| 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 |
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 [link] and [link] 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:
- Each element is composed of very small, identical particles called atoms.
- All atoms of a single element have the same characteristic mass.
- The number and masses of these atoms do not change during a chemical transformation.
- 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
- 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?
- 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.
- 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.
- The following question was posed on an exam:
An unknown non-metal element (Q) forms two gaseous fluorides of unknown molecular formula. A 3.2 g sample of Q reacts with fluorine to form 10.8 g of the unknown fluoride A. A 6.4 g sample of Q reacts with fluorine to form 29.2 g of unknown fluoride 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