that everything is made of atoms. On the other hand, this particulate view of matter does seem counter to almost all of our own observations. The desks in front of us, the air we breathe, and the water we drink, and even our own mesh show no signs of these particles. Quite the opposite: they seem to be either very solid or quite liquid, and certainly not grainy like a collection of particles might be expected to be. In this concept development study, then, we set aside our knowledge of these atoms and molecules and ask, quite skeptically, why do we believe that there are atoms that combine to form molecules? Or asked another way, if we believe that all matter is made up of atoms, how would we show that this is true? What is the evidence? Does the proof require us to see atoms, or is it possible to prove that they exist without actually seeing them?

FOUNDATION Chemistry is the study of matter, so it makes sense for us to agree on what we mean by matter and what we want to know about it. Technically, matter is anything that has mass, but more commonly, matter is what we regard as anything that has physical properties and takes up space, whether a solid, a liquid, or gas, is matter. Matter can be anything from microscopic to galactic, or from rocks and air to butteries and humans. But we can go further than this and focus on a specific type of matter called a pure substance. This is a material that is completely uniform in properties regardless of the size of the sample we take or from where we take the sample. It is easiest to understanding a pure substance by comparing it to a mixture, which may or may not be uniform in its properties such as color, density, and texture and can vary depending on how we make the mixture or its origin. Showing that a substance is either a pure substance or a mixture requires a lot of experimentation, but we will assume for our foundation that we have already identified which samples of matter are pure substances and which are mixtures. As of 2013, the most comprehensive list of chemical substances numbered over 70 million entries. This huge number of materials seems incomprehensible, far beyond our understanding. However, it turns out that these 70 million substances are all made up from a much smaller set of pure substances called elements. An element is a substance, which cannot be broken down into simpler substances. There are only about 90 commonly occurring elements on earth. The remaining 70 million pure substances are combinations of these elements called compounds, and these are distinguishable from the elements in that a compound can be broken down into the elements from which it is made. For example, metallic iron and gaseous oxygen are both elements, which cannot be reduced into simpler substances, but common iron rust, ferrous oxide, is a compound made up from iron and oxygen. Therefore, rust can be reduced to iron and oxygen, and rust can be created by combining iron and oxygen. But iron and oxygen are elements; they cannot be transformed into one another and are not composed of simpler or common materials. Determining whether a pure substance is an element or a compound is a difficult and time-consuming process of experimentation. We will assume for our study that the elements have all been identied. Since matter is anything that can have mass, we will spend much of our time in this study analyzing mass. Without proving it, we will assume the validity of the Law of Conservation of Mass, an experimental result that simply says, The total mass of all products of a chemical reaction is equal to the total mass of all reactants of the reaction. In other words, matter cannot be created or destroyed by chemical or physical processes. This law makes it possible for us to measure masses of materials during reactions knowing that these masses aren’t variable or unpredictable. With these assumptions in mind, we can proceed directly to experiments which led to the development of the Atomic Molecular Theory.

Compound Total Mass (g) Mass of Hydrogen (g) Mass of Nitrogen (g) Mass of Oxygen ( g ) Water 100.0 11.2 - 88.8 Ammonia 100.0 17.7 82.3 - Nitric Oxide 100.0 - 46.7 53.3 Table 2.1

Do these fixed masses mean that we are combining tiny particles of fixed mass together to form these compounds? To test this hypothesis, let’s look at these numbers more closely to see if we can make any sense of them. One way to look at these data is to imagine taking a sample of water that contains exactly 1.00 g of hydrogen, and also a sample of ammonia that contains exactly 1.00 g of hydrogen. If we do this, the data now look as shown in the first two lines of Table

2.2: Mass Relationships of Simple Compounds of Hydrogen, Nitrogen and Oxygen. Compound Total Mass (g) Mass of Hydrogen (g) Mass of Nitrogen (g) Mass of Oxygen ( g ) Water 8.93 1.00 - 7.93 Ammonia 5.65 1.00 4.65 - Nitric Oxide 2.14 - 1.00 1.14 Table 2.2

Looking at the data this way allows us to compare how a fixed amount of hydrogen combines with either nitrogen or oxygen. From the Law of Definite Proportions, we know we will always get the fixed mass ratios shown in Table 2.2: Mass Relationships of Simple Compounds of Hydrogen, Nitrogen and Oxygen. We might imagine that this means that water is formed from 1 atom of hydrogen and 1 atom of oxygen, and that therefore the mass of 1 atom of oxygen is 7.93 times greater than the mass of 1 atom of hydrogen. If this is true, then ammonia might also be formed from 1 atom of hydrogen and 1 atom of nitrogen, in which case 1 atom of nitrogen has a mass 4.65 times greater than 1 atom of hydrogen. This all seems consistent with the idea that these elements are made up of atoms combining in one-to-one ratios. But now we find a problem: if an atom of oxygen is 7.93 times as massive as an atom of hydrogen and if an atom of nitrogen is 4.65 times as massive as an atom of hydrogen, then it must be that an atom of oxygen is more massive than an atom of nitrogen by the ratio of 7.93/4.65 = 1.70. When we now look at the third row of Table 2.2: Mass Relationships of Simple Compounds of Hydrogen, Nitrogen and Oxygen, the data tell us if nitric oxide is made up 1 atom of nitrogen and 1 atom of oxygen, an oxygen atom has a mass 1.14 times greater than the mass of a nitrogen. Our numbers and our conclusion aren’t consistent with the experimental data, so we must have made an incorrect assumption. One possibility is that we were wrong when we assumed that there are atoms of the three elements combining to form these three compounds. But this does not seem likely, since it is hard to understanding the fixed mass proportions without thinking that we are combining particles with fixed mass proportions. Still, we must have made an incorrect assumption since our conclusions were contradictory. Recall that in doing our calculations of the masses of the atoms, we assumed that in each compound one atom of each element combined with one atom of the other element. Although this is a simple assumption, there is no reason why only one atom of each type might combine. Perhaps the ratios are different than this, and atoms combine in ratios of 1-to-2, 2-to-3, or any other simple combination. The problem that this poses is that we don’t have a way to proceed from here. Even if we assume that the Law of Definite Proportions tells us that the elements are made up of atoms, we have no way to determine anything about these atoms. Without knowing the ratios of atoms in different compounds, we cannot determine the masses of the atoms of the elements. And without knowing the masses of the atoms of the elements, we cannot determine the ratios of the atoms in different compounds. Without knowing anything about the atoms of these elements, we do not have a basis for believing that these elements are made up of atoms. The Atomic Molecular Theory is still outside our reach. Without further observations, we cannot say for certain whether matter is composed of atoms or not.

MULTIPLE MASS RATIOS We discovered above that we cannot conclude from the Law of Definite Proportions how many atoms of each element combine to form a particular compound, even if we assume that this is how a compound is formed. There is additional evidence that the Law of Definite Proportions is not final proof of the existence of atoms. It is easy to find different compounds with different chemical and physical properties, which are formed from the same two elements. This means that, if there are atoms, they can combine in many different ways. For example, there are a huge number of simple hydrocarbon compounds formed just from hydrogen and carbon. Table 2.3: Mass Relationships of Simple Compounds of Hydrogen and Carbon lists the mass percentages of just a few of these: Mass Relationships of Simple Compounds of Hydrogen and Carbon Compound Total Mass(g) Mass of Hydrogen(g) Mass of Carbon(g) Methane 100.0 25.1 74.9 Ethane 100.0 20.1 79.9 Benzene 100.0 7.7 92.3

                                                                       Table 2.3


The Law of Definite Proportions says that the ratio of the masses of two elements in a compound is fixed. In Table 2.3: Mass Relationships of Simple Compounds of Hydrogen and Carbon we see several ratios of the masses of carbon and hydrogen. This is consistent with the Law of Definite Proportions, though, because each fixed ratio gives us a different compound with different chemical and physical properties. Therefore, different proportions of elements are possible, and depending on the elements, there may be one or many possible proportions and compounds. This is referred to as multiple proportions. Each compound gives us one definite proportion of the elements, but because there can be many compounds, there can be multiple different but definite proportions. Table 2.3: Mass Relationships of Simple Compounds of Hydrogen and Carbon provides just three examples of compounds formed from carbon and hydrogen. The number of such compounds is huge, each with a different definite mass ratio and each with its own distinct physical and chemical properties. For example, methane gas is commonly burned in gas stoves and liquid octane is commonly used in cars; yet both are compounds of carbon and hydrogen only. We will now look in great detail at a few compounds formed just from nitrogen and oxygen, simply called nitrogen oxides. Since we don’t know anything about these compounds, for now we’ll just call them Oxide A, Oxide B, and Oxide C. These three compounds are very different from one another. Two of these are quite toxic, but one is used as an anesthetic, particularly by dentists. Two of these are colorless, but one is a dark brown color. Let’s look at the mass ratios for these three compounds in Table 2.4: Mass Relationships of Simple Compounds of Nitrogen and Oxygen. Mass Relationships of Simple Compounds of Nitrogen and Oxygen Compound Total Mass(g) Mass of Nitrogen(g) Mass of Oxygen(g) Oxide A 100.0 30.5 69.5 Oxide B 100.0 46.7 53.3 Oxide C 100.0 63.7 36.3

                                                                    Table 2.4


At first glance, there is nothing special about these numbers. There are no obvious patterns or relationships amongst the masses or mass ratios. But let’s look at this data in the same way as we did in Table 2.2: Mass Relationships of Simple Compounds of Hydrogen, Nitrogen and Oxygen by finding the mass of oxygen that combines with 1.00 g of nitrogen. This is in Table 2.5: Mass Relationships of Simple Compounds of Nitrogen and Oxygen.

Mass Relationships of Simple Compounds of Nitrogen and Oxygen. Compound Total Mass(g) Mass of Nitrogen(g) Mass of Oxygen(g) Oxide A 3.28 1.00 2.28 Oxide B 2.14 1.00 1.14 Oxide C 1.57 1.00 0.57

                                                           Table 2.5


You might have to look at these data very hard to see it, but there is a pattern that is obvious once you see it. In the column for the Mass of Oxygen, the three values listed have a simple relationship: each one is a multiple of 0.57. We can see this most clearly if we divide each of the masses for the three oxides by 0.57. This shows us that the ratio 2.28: 1.14: 0.57 is equal to the ratio 4: 2: 1. What does this tell us? It means that if we have a fixed mass of nitrogen, the mass of oxygen which will combine with it cannot be simply any amount. In fact, the opposite is true. There are a few specific masses of oxygen which will combine with the fixed nitrogen, and those specific masses are integer multiples of a fixed unit of mass. It is particularly interesting that the masses of oxygen are in integer ratios. Integers are a special set of numbers used for one primary purpose, which is to count objects. In this case, the object must be a fixed unit of mass of oxygen. The data in Table 2.5: Mass Relationships of Simple Compounds of Nitrogen and Oxygen tell us that when we have a fixed amount of nitrogen, it can be combined only with some integer number of a fixed unit of mass of oxygen. Why would there be a fixed unit of mass of oxygen? The simplest and best explanation is that oxygen exists as fixed units of mass, or particles, and we call these particles atoms of oxygen. Thus, the data in Table 2.5: Mass Relationships of Simple Compounds of Nitrogen and Oxygen lead us to a conclusion that the element oxygen is composed of individual atoms with identical mass. We have shown that matter is made up of particles and that elements consist of identical particles or atoms. We can see these simple integer ratios in other compounds, as well. Let’s look back at Table 2.3: Mass Relationships of Simple Compounds of Hydrogen and Carbon, which shows compounds of carbon and hydrogen. The ratios of the masses don’t appear to be interesting until we do the same type of analysis that we did on the nitrogen oxides. Let’s x the mass of hydrogen in each of these compounds and nd out the masses of carbon. The results are in Table 2.6: Mass Relationships of Simple Compounds of Hydrogen and Carbon. Mass Relationships of Simple Compounds of Hydrogen and Carbon Compound Total Mass(g) Mass of Hydrogen(g) Mass of Carbon(g) Methane 3.98 1.00 2.98 Ethane 4.97 1.00 3.97 Benzene 12.99 1.00 11.99

                                                              Table 2.6


The ratio 2.98 : 3.97 : 11.99 is the same as the ratio 3 : 4 : 12. Once again for a fixed amount of hydrogen, the mass of carbon that can combine is a multiple of a fixed mass unit. Therefore, carbon can only react in small fixed units of mass, so carbon is made up of atoms. These data also show the same conclusion for hydrogen. All we have to do is fix the carbon mass and compare the masses of hydrogen that will combine with that amount of carbon.

The observations we have made for carbon and hydrogen compounds and nitrogen and oxygen compounds are general. They apply to all simple compounds. Thus, we state a new natural law which summarizes these observations, the Law of Multiple Proportions: Law of Multiple Proportions: When two elements combine to form more than one compound, the masses of one element that combine with a fixed mass of the other element are in simple integer ratio. The Law of Multiple Proportions is rather wordy and difficult to state, but the data in Table 2.5: Mass Relationships of Simple Compounds of Nitrogen and Oxygen and Table 2.6: Mass Relationships of Simple Compounds of Hydrogen and Carbon illustrate it clearly. If we fix the mass of one element, the masses of the other element in the three compounds are always in a simple integer ratio. Since these observations are general, then the conclusions that follow are also general: all elements are made up of fixed units of mass, and we call these particles atoms. These conclusions point to other very important conclusions, as well. Since compounds are formed from the elements, then compounds consist of atoms of the elements in various combinations. Very importantly, the integer ratios of the masses of the atoms are always simple, that is, small integers. Therefore, the atoms of the different elements combine in simple ratios, too. This means that the small particles called atoms are combining in simple ways to form small particles of the compound. We call these particles molecules, and compounds consist of identical molecules made up of atoms in simple integer ratios. The Atomic Molecular Theory: We have now observed experimental data which reveal to us several important conclusions. We call these conclusions postulates, and taken together these postulates form the Atomic Molecular Theory: 1. Each element is composed of very small, identical particles called atoms. 2. All atoms of a single element have the same characteristic mass. 3. The number and masses of these atoms do not change during a chemical transformation. 4. Each compound consists of identical molecules, which are small, identical particles formed of atoms combined in simple whole number ratios. At this point, we know very little about these atoms, other than that they exist, have fixed mass for each element, and combine to form molecules. We don’t know what the atomic masses are, even in comparison to each other, and we don’t know the simple integer ratios by which they combine to form molecules and compounds. We have made a major step forward in proving that matter is made up of atoms and molecules, but we have a long way to go to make this theory useful.

REVIEW AND DISCUSSION QUESTIONS 1. Assume that matter does not consist of atoms. Show by example how this assumption leads to hypothetical predictions which contradict the Law of Multiple Proportions. Do these hypothetical examples contradict the Law of Definite Proportions? Are both observations required for confirmation of the atomic theory? 2. Two compounds, A and B, are formed entirely from hydrogen and carbon. Compound A is 80.0 % carbon by mass, and 20.0% hydrogen, whereas Compound B is 83.3% carbon by mass and 16.7 % hydrogen. Demonstrate that these two compounds obey the Law of Multiple Proportions. Explain why these results strongly indicate that the elements carbon and hydrogen are composed of atoms. 3. In many chemical reactions, mass does not appear to be a conserved quantity. For example, when a tin can rusts, the resultant rusty tin can has a greater mass than before rusting. When a candle burns, the remaining candle has invariably less mass than before it was burned. Provide an explanation of these observations, and describe an experiment which would demonstrate that mass is actually conserved in these chemical reactions. 4. The following question was posed on an exam: An unknown non-metal element (Q) forms two gaseous Chlorides of unknown molecular formula. A 3.2 g sample of Q reacts with Chorine to form 10.8 g of the unknown Chloride A. A 6.4 g sample of Q reacts with Chorine to form 29.2 g of unknown Chloride B. Using these data only, demonstrate by calculation and explanation that these unknown compounds obey the Law of Multiple Proportions. A student responded with the following answer: The Law of Multiple Proportions states that when two elements form two or more compounds, the ratios of the masses of the elements between the two compounds are in a simple whole number ratio. So, looking at the data above, we see that the ratio of the mass of element Q in compound A to the mass of element Q in compound B is 3.2:6.4 = 1:2, which is a simple whole number ratio. This demonstrates that these compounds obey the Law of Multiple Proportions. Assess the accuracy of the students answer. In your assessment, you must determine what information is correct or incorrect, provide the correct information where needed, explain whether the reasoning is logical or not, and provide logical reasoning where needed. By John S. Hutchinson, Rice University, 2011

Like and reshare if it helped you.

Note by Swapnil Rajawat
5 years, 3 months ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

My God!! Such a big note.

- 5 years, 3 months ago