Atomic Masses

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 masses based on the combining masses of the elements.

In this section we will look at those relative atomic masses, 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 masses to determine the formula masses of chemicals.

Relative Atomic Masses

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 mass ratio of the elements in each compound is fixed. That is why we came up with the Law of Constant Composition.

This idea of the Law Constant Composition is an important one to fully internalize. Taking the example of magnesium oxide, here are a few different ways of stating this law; hopefully, seeing it expressed in a variety of ways will help you develop a strong understanding of it.

• When 1.00 g of oxygen reacts fully with magnesium, it always reacts with 1.52 g of magnesium, never more or less, forming 2.52 g of magnesium oxide.

• Any time you find magnesium oxide, it will always have 39.7% of its mass made up of oxygen and 60.3% of its mass made up of magnesium (because 1.00 g is 39.7% of 2.52 g).

• If you were to make some magnesium oxide starting with 8.5 g of oxygen, the mass of magnesium required would be 12.9 g, because 8.5*1.52 = 12.9

The table below shows the mass ratios of a few different compounds.

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 mass 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 masses of the elements. If we take 1 g of hydrogen as its combining mass and use it as a starting point, then 7.94 g is the combining mass of oxygen and 2.98 g is the combining mass of carbon. Not only will those masses of those elements combine with 1 g of hydrogen, they will combine with one another.

With a more complete list of mass 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 masses. Dalton took this a step further and compiled a list of relative atomic masses. Because of limited precision, he presumed that the masses were integer values. The atomic mass of hydrogen was 1 and the atomic mass of oxygen was 8. These masses were relative atomic masses because the actual size and mass 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 mass. But they were generally multiples of one another. Dalton theorized that the smaller combining mass was the actual atomic mass 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 masses. 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 masses were off by a factor of two or three. Oxygen is a notable example. Dalton determined that the atomic mass 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 mass of oxygen was 16.

Atomic Masses of Elements

Determining the masses of atoms of all the various elements was a slow process, and the techniques used to do so are beyond the scope of this class. However, throughout the 19th and early 20th centuries, physicists and chemists established a few important principles.

• Hydrogen was unambiguously found to be the lightest element, which lead to the relative masses of other elements being measured in comparison to hydrogen.

• Most elements, especially lighter ones, have atomic masses that appear at first to be integer multiples of hydrogen's. That is, oxygen is almost exactly 16 times heavier than hydrogen, carbon is almost exactly 12 times heavier, etc.

• However, with more precise measuring techniques, it became clear that these values were only close to being integers. For instance, by the mid-1800s it was clear that the actual oxygen:hydrogen mass ratio is not 16, but rather 15.89. Further, some elements had relative atomic masses that were decidedly not integers, like 35.45 for chlorine. This phenomenon - integers sometimes appearing, sometimes not, and being not-quite-exact when they did appear - puzzled chemists for a long time until the discovery of isotopes in the early 1900s, which will be addressed later in the course.

Atomic Mass Units

If you fully internalized Lesson 1, it may make you nervous that the atomic masses on the periodic table are listed without any units. This is generally taboo in science! The reason for this goes back to the origin of atomic masses as relative values. However, since they are now absolute masses, it is important you know the units they are measured in. They are called "atomic mass units" (sensibly enough). They also go by the name "Daltons" (as in: "the atomic mass of oxygen is 15.999 Daltons") in honor of John Dalton. The abbreviation is "amu" (although you will sometimes see it further abbreviated to just "u").

The precise definition of the atomic mass unit is "one twelfth the mass of a single atom of carbon-12." Understanding this definition requires understanding isotopes, which will come later in the course. An alternate definition that should be easier for you to understand is this: 1 amu = 1.66*10^-24 g . As you can see, the amu is a very small unit of mass.

Formula Masses

When atoms combine into molecules or other structures, the total mass of the molecule is equal to the combined atomic masses of the atoms that make it up. Thus, you can use the atomic masses from the periodic table to calculate a formula mass for any chemical formula.

For example, take the very simple formula H₂. This formula uses only hydrogen, which has an atomic mass of 1.008 amu (see the periodic table). To find the formula mass of H₂, the calculation is 2*1.008 amu, which gives a value of 2.016 amu.

We can next take the more complicated example of ammonia, NH₃. This time we must account for the atomic masses of all four atoms in the formula (one nitrogen, three hydrogen). So our formula mass calculation goes 1*14.007 + 3*1.008, which gives 17.031 amu.

Finally, we can take a much larger and more complex molecule: caffeine (C₈H₁₀N₄O₂). There are four elements involved, and many more atoms than before, but the process is the same. We calculate the formula mass as 8*12.011 + 10*1.008 + 4*14.007 + 2*15.999, giving 194.194 amu.

Lastly, let's look at how to deal with parentheses in formulas when finding a formula mass. In the compound magnesium nitrate, which has formula Mg(NO₃)₂, the formula mass must account for the presence of two nitrogen atoms and six oxygen atoms (see previous page of this lesson for a refresher). Thus, the formula mass is 1*24.305 + 2*14.007 + 6*15.999, or 74.309 amu.

Calculating formula masses in this way is a core skill for this class, which you must learn to do quickly and unerringly. Your periodic table gives you at least two and often three places after the decimal point; proper rules for significant figures require you to keep all these places in your answers and not round.

Practice With Formula Masses

Determine the formula masses of the following compounds: HF, CH₄, C₃H₇O₂, and Fe₂(CO₃)₃.

Answers

You should obtain the following values for your formula masses. Check with your instructor if you get different ones.

HF: 20.006 amu

CH₄: 16.043 amu

C₃H₇O₂: 75.087 amu

Fe₂(CO₃)₃: 291.714 amu