Lesson 2: Atomic Weights
For Dalton, the difference in the mass of the atoms of different elements became the focus of the elemental atomic properties, and he was able to establish relative atomic weights based on the combining weights of the elements.
In this section we will look at those relative atomic weights, how they were based on hydrogen as a standard, and then how and why that standard was changed. We will also look at atomic mass units which were developed to measure mass at the atomic level. Then we will look at how to use atomic weights to determine the formula weights of chemicals.
Relative Atomic Weights | Changes in Atomic Weight Standards
Atomic Mass Units | Formula Weights
Relative Atomic Weights
Let's look at some of the things you have already learned in this course. You know that elements can combine with one another to form compounds. For example, hydrogen and oxygen combine to form water. Magnesium and oxygen combine with one another to form magnesium oxide. Other elements combine with one another to form a wide variety of compounds. You also know that the weight ratio of the elements in each compound is fixed. That is why we came up with the Law of Constant Composition. Weight ratios for quite a number of compounds are listed in Example 11 for this lesson. A few of those are shown here.
| Compound | Elements | Weight Ratio | ||||
| Water | O:H | 7.94:1 |
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| Methane | C:H | 2.98:1 | ||||
| Carbon dioxide | O:C | 2.66:1 |
Consider the first two compounds listed in this table. Let's compare the amount of oxygen that combines with 1 gram of hydrogen in water to the amount of carbon that combines with 1 gram of hydrogen in methane. Dividing 7.94 g of oxygen by 2.98 g of carbon we get a 2.66:1 ratio of oxygen to carbon. Note how that compares very nicely with the weight ratio of oxygen to carbon in the compound we call carbon dioxide. Coincidence? Not at all. It is the basis of the idea of combining weights of the elements. If we take 1 g of hydrogen as its combining weight and use it as a starting point, then 7.94 g is the combining weight of oxygen and 2.98 g is the combining weight of carbon. Not only will those weights of those elements combine with 1 g of hydrogen, they will combine with one another.
With a more complete list of weight ratios for compounds, we would see many more of these interrelationships. Chemists, including Dalton, did compile a more complete list, did see many more interrelationships, and did summarize those relationships by making a list of combining weights. Dalton took this a step further and compiled a list of relative atomic weights. Because of limited precision, he presumed that the weights were integer values. The atomic weight of hydrogen was 1 and the atomic weight of oxygen was 8. These weights were relative atomic weights because the actual size and weight of the atoms was not known. But still they were fairly real and useful in explaining the composition of compounds.
Many elements seemed to have more than one combining weight. But they were generally multiples of one another. Dalton theorized that the smaller combining weight was the actual atomic weight and the larger value represented more than one atom of the element. This use of his theory prompted the formulation of the Law of Simple Multiple Proportions. (The Law of Simple Multiple Proportions states that when elements can combine to form two or more different compounds, their mass ratio in one compound is a “simple multiple” of their mass ratio in any other compound.)
There were at least two significant problems with values that Dalton used for his atomic weights. One is the presumption that they were integer values. That was taken care of by more precise and accurate measurements. The other was that some of the atomic weights were off by a factor of two or three. Oxygen is a notable example. This was taken care of by the application of Avogadro's Hypothesis to the determination of correct molecular formulas and molecular weights. Dalton determined that the atomic weight of oxygen was 8 based on the presumption that the formula of water was HO. When the formula of water was determined to be H2O, that showed that the correct atomic weight of oxygen was 16.
Changes in Atomic Weight Standards
Values for relative atomic weights have not remained the same since Dalton's time. They have changed over the years. This table shows a little bit of the history of atomic weight standards and the changes that have been made over the years. (This is also shown in Example 11 in your workbook.)
| Early 1800s | Middle 1800s | Chemists to 1961 | Physicists to 1961 | Since 1961 | |
| Standard | H = 1 | H = 1 | O = 16 | O-16 = 16 | C-12 = 12 |
| Hydrogen | 1 | 1.000 | 1.0080 | 1.0083 | 1.00797 |
| Oxygen | 16 | 15.87 | 16.000 | 16.0045 | 15.9994 |
| Carbon | 12 | 11.92 | 12.011 | 12.0150 | 12.01115 |
| Nitrogen | 14 | 13.90 | 14.008 | 14.0112 | 14.0067 |
| Gold | 196 | 196.41 | 197.0 | 197.030 | 196.967 |
In the early 1800s hydrogen was used as the standard with a weight of one unit. Other elements are compared to it. Oxygen had a relative weight of 16, carbon a relative weight of 12, nitrogen a relative weight of 14, and gold a relative weight of 196. By the middle 1800s chemists had done enough research to realize that the relative atomic weights were not really integer values. They were dealing with measured values that were close to integers in many cases but they were not exact whole numbers. (Berzelius published a list of atomic weights in 1828.) With additional precision and care taken in the measurements and still using hydrogen as a standard of exactly one, oxygen was found to have an atomic weight of 15.87, and carbon was found to have a relative weight of 11.92, nitrogen 13.90, and gold 196.41. Sometime in the mid-1800s, chemists switched to oxygen as the standard. Oxygen became the standard because it was more readily available and it made more combinations with other elements. But rather than set oxygen = 1, they assigned oxygen the value of 16 units so that the relative atomic weights stayed about the same as they were before. They actually turned out to be closer to integer values, although that is not important. Precision and accuracy of atomic weights continued to improve. (In 1914 the American chemist Theodore Richards received the Nobel Prize for his exact determination of many atomic weights.)
In the early 1900s, physicists made a shift to a new standard. The reason behind this change was that they learned about isotopes in the early 1900s. They discovered that not all atoms of a particular element had the same weight. Although most oxygen atoms weighed 16 units, some weighed 17 units and some weighed 18 units. Each isotope of an element had its own isotopic weight and the atomic weight for each element was an average value of those isotopic weights. To talk about the average weight became quite a problem in some of the work that they were doing, so they shifted their reference standard to one particular isotope of oxygen called oxygen-16. If you look down those two columns, you can see that the weights are pretty much the same. You have to go out about to the fourth or fifth significant digit before you start getting any discrepancy between the weights that the physicists and the chemists used. (There is a 0.027% difference between the values.) Nevertheless, that difference was there, and it was not a good thing when measurements of great precision are needed.
The last column shows the current standard. Chemists and physicists simply have too much in common to abide by two different sets of atomic weights; and so in 1961, they settled on the isotope carbon-12 as the standard at exactly 12. Settling on a particular isotope rather than an elemental average gave physicists the precision and reliability that they needed. Settling on that particular isotope kept the numbers pretty close to the previous weights that the chemists had been using. So there you have a brief history of the atomic weights standards.
You will soon be using atomic weights to do a variety of calculations. A short list of atomic weights is in Example 12 in your workbook. Working with just the seven elements listed in Example 5 will be much too limiting before long. For the atomic weights of the other elements, you can refer to a periodic table (one is provided at the end of the lesson in your workbook).
Atomic Mass Units
I mentioned that these are relative atomic weights because they were compared to hydrogen (then oxygen and then carbon-12). One way of dealing with atomic weights that gets around the "relative" aspect would be to find out how much each atom actually weighs. That was difficult and describing how it was done will have to wait for another lesson. Another way is to define a new mass unit and say that it is equal to the mass of one hydrogen atom. That unit is called the atomic mass unit (amu) and is defined, for the moment, as the mass of one hydrogen atom. Then if oxygen atoms weigh 16.00 times as much as hydrogen atoms, they weigh 16.00 amu. Similarly for any element, whatever the relative atomic weight is, that is how many amu's each atom of that element weighs. Using the current standard, the actual definition of an atomic mass unit is that it is 1/12th of the mass of one atom of the carbon-12 isotope.
Because the relative weights of hydrogen, carbon and nitrogen are 1.01, 12.01 and 14.01. We can also say that the weight of hydrogen is 1.01 amu per atom, the weight of carbon is 12.01 amu per atom and the weight of nitrogen is 14.01 amu per atom. (Actually we should say "the average weight per atom" because the weight of an atom depends not only on which element it is, but also on which isotope it is.)
In honor of John Dalton's groundbreaking work, another name for the unified "atomic mass unit" is the dalton, or Da. This unit is used in biochemistry and molecular biology, usually in kilodaltons or kDa, for the masses of large biochemical molecules like proteins.
Formula Weights
A simple but very important skill that you will be called upon to do many, many times during this course is to calculate the formula weight of a chemical based on its formula. You can do that very easily as long as you know the formula of the chemical with which you are dealing. I will present three examples (which are also shown in Example 13 in your workbook) and then have you try your hand at a few. If you are already familiar with determining formula weights, move on to the Study Check on Calculating Formula Weights.
The first example is H2O. The formula weight is the sum of the atomic weights of everything that's in that particular formula. In the case of H2O, the formula weight of H2O is the sum of the weights of two hydrogens and one oxygen. To get the formula weight for H2O, you need twice the atomic weight of hydrogen and add to that the atomic weight of one oxygen. It is shown in the example that the formula weight of H2O is 18.0. |
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The next formula is HNO3. The formula contains 1 hydrogen, 1 nitrogen and 3 oxygens. So the weights come out to be 1.0 plus 14.0 plus 48.0, a total of 63.0. |
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When you are dealing with parentheses, as in Fe(NO3)2, that's one more factor to take into account. However, you can easily interpret the formula to see that it represents 1 iron, 2 nitrogens and 6 oxygens. Then multiply the 1, 2, and 6 by the atomic weights for iron, nitrogen, and oxygen, add all those together and you get 179.8. |
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There is another way of doing this. That is to focus on what's in the parentheses. The NO3 portion of that compound has its own formula weight and the formula weight of NO3 comes out to be 62. (14.0 for the nitrogen and 3 times 16.0 gives 48.0 for the oxygen which comes to a total of 62.0.) This compound as a whole has 1 iron and 2 NO3's and so if you take the weight of the iron (55.8) and double the weight of the NO3 (which is 124.0) and add those together you come up with the formula weight of 179.8 which of course is the same as what we got using the first method.
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Something I should point out before we continue is that formula weights apply to any kind of formula. Whether you're dealing with molecular formulas or empirical formulas or whatever kind of formula you're dealing with you can calculate a formula weight for it. If you happen to be dealing with a molecular formula, the formula weight for it can also be called the molecular weight.
Practice Determining Formula Weights
Determining formula weights is very simple, straightforward, and important and I would like you to practice by determining the formula weights for the compounds in example 14 in your workbook. (Use the partial list of relative atomic weights, Ex. 12; for this practice you can round those weights to one decimal place.)
So please take a moment to do that and check your answers below.
Answers
For your answers you should have HF is 20.0; CH4 is 16.0; C3H7O2 is 75.0; Fe2(CO3)3 is 291.6. If you did not get these answers, check with the instructor to figure out why before continuing. Since these are relative formula weights, we do not have units listed. However, most formula weights are listed with units of a.m.u. or g/mole; we will almost exclusively have units of g/mole for formula weights in this class. Read on to the next section for a discussion of moles.
Note: One thing that students often ask about is how many significant digits to use when calculating the formula weights. Different periodic tables will report atomic weights to different precisions - one table might only show one decimal place (like the previous examples) while another periodic table might show 5 or more decimal places! For a class at this introductory level, atomic weights are generally rounded to one or two decimal places; we used only one decimal place in the previous examples for simplicity and to get you started. From now on, for this class, I would like you to get in the habit of using two decimal places for atomic and formula weights.